Skip to main content

SCEPTRE improves calibration and sensitivity in single-cell CRISPR screen analysis

Single-cell CRISPR screens are a promising biotechnology for mapping regulatory elements to target genes at genome-wide scale. However, technical factors like sequencing depth impact not only expression measurement but also perturbation detection, creating a confounding effect. We demonstrate on two single-cell CRISPR screens how these challenges cause calibration issues. We propose SCEPTRE: analysis of single-cell perturbation screens via conditional resampling, which infers associations between perturbations and expression by resampling the former according to a working model for perturbation detection probability in each cell. SCEPTRE demonstrates very good calibration and sensitivity on CRISPR screen data, yielding hundreds of new regulatory relationships supported by orthogonal biological evidence.

The noncoding genome plays a crucial role in human development and homeostasis: over 90% of loci implicated by GWAS in diseases lie in regions outside protein-coding exons [1]. Enhancers and silencers, segments of DNA that modulate the expression of a gene or genes in cis, harbor many or most of these noncoding trait loci. While millions of cis-regulatory elements (CREs) have been nominated through biochemical annotations, the functional role of these CREs, including the genes that they target, remain essentially unknown [2]. A central challenge over the coming decade, therefore, is to unravel the cis-regulatory landscape of the genome across various cell types and diseases.

Single-cell CRISPR screens (implemented by Perturb-seq [3, 4], CROP-seq [5], ECCITE-seq [6], and other protocols) are among the most promising technologies for mapping CREs to their target genes at genome-wide scale. Single-cell CRISPR screens pair CRISPR perturbations with single-cell sequencing to survey the effects of perturbations on cellular phenotypes, including the transcriptome. High multiplicity of infection (MOI) screens deliver dozens perturbations to each cell [79], enabling the interrogation of hundreds or thousands of CREs in a single experiment. Single-cell screens overcome the limitations of previous technologies for mapping CREs [9]: unlike eQTLs, single-cell screens are high-resolution and can target rare variants, and unlike bulk screens, single-cell screens measure the impact of perturbations on the entire transcriptome.

Despite their promise, high-MOI single-cell CRISPR screens pose significant statistical challenges. In particular, researchers have encountered substantial difficulties in calibrating tests of association between a CRISPR perturbation and the expression of a gene. Gasperini et al. [9] found considerable inflation in their negative binomial regression-based p-values for negative control perturbations. Similarly, Xie et al. [8] found an excess of false-positive hits in their rank-based Virtual FACS analysis. Finally, Yang et al. [10] found that their permutation-based scMAGeCK-RRA method deems almost all gene-enhancer pairs significant in a reanalysis of the Gasperini et al. data. These works propose ad hoc fixes to improve calibration, but we argue that these adjustments are insufficient to address the issue. Miscalibrated p-values can adversely impact the reliability of data analysis conclusions by creating excesses of false-positive and false-negative discoveries.

In this work, we make two contributions. We (i) elucidate core statistical challenges at play in high-MOI single-cell CRISPR screens and (ii) present a novel analysis methodology to address them. We identify a key challenge that sets single-cell CRISPR screens apart from traditional differential expression experiments: the “treatment”—in this case the presence of a CRISPR perturbation in a given cell—is subject to measurement error [3, 11, 12]. In fact, underlying this measurement error are the same technical factors contributing to errors in the measurement of gene expression, including sequencing depth and batch effects. These technical factors therefore act as confounders, invalidating traditional nonparametric calibration approaches. On the other hand, parametric modeling of single-cell expression data is also fraught with unresolved difficulties.

To address these challenges, we propose SCEPTRE (analysis of Single-CEll PerTurbation screens via conditional REsampling; pronounced “scepter”). SCEPTRE is based on the conditional randomization test [13], a powerful and intuitive statistical methodology that, like parametric methods, enables simple confounder adjustment, and like nonparametric methods, is robust to expression model misspecification. We used SCEPTRE to analyze two recent, large-scale, high-MOI single-cell CRISPR screen experiments. SCEPTRE demonstrated excellent calibration and sensitivity on the data and revealed hundreds of new regulatory relationships, validated using a variety of orthogonal functional assays. In the “Discussion” section, we describe an independent work conducted in parallel to the current study in which we leveraged biobank-scale GWAS data, single-cell CRISPR screens, and SCEPTRE to dissect the cis and trans effects of noncoding variants associated with blood diseases [14]. This work highlights what we see as a primary application of SCEPTRE: dissecting regulatory mechanisms underlying GWAS associations.

Analysis challenges

We examined two recent single-cell CRISPR screen datasets — one produced by Gasperini et al. [9] and the other by Xie et al. [8] — that exemplify several of the analysis challenges in high-MOI single-cell CRISPR screens. Gasperini et al. and Xie et al. used CRISPRi to perturb putative enhancers at high MOI in K562 cells. They sequenced polyadenylated gRNAs alongside the whole transcriptome and assigned perturbation identities to cells by thresholding the resulting gRNA UMI counts.

Both Gasperini et al. and Xie et al. encountered substantial difficulties in calibrating tests of association between candidate enhancers and genes. Gasperini et al. computed p-values using a DESeq2 [15]-inspired negative binomial regression analysis implemented in Monocle2 [16], and Xie et al. computed p-values using Virtual FACS, a nonparametric method proposed by these authors. Gasperini et al. assessed calibration by pairing each of 50 non-targeting (or negative) control gRNAs with each protein-coding gene. These “null” p-values exhibited inflation, deviating substantially from the expected uniform distribution (Fig. 1a, red). To assess the calibration of Virtual FACS in a similar manner, we constructed a set of in silico negative control pairs of genes and gRNAs on the Xie et al. data (see the “Methods” section). The resulting p-values were likewise miscalibrated, with some pairs exhibiting strong conservative bias and others strong liberal bias (Fig. 1a, gray-green).

Fig. 1
figure 1

CRISPR screen analysis challenges can lead to false positives and false negatives. a QQ-plot of negative control p-values produced by Gasperini et al. (red; downsampled for visualization) and Xie et al. (gray-green). These p-values deviate substantially from the expected uniform distribution, indicating test miscalibration. b–d Technical factors, such as sequencing depth and batch, impact gRNA detection probability and observed gene expression levels in both Gasperini et al. (b) and Xie et al. (c) data. Thus, technical factors act as confounders (d), differentiating CRISPR screens from traditional differential expression applications. e Monocle2 estimates the dispersion of each gene by projecting each gene’s raw dispersion estimate onto the fitted raw dispersion-mean expression curve. This estimation procedure leads to miscalibration for high-dispersion genes

A core challenge in the analysis of single-cell CRISPR screens is the presence of confounders, technical factors that impact both gRNA detection probability and gene expression. The total number of gRNAs detected in a cell increases with the total number of mRNA UMIs detected in a cell (ρ=0.35,p<10−15 in Gasperini et al. data; ρ=0.25,p<10−15 in Xie et al. data; Figs. 1b, c). Technical covariates, such as sequencing depth and batch, induce a correlation between gRNA detection probability and gene expression, even in the absence of a regulatory relationship (Fig. 1d). This confounding effect can lead to severe test miscalibration and is especially problematic for traditional nonparametric approaches, which implicitly (and incorrectly) treat cells symmetrically with respect to confounders.

Parametric regression approaches, like negative binomial regression, are the most straightforward way to adjust for confounders. However, parametric methods rely heavily on correct model specification, a challenge in single-cell analysis given the heterogeneity and complexity of the count data. We hypothesized that inaccurate estimation of the negative binomial dispersion parameter was (in part) responsible for the p-value inflation observed by Gasperini et al. Monocle2 estimates a raw dispersion for each gene, fits a parametric mean-dispersion relationship across genes, and finally collapses raw dispersion estimates onto this fitted line (Fig. 1e). We computed the deviation from uniformity of the negative control p-values for each gene using the Kolmogorov-Smirnov (KS) test, represented by the color of each point in Fig. 1e. Circled genes had significantly miscalibrated p-values based on a Bonferroni correction at level α=0.05. Genes significantly above the curve showed marked signs of p-value inflation, suggesting model misspecification. Analysis challenges are summarized in Table 1.

Table 1 Statistical methods employed in single-cell CRISPR screen analysis. Parametric methods are non-robust to misspecified gene expression distributions, and classical nonparametric methods cannot adjust for confounders. Conditional resampling (implemented in this work as SCEPTRE) addresses both challenges

Gasperini et al. and Xie et al. incorporated ad hoc adjustments into their analyses to remedy the observed calibration issues. On closer inspection, however, these efforts were not satisfactory to ensure reliability of the results. Gasperini et al. attempted to calibrate p-values against the distribution negative control p-values instead of the more standard uniform distribution. This adjustment lead to overcorrection for some gene-enhancer pairs (false negatives) and undercorrection for others (false positives) (Fig. S1). Along similar lines Xie et al. compared their Virtual FACS p-values to gene-specific simulated null p-values to produce “significance scores” that were used to determine significance. These significance scores were challenging to interpret and could not be subjected to multiple hypothesis testing correction procedures, as they are not p-values.

Improvements to the negative binomial approach

We attempted to alleviate the miscalibration within the negative binomial regression framework by following the recommendations of Hafemeister and Satija, who recently proposed a strategy for parametric modeling of single-cell RNA-seq data [17]. First, we abandoned the DESeq2-style size factors of Monocle2 and instead corrected for sequencing depth by including it as a covariate in the negative binomial regression model. Second, we adopted a more flexible dispersion estimation procedure: we (i) computed raw dispersion estimates for each gene, (ii) regressed the raw dispersion estimates onto the mean gene expressions via kernel regression, and (iii) projected the raw dispersion estimates onto the fitted nonparametric regression curve.

We reanalyzed the Gasperini et al. and Xie et al. negative control data using the improved negative binomial regression approach. In addition to sequencing depth, we included as covariates in the regression model the total number of expressed genes per cell and the technical factors accounted for in the original analysis (total number of gRNAs detected per cell, percentage of transcripts mapped to mitochondrial genes, and sequencing batch). Improved negative binomial regression exhibited better calibration than Monocle regression on both Gasperini et al. and Xie et al. datasets. Still, improved negative binomial regression demonstrated clear p-value inflation. We concluded that parametric count models likely are challenging to calibrate to high-MOI single-cell CRISPR screen data.

SCEPTRE: analysis of single-cell perturbation screens via conditional resampling

To address the challenges identified above, we propose SCEPTRE, a methodology for single-cell CRISPR screen analysis based on the simple and powerful conditional randomization test [13] (Fig. 2). To test the association between a given gRNA and gene, we first fit the improved negative binomial statistic described above. This yields a z-value, which typically would be compared to a standard normal null distribution based on the parametric negative binomial model. Instead, we build a null distribution for this statistic via conditional resampling. First, we estimate the probability that the gRNA will be detected in a given cell based on the cell’s technical factors, such as sequencing depth and batch. Next, we resample a large number of “null” datasets, holding gene expression and technical factors constant while redrawing gRNA assignment independently for each cell based on its fitted probability. We compute a negative binomial z-value for each resampled dataset, resulting in an empirical null distribution (gray histogram in Fig. 2). Finally, we compute a left-, right-, or two-tailed probability of the original z-value under the empirical null distribution, yielding a well-calibrated p-value. This p-value can deviate substantially from that obtained based on the standard normal (Fig. 2, Fig. S2). While we used a negative binomial regression test statistic for this work, SCEPTRE in principle is compatible with any test statistic that reasonably tracks the expression data, including, for example, statistics based on machine learning algorithms.

Fig. 2
figure 2

SCEPTRE: Analysis of single-cell perturbation screens via conditional resampling. A schematic and outline of the SCEPTRE methodology for one gene and one gRNA. SCEPTRE estimates the probability of gRNA detection in each cell based on its technical factors. It then builds a null distribution for the negative binomial z-value by independently resampling gRNA presence or absence for each cell according to these probabilities to form “negative control” datasets. A skew-t distribution is fit to the resulting histogram to obtain precise p-values based on a limited number of resamples, against which the original NB z-value is compared. The dashed line shows the standard normal distribution, against which the NB z-value typically would be compared

We leverage several computational accelerations to enable SCEPTRE to scale to large single-cell CRISPR screen datasets. First, we approximate the null histogram of the resampled test statistics using a skew-t distribution to obtain precise p-values based on a limited number of resamples (500 in the current implementation). Second, we employ statistical shortcuts that reduce the cost of each resample by a factor of about 100 (see the “Methods” section). Finally, we implement the method so that it can run in parallel on hundreds or thousands of processors on a computer cluster. (We used this approach in our independent study of noncoding blood trait GWAS loci [14].) We estimate that SCEPTRE can analyze 2.5 million gene-gRNA pairs on a dataset of 200,000 cells in a single day using 500 processors.

SCEPTRE demonstrates good calibration and sensitivity on real and simulated data

First, we investigated the calibration of SCEPTRE in a small, proof-of-concept simulation study (Fig. 3a). We considered a class of negative binomial regression models with fixed dispersion and two technical covariates (sequencing depth and batch). We simulated expression data for a single gene in 1000 cells using four models selected from this class: the first with dispersion =1, the second with dispersion =0.2, the third with dispersion =5, and the last with dispersion =1, but with 25% zero-inflation. We also simulated negative control gRNA data using a logistic regression model with the same covariates as the gene expression model. We assessed the calibration of SCEPTRE and negative binomial regression across the four simulated datasets. To explore the impact of model misspecification on SCEPTRE and the negative binomial method (on which SCEPTRE relies), we fixed the dispersion of the negative binomial method to 1. The negative binomial method worked as expected when the model was correctly specified. However, negative binomial regression broke down in all three cases of model misspecification. SCEPTRE demonstrated good calibration in all settings.

Fig. 3
figure 3

SCEPTRE demonstrates good calibration and sensitivity under known ground truth. a Numerical simulation comparing SCEPTRE and improved negative binomial regression on four simulated datasets. The negative binomial model was incorrectly specified on three of the four datasets. SCEPTRE maintained good calibration across all four datasets, despite model misspecification and confounder presence. b, c Application of SCEPTRE, improved negative binomial regression, Monocle regression, and Virtual FACS to pairs of negative control gRNAs and genes in b the Gasperini et al. data and c the Xie et al. data. Compared to the other methods, SCEPTRE showed good calibration. d SCEPTRE p-values for Gasperini et al. TSS-targeting controls were highly significant, and in general, more significant than the original empirical p-values. e Comparison of p-values produced by SCEPTRE for ARL15-enh to p-values produced by an arrayed, bulk RNA-seq CRISPR screen of ARL15-enh. The results of the two analyses coincided almost exactly, with both analyses rejecting gene ARL15 with high confidence after a BH correction. Dotted blue lines, rejection thresholds

Next, to assess the calibration of SCEPTRE on real data, we applied SCEPTRE to test the association between negative control gRNAs and genes in the Gasperini et al. data (Fig. 3b) and Xie et al. data (Fig. 3c). We compared SCEPTRE to Monocle regression and the improved negative binomial method. For the Xie et al. data, we also compared to Virtual FACS, the method originally applied to the data. SCEPTRE showed good calibration on both datasets; by contrast, Monocle regression and improved negative binomial regression demonstrated signs of severe p-value inflation, while Virtual FACS exhibited a bimodal p-value distribution peaked at 0 and 1.

SCEPTRE demonstrated modestly better calibration on the Gasperini et al. data than on the Xie et al. data. This likely is because the Gasperini et al. negative control pairs — which consisted of real, non-targeting gRNAs — were higher-quality than the Xie et al. negative control pairs — which were constructed in silico using enhancer-targeting gRNAs (see the “Methods” section). We reasoned that the Xie et al. negative controls carried mild regulatory signal, resulting in slight inflation of the SCEPTRE p-values on these data relative to the Gasperini et al. data.

To assess the sensitivity of SCEPTRE, we applied SCEPTRE to test the 381 positive control pairs of genes and TSS-targeting gRNAs assayed by Gasperini et al. (Fig. 3d). Allowing for the fact that the empirical correction employed by Gasperini et al. limited the accuracy of p-values to about 10−6, the SCEPTRE p-values for the positive controls were highly significant, and in particular, almost always more significant than the original empirical p-values, indicating greater sensitivity. Finally, we assessed the sensitivity of SCEPTRE on the Xie et al. data. Xie et al. conducted an arrayed CRISPR screen with bulk RNA-seq readout of ARL15-enh, a putative enhancer of gene ARL15. Both SCEPTRE and the bulk RNA-seq differential expression analysis rejected ARL15 at an FDR of 0.1 after a Benjamini-Hochberg (BH) correction, increasing our confidence in the calibration and sensitivity of SCEPTRE (Fig. 3e).

Analysis of candidate cis-regulatory pairs

We applied SCEPTRE to test all candidate cis-regulatory pairs in the Gasperini et al. (n=84,595) and Xie et al. (n=5,209) data. A given gene and gRNA were considered a “candidate pair” if the gRNA targeted a site within one Mb the gene’s TSS. SCEPTRE discovered 563 and 139 gene-enhancer links at an FDR of 0.1 on the Gasperini et al. and Xie et al. data, respectively. We used several orthogonal assays to quantify the enrichment of SCEPTRE’s discovery set for regulatory biological signals, and we compared the SCEPTRE results to those of other methods.

SCEPTRE’s discovery set on the Gasperini et al. data was highly biologically plausible, and in particular, more enriched for biological signals of regulation than the original discovery set. Gasperini et al. discovered 470 gene-gRNA pairs at a reported FDR of 0.1. The SCEPTRE p-values and original empirical p-values diverged substantially: of the 670 gene-enhancer pairs discovered by either method, SCEPTRE and the original method agreed on only 363, or 54% (Fig. 4a). Gene-enhancer pairs discovered by SCEPTRE were physically closer (mean distance =65 kb) to each other than those discovered by the original method (mean distance =81 kb; Fig. 4b). Furthermore, SCEPTRE’s gene-enhancer pairs fell within the same topologically associating domain (TAD) at a higher frequency (74%) than the original pairs (71%). Pairs within the same TAD showed similar levels of HI-C interaction frequency across methods, despite the fact that SCEPTRE discovered 85 more same-TAD pairs (Fig. 4c). Finally, enhancers discovered by SCEPTRE showed improved enrichment across all eight cell-type relevant ChIP-seq targets reported by Gasperini et al. (Fig. 4d, Fig. S5a).

Fig. 4
figure 4

Application of SCEPTRE to Gasperini et al. data yields biologically plausible gene-enhancer links. a Comparison of the original empirical p-values to those obtained from SCEPTRE. The two analysis methods differed substantially, with 200 gene-enhancer links discovered only by SCEPTRE and 107 discovered only by the original analysis. Annotations correspond to pairs in panel (e). b Distribution of distances from TSS to upstream paired enhancers. Compared to Monocle NB (original) and improved NB analyses, SCEPTRE paired genes with nearer enhancers on average. c For those gene-enhancer pairs falling in the same TAD, the cumulative distribution of the fractional rank of the HI-C interaction frequency compared to other distance-matched loci pairs within the same TAD. SCEPTRE showed similar enrichment despite finding 25% more within-TAD pairs compared to the original analysis. Inset table shows gene-enhancer pairs falling in the same TAD. SCEPTRE found 93 more total pairs compared to the original analysis, and a higher percentage of pairs fell within the same TAD. d Enrichment of ChIP-seq signal from seven cell-type relevant transcription factors and one histone mark (H3K27ac) among paired enhancers. SCEPTRE showed stronger enrichment across all ChIP-seq targets. e Five gene-enhancer pairs discovered by SCEPTRE but not the original analysis, each supported by a whole blood GTEx eQTL or FANTOM enhancer RNA correlation p-value

When we compared discoveries unique to SCEPTRE (n=200) against those unique to the original method (n=107), the disparities became more extreme (Fig. S3). For example, only 57% of pairs unique to the original method fell within the same TAD, compared to 73% unique to SCEPTRE. We concluded that many pairs in the Gasperini et al. discovery set likely were false positives. Finally, when we compared SCEPTRE to the improved negative binomial method (n = 824 discoveries), we observed even greater differences in discovery set quality in favor of SCEPTRE (Figs. 4b–d).

We highlight several especially interesting gene-enhancer pairs discovered by SCEPTRE. Five discoveries (Fig. 4a, labels 1–5; Fig. 4e) were nominated as probable gene-enhancer links by eQTL [18] and eRNA [19] p-values in relevant tissue types. The SCEPTRE p-values for these pairs were 1–2 orders of magnitude smaller than the original empirical p-values, hinting at SCEPTRE’s greater sensitivity. Additionally, six pairs (Fig. 4a, blue triangles) were discovered by SCEPTRE but discarded as outliers by the original analysis, underscoring SCEPTRE’s ability to handle genes with arbitrary expression distributions.

We repeated the same orthogonal analyses for the SCEPTRE discoveries on the Xie et al. data, comparing SCEPTRE’s results to those of Xie et al. Xie et al.’s analysis method, Virtual FACS, outputted “significance scores” rather than p-values (see the “Analysis challenges” section). Because significance scores cannot be subjected to multiple hypothesis testing correction procedures (like BH), we compared the top 139 Virtual FACS pairs (ranked by significance score) against the set of 139 (FDR =0.1) SCEPTRE discoveries (Fig. 5a; see the “Methods” section). Of the 195 pairs in either set, SCEPTRE and Virtual FACS agreed on only 83, or 43%. The SCEPTRE discoveries were more biologically plausible: compared to the Virtual FACS pairs, the SCEPTRE pairs were (i) physically closer (Fig. 5b), (ii) more likely to fall within the same TAD (Fig. 5c), (iii) more likely to interact when in the same TAD (Fig. 5c), and (iv) more enriched for all eight cell-type relevant ChIP-seq targets (Fig. 5d, Fig. S5b). When we examined the symmetric difference of the discovery sets, these differences became more pronounced (Fig. S4).

Fig. 5
figure 5

SCEPTRE discovers biologically plausible gene-enhancer links on Xie et al. data. a Comparison of SCEPTRE p-values to Virtual FACS significance scores. Significant SCEPTRE p-values (n=139) are colored in blue and purple, and the top 139 Virtual FACS pairs, as ranked by significance score, are colored in gray-green and purple. The two sets diverged substantially, with only 43% of pairs in shared across sets. b–d These panels are similar to the corresponding panels in Fig. 4. SCEPTRE pairs showed strong enrichment for biological signals associated with enhancer activity on b physical distance, c HIC interaction, and d ChIP-seq metrics relative to other methods

We additionally compared SCEPTRE to Monocle regression (n=180 discoveries) and improved negative binomial regression (n=156 discoveries) on the Xie et al. data. SCEPTRE uniformly dominated Monocle: SCEPTRE pairs were physically closer to one another (median distance = 44kb versus 110kb; Fig. 5b); SCEPTRE pairs interacted more frequently and were more likely to fall within the same TAD (68% versus 61%; Fig. 5c); and SCEPTRE pairs were more enriched for seven of eight cell type-relevant ChIP-seq targets (one target, DP22, was a tie; Fig. 5d). Improved negative binomial regression was more competitive than Monocle across metrics (Fig. 5b–d). However, as noted earlier, improved negative binomial regression exhibited severe miscalibration on the negative control pairs (Fig. 3d), rendering its discovery set less reliable than that of SCEPTRE.

Gene expression level and sensitivity

To better understand when SCEPTRE works best, we investigated the impact of gene expression level on the sensitivity of SCEPTRE. We binned candidate gene-enhancer pairs into non-overlapping categories based on mean expression level of the gene. On both the Gasperini et al. and Xie et al. data, we found that candidate pairs containing a highly expressed gene were more likely to be rejected than candidate pairs containing a lowly-expressed gene (Tables S1, S2), indicating SCEPTRE’s greater sensitivity for highly expressed genes. We observed similar trends for the other methods (not shown), consistent with the intuition that highly-expressed genes carry more information.

In this work we illustrated a variety of statistical challenges arising in the analysis of high-MOI single-cell CRISPR screens, leaving existing methods (based on parametric expression models, permutations, or negative control data) vulnerable to miscalibration. To address these challenges, we developed SCEPTRE, a resampling method based on modeling the probability a given gRNA will be detected in a given cell, based on that cell’s technical factors. We found that SCEPTRE exhibited very good calibration despite the presence of confounding technical factors and misspecification of single-cell gene expression models. We implemented computational accelerations to bring the cost of the resampling-based methodology down to well within an order of magnitude of the traditional negative binomial parametric approach, making it quite feasible to apply for large-scale data. We used SCEPTRE to reanalyze the Gasperini et al. and Xie et al. data. While our analysis replicated many of their findings, it also clarified other relationships, removing a large set (>20% for Gasperini) of pairs that exhibited a weak relationship and adding an even larger set (>40% for Gasperini) of new, biologically plausible gene-enhancer relationships. These links were supported by orthogonal evidence from eQTL, enhancer RNA co-expression, ChIP-seq, and HI-C data.

As an example application of SCEPTRE, we highlight STING-seq, a platform that we developed in parallel to the current work in an independent study [14]. STING-seq leverages biobank-scale GWAS data and single-cell CRISPR screens to map noncoding, disease-associated variants at scale. First, we used statistical fine-mapping to identify a set of 88 putatively causal variants from 56 loci associated with quantitative blood traits. We perturbed the selected variants at high MOI in K562 cells using an improved CRISPRi platform and sequenced gRNAs and transcriptomes in individual cells using ECCITE-seq [6], a protocol that enables the profiling of multiple modalities and the direct capture of gRNAs.

We then applied SCEPTRE to quantify associations between perturbations and changes in gene expression in cis (within 500 kb) and trans. SCEPTRE confidently mapped 37 noncoding variants to their cis target genes, in some cases identifying a causal variant among a set of candidate variants in strong LD. Nine variants were found to regulate a gene other than the closest gene, and four variants were found to regulate multiple genes, an apparent example of pleiotropy. Several perturbations lead to widespread changes in gene expression, illuminating trans-effects networks. For example, two variants that were found to regulate the transcription factor GFI1B in cis altered the expression of hundreds of genes in trans upon perturbation; these differentially expressed genes were strongly enriched for GFI1B binding sites and blood disease GWAS hits. We concluded on the basis of this study SCEPTRE can power the systematic dissection regulatory networks underlying GWAS associations.

Despite these exciting results, key challenges remain in the analysis of single-cell CRISPR screens. Currently, SCEPTRE does not estimate the effect sizes of perturbations, disentangle interactions among perturbed regulatory elements [20, 21], or leverage information from off-targeting gRNAs to improve power. Such extensions could be implemented by harnessing more sophisticated, multivariate models of gRNA detection or applying methods for estimating variable importance in the presence of possibly misspecified models [22]. The statistical challenges that we identified in this study — specifying an accurate expression model and accounting for technical factors — and the solutions that we proposed — conditional resampling and massively parallel association testing — will help guide the development of future versions of SCEPTRE.

Single-cell CRISPR screens will play a key role in unraveling the regulatory architecture of the noncoding genome [23]. Technological improvements and methodological innovations will increase the scope, scale, and variety of theses screens over the coming years. For example, screens of candidate CREs could be extended to different, disease-relevant cell types and tissues (although this remains a challenge); new combinatorial indexing strategies, such as scifi-RNA-seq, could enable the scaling-up of such screens to millions of cells [24]; different CRISPR technologies, such as CRISPRa, could enable the activation, rather than repression, of candidate CREs, yielding new insights; and information-rich, multimodal single-cell readouts could strengthen conclusions drawn about regulatory relationships [25]. SCEPTRE is a flexible, robust, and efficient method: it has now successfully been applied to three single-cell CRISPR screen datasets, across two technologies (CROP-seq and ECCITE-seq), to map regulatory relationships both in cis and in trans. We expect SCEPTRE to facilitate the analysis of future single-cell screens of the noncoding genome, advancing understading of CREs and enabling the detailed interpretation of GWAS results.

Gasperini et al. and Xie et al. data

Gasperini et al. used CROP-seq [5, 11] to transduce a library of CRISPR guide RNAs (gRNAs) into a population of 207,324 K562 cells expressing the Cas9-KRAB repressive complex at a high multiplicity of infection. Each cell received an average of 28 perturbations. The gRNA library targeted 5779 candidate enhancers, 50 negative controls, and 381 TSS-targeting positive controls. Xie et al. used Mosaic-seq [7, 8] to perturb at a high multiplicity of infection 518 putative enhancers in a population of 106,670 Cas9-KRAB-expressing K562 cells. Each putative enhancer was perturbed in an average of 1276 cells.

Cis and in silico negative control pairs for Xie et al. data

We generated the set of candidate cis gene-enhancer relationships on the Xie et al. data by pairing each protein-coding gene with each gRNA targeting a site within 1 Mb of the TSS of the gene. This procedure resulted in 3553 candidate cis gene-enhancer links that we tested using SCEPTRE and Virtual FACS.

To generate the set of in silico negative control pairs for calibration assessment, we (i) identified gRNAs that targeted sites far (>1 Mb) from the TSSs of known transcription factor genes and (ii) paired these gRNAs with genes located on other chromosomes. We excluded all pairs containing genes known to be transcription factors, and we downsampled the pairs so that each gRNA was matched to 500 genes. The final in silico negative control set consisted of 84,500 pairs, the elements of which were not expected to exhibit a regulatory relationship.

Conditional randomization test

Consider a particular gene-gRNA pair. For each cell \(i = 1, \dots, n\), let Xi{0,1} indicate whether the gRNA was present in the cell, let \(Y_{i} \in \{0,1,2,\dots \}\) be the gene expression in the cell, defined as the number of unique molecular identifiers (UMIs) from this gene, and let \(Z_{i} \in \mathbb R^{d}\) be a list of cell-level technical factors. Letting \((X, Y, Z) = \{(X_{i}, Y_{i}, Z_{i})\}_{i = 1}^{n}\), consider any test statistic T(X,Y,Z) measuring the effect of the gRNA on the expression of the gene. The conditional randomization test [13] is based on resampling the gRNA indicators independently for each cell. Letting \(\pi _{i} = \mathbb P[X_{i} = 1 | Z_{i}]\), define random variables

$$ \widetilde X_{i} \overset{\text{ind}}\sim \text{Ber}(\pi_{i}). $$

Then, the CRT p-value is given by

$$ p_{\text{CRT}} = \mathbb{P}[T(\widetilde X, Y, Z) \geq T(X,Y,Z)\mid X,Y,Z]. $$

This translates to repeatedly sampling \(\widetilde X\) from the distribution (1), recomputing the test statistic with X replaced by \(\widetilde X\), and defining the p-value as the probability the resampled test statistic exceeds the original. Under the null hypothesis that the gRNA perturbation does not impact the cell (adjusting for technical factors), i.e., Y XZ, we obtain a valid p-value (2), regardless of the expression distribution Y|X,Zand regardless of the test statistic T. We choose as a test statistic T the z-score of Xi obtained from a negative binomial regression of Yi on Xi and Zi:

$$ Y_{i} \overset{\text{ind}} \sim \text{NegBin}(\mu_{i}, \alpha); \quad \log(\mu_{i}) = \beta_{0} + X_{i} \beta + Z_{i}^{T} \gamma, $$

where α is the dispersion. Following Hafemeister and Satjia [17], we estimate α by pooling dispersion information across genes, and we include sequencing depth as an entry in the vector of technical factors Zi (see the “Improvements to the negative binomial approach” section).

Accelerations to the conditional randomization test

We implemented computational accelerations to the conditional randomization test. First, we employed the recently proposed [26] distillation technique to accelerate the recomputation of the negative binomial regression for each resample. The idea is to use a slightly modified test statistic, consisting of two steps:

  1. 1

    Fit \((\widehat \beta _{0}, \widehat \gamma)\) from the negative binomial regression (3) except without the gRNA term:

    $$ Y_{i} \overset{\text{ind}}\sim \text{NegBin}(\mu_{i}, \alpha); \quad \log(\mu_{i}) = \beta_{0} + Z_{i}^{T} \gamma. $$
  2. 2

    Fit \(\widehat \beta \) from a negative binomial regression with the estimated contributions of Zi from step 1 as offsets:

    $$ Y_{i} \overset{\text{ind}}\sim \text{NegBin}(\mu_{i}, \alpha); \quad \log(\mu_{i}) = X_{i} \beta + \widehat \beta_{0} + Z_{i}^{T} \widehat \gamma. $$

Conditional randomization testing with this two-step test statistic, which is nearly identical to the full negative binomial regression (3), is much faster. Indeed, since the first step is not a function of Xi, it remains the same for each resampled triple \((\widetilde X, Y, Z)\). Therefore, only the second step must be recomputed with each resample, and this step is faster because it involves only a univariate regression.

Next, we accelerated the second step above using the sparsity of the binary vector \((X_{1}, \dots, X_{n})\) (or a resample of it). To do so, we wrote the log-likelihood of the reduced negative binomial regression (5) as follows, denoting by (Yi, log(μi)) the negative binomial log-likelihood:

$$\begin{aligned} \sum_{i = 1}^{n} \ell(Y_{i}, X_{i} \beta + \widehat \beta_{0} + Z_{i}^{T} \widehat \gamma) &= \sum_{i: X_{i} = 0} \ell(Y_{i}, \widehat \beta_{0} + Z_{i}^{T} \widehat \gamma) + \sum_{i: X_{i} = 1} \ell(Y_{i}, \beta + \widehat \beta_{0} + Z_{i}^{T} \widehat \gamma) \\ &= C + \sum_{i: X_{i} = 1} \ell(Y_{i}, \beta + \widehat \beta_{0} + Z_{i}^{T} \widehat \gamma). \end{aligned} $$

This simple calculation shows that, up to a constant that does not depend on β, the negative binomial log-likelihood corresponding to the model (5) is the same as that corresponding to the model with only intercept and offset term for those cells with a gRNA:

$$ Y_{i} \overset{\text{ind}}\sim \text{NegBin}(\mu_{i}, \alpha); \quad \log(\mu_{i}) = \beta + \widehat \beta_{0} + Z_{i}^{T} \widehat \gamma, \quad \text{for} i \text{ such that} X_{i} = 1. $$

The above negative binomial regression is therefore equivalent to Eq. 5, but much faster to compute, because it involves much fewer cells. For example, in the Gasperini et al. data, each gRNA is observed in only about 1000 of the 200,000 total cells.

SCEPTRE methodology

In practice, we must estimate the gRNA probabilities πi as well as the p-value pCRT. This is because usually we do not know the distribution X|Z and cannot compute the conditional probability in Eq. 2 exactly. We propose to estimate πi via logistic regression of X on Z, and to estimate pCRT by resampling \(\widetilde X\) a large number of times and then fitting a skew-t distribution to the resampling null distribution \(T(\widetilde X, Y, Z)|X,Y,Z\). We outline SCEPTRE below:

  1. 1

    Fit technical factor effects \((\widehat \beta _{0},\widehat \gamma)\) on gene expression using the negative binomial regression (4).

  2. 2

    Extract a z-score z(X,Y,Z) from the reduced negative binomial regression (6).

  3. 3

    Assume that

    $$ X_{i} \overset{\text{ind}}\sim \text{Ber}(\pi_{i}); \quad \log\left(\frac{\pi_{i}}{1-\pi_{i}}\right) = \tau_{0} + Z_{i}^{T} \tau $$

    for \(\tau _{0} \in \mathbb R\) and \(\tau \in \mathbb R^{d}\), and fit \((\widehat \tau _{0}, \widehat \tau)\) via logistic regression of X on Z. Then, extract the fitted probabilities \(\widehat \pi _{i} = (1+\exp (-(\widehat \tau _{0} + Z_{i}^{T} \widehat \tau)))^{-1}\).

  4. 4

    For \(b = 1, \dots, B\),

    • Resample the gRNA assignments based on the probabilities \(\widehat \pi _{i}\) to obtain \(\widetilde X^{b}\) (1).

    • Extract a z-score \(z(\widetilde X^{b}, Y, Z)\) from the reduced negative binomial regression (6).

  5. 5

    Fit a skew-t distribution \(\widehat F_{\text {null}}\) to the resampled z-scores \(\{z(\widetilde X^{b}, Y, Z)\}_{b = 1}^{B}\).

  6. 6

    Return the p-value \(\widehat p_{\text {SCEPTRE}} = \mathbb P[\widehat F_{\text {null}} \leq z(X,Y,Z)]\).

In our data analysis, we used B=500 resamples.

Numerical simulation to assess calibration

We simulated one gene Yi, one gRNA Xi, and two confounders Zi1,Zi2 in n=1000 cells. We generated the confounders Zi1 and Zi2 by sampling with replacement the batch IDs and log-transformed sequencing depths of the cells in the Gasperini dataset. The batch ID confounder Zi1 was a binary variable, as the Gasperni data included two batches. Next, we drew the gRNA indicators Xi i.i.d. from the logistic regression model (7), with τ0=−7,τ1=−2, and τ2=0.5. We selected these parameters to make the probability of gRNA occurrence about 0.04 across cells. Finally, we drew the gene expression Yi from the following zero-inflated negative binomial model:

$$Y_{i} \sim \lambda \delta_{0} + (1 - \lambda) \text{NegBin}(\mu_{i}, \alpha), \log(\mu_{i}) = \beta_{0} + Z_{i}^{T} \beta.$$

Note that gRNA presence or absence does not impact gene expression in this model. We set β0=−2.5,β1=−2,β2=0.5 to make the average gene expression about 4 across cells. We generated the four datasets shown in Fig. 3a by setting the dispersion parameter α and the zero inflation rate parameter λ equal to the following values:

$$(\lambda_{1}, \alpha_{1}) = (0,1) ; (\lambda_{2}, \alpha_{2}) = (0, 5); (\lambda_{3}, \alpha_{3}) = (0, 0.2); (\lambda_{4}, \alpha_{4}) = (0.25, 1).$$

For the first, the negative binomial model is correctly specified. For the second and third, the dispersion estimate of 1 is too small and too large, respectively. The last setting exhibits zero inflation. We applied SCEPTRE and negative binomial regression to the four problem settings, each with nsim=500 repetitions. The negative binomial method, and in turn SCEPTRE, was based on the z statistic from the Hafemeister-inspired negative binomial model (3) with α=1. We used B=500 resamples for SCEPTRE, the default choice.

scMAGeCK-LR [10] is a method for high MOI single-cell CRISPR screen analysis. (A complimentary method, scMAGeCK-RRA, is designed for the low-MOI setting.) scMAGeCK-LR (henceforth scMAGeCK) uses a permutation test with ridge regression test statistic to compute p-values for pairs of genes and gRNAs. Unfortunately, we were unable to apply scMAGeCK to the real data. First, we were unable to understand the documentation of the scMAGeCK software well enough to confidently apply the method. Second, scMAGeCK is prohibitively expensive to apply at-scale. The authors of the original scMAGeCK study applied their method only to a small subset of pairs in the Gasperini et al. data. We could not meaningfully compare scMAGeCK to SCEPTRE on calibration and sensitivity metrics without applying scMAGeCK to the full set of gRNA-gene pairs, which, to our knowledge, never has been done (and likely is infeasible).

To enable a simple comparison to scMAGeCK on the simulated data, we implemented a custom, in-house version of scMAGeCK based on a careful examination of the scMAGeCK codebase and a close reading of the original paper. We view this custom implementation as a faithful interpretation of the method in the specialized one-gene to one-NTC setting. We applied our implementation of scMAGeCK to the simulated data, using B=1,000 permutations, the default option. To reduce confusion, we reported the results of the scMAGeCK simulation study in the supplementary materials (Fig. S6) rather than the “Results” section. We could not apply our custom implementation of scMAGeCK to the real data, because the real data are significantly more complex than the simulated data. For example, the real data consist of many genes and gRNAs, and the gRNAs are differently typed (e.g., negative control, positive control, enhancer-targeting, etc.), complicating the analysis considerably.

Definition of Gasperini et al. discovery set

Gasperini et al. reported a total of 664 gene-enhancer pairs, identifying 470 of these as “high-confidence.” We chose to use the latter set, rather than the former, for all our comparisons. Gasperini et al. carried out their ChIP-seq and HI-C enrichment analyses only on the high-confidence discoveries, so for those comparisons we did the same. Furthermore, the 664 total gene-enhancer pairs reported in the original analysis were the result of a BH FDR correction that included not only the candidate enhancers but also hundreds of positive controls. While Bonferroni corrections can only become more conservative when including more hypotheses, BH corrections are known to become anticonservative when extra positive controls are included [27]. To avoid this extra risk of false positives, we chose to use the “high-confidence” set throughout.

Xie et al. significance scores and discovery set

Xie et al. reported a local (or cis) discovery set, which consisted of gene-gRNA pairs with a significance score of greater than zero (see original manuscript for definition of “significance score” [8]; cutoff of zero arbitrary). This discovery set was not directly comparable to the SCEPTRE discovery set. First, the candidate set of cis gene-gRNA pairs tested by Xie et al. consisted of gRNAs within two Mb of a protein-coding gene or long-noncoding RNA. Our candidate cis set, by contrast, consisted of gRNAs within one Mb of a protein-coding gene. We defined our candidate cis set differently than Xie et al. to maintain consistency with Gasperini et al. Second, Xie et al. appear to have used a significantly more conservative threshold than Gasperini et al. in defining their discovery set, but this was challenging to ascertain given the impossibility of FDR correction on the significance scores. To enable a meaningful comparison between Virtual FACS and SCEPTRE, we therefore ranked the Virtual FACS pairs by their significance score and selected the top n pairs, where n was the size of the SCEPTRE discovery set at FDR 0.1.

ChIP-seq, HI-C enrichment analyses

ChIP-seq and HI-C enrichment analyses on the Gasperini et al. data (see Figs. 4e, f and S5a) were carried out almost exactly following Gasperini et al. The only change we made is in our quantification of the ChIP-seq enrichment (Fig. 4f). We used the odds ratio of a candidate enhancer being paired to a gene, comparing the top and bottom ChIP-seq quintiles. On the Xie et al. data, we binned the candidate enhancers into two (rather than five) quantiles due to the fewer number of candidate cis pairs. We computed odds ratios by comparing enhancers in the upper quantile to those that did not intersect a ChIP-seq peak at all (Fig. S5b).

Availability of data and materials

Analysis results are available online at All analysis was performed on publicly available data. The Gasperini et al. CRISPR screen data [9] are available at The Xie et al. single-cell and bulk CRISPR screen data are available at The ChIP-seq data are taken from the ENCODE project [30] and are available at The HI-C enrichment analysis is based on the data from Rao et al. [31], available at The eQTL and eRNA co-expression p-values are taken from the GeneHancer, database [32] available as part of GeneCards (

The sceptre R package is available at Vignettes and tutorials are available at The scripts used to run the analyses reported in this paper are available at (permanent version deposited at Zenodo; DOI 10.5281/zenodo.5643541 [33]). All software is released under an MIT license.

  1. Gallagher MD, Chen-Plotkin AS. The post-GWAS era: from association to function. Am J Hum Genet. 2018; 102(5):717–30.

    Article  CAS  Google Scholar

  2. Gasperini M, Tome JM, Shendure J. Towards a comprehensive catalogue of validated and target-linked human enhancers. Nat Rev Genet. 2020; 21(5):292–310.

    Article  CAS  Google Scholar

  3. Dixit A, Parnas O, Li B, Chen J, Fulco CP, Jerby-Arnon L, Marjanovic ND, Dionne D, Burks T, Raychowdhury R, Adamson B, Norman TM, Lander ES, Weissman JS, Friedman N, Regev A. Perturb-Seq: dissecting molecular circuits with scalable single-cell RNA profiling of pooled genetic screens. Cell. 2016; 167:1853–66.

    Article  CAS  Google Scholar

  4. Adamson B, Norman TM, Jost M, Cho MY, Nuñez JK, Chen Y, Villalta JE, Gilbert LA, Horlbeck MA, Hein MY, Pak RA, Gray AN, Gross CA, Dixit A, Parnas O, Regev A, Weissman JS. A multiplexed single-cell CRISPR screening platform enables systematic dissection of the unfolded protein response. Cell. 2016; 167(7):1867–82.

    Article  CAS  Google Scholar

  5. Datlinger P, Rendeiro AF, Schmidl C, Krausgruber T, Traxler P, Klughammer J, Schuster LC, Kuchler A, Alpar D, Bock C. Pooled CRISPR screening with single-cell transcriptome readout. Nat Methods. 2017; 14(3):297–301.

    Article  CAS  Google Scholar

  6. Mimitou EP, Cheng A, Montalbano A, Hao S, Stoeckius M, Legut M, Roush T, Herrera A, Papalexi E, Ouyang Z, Satija R, Sanjana NE, Koralov SB, Smibert P. Multiplexed detection of proteins, transcriptomes, clonotypes and CRISPR perturbations in single cells. Nat Methods. 2019; 16(5):409–12.

    Article  CAS  Google Scholar

  7. Xie S, Duan J, Li B, Zhou P, Hon GC. Multiplexed engineering and analysis of combinatorial enhancer activity in single cells. Mol Cell. 2017; 66:85–299.

    Article  Google Scholar

  8. Xie S, Armendariz D, Zhou P, Duan J, Hon GC. Global analysis of enhancer targets reveals convergent enhancer-driven regulatory modules. Cell Rep. 2019; 29(9):2570–8.

    Article  CAS  Google Scholar

  9. Gasperini M, Hill AJ, McFaline-Figueroa JL, Martin B, Kim S, Zhang MD, Jackson D, Leith A, Schreiber J, Noble WS, Trapnell C, Ahituv N, Shendure J. A genome-wide framework for mapping gene regulation via cellular genetic screens. Cell. 2019; 176(1-2):377–90.

    Article  CAS  Google Scholar

  10. Yang L, Zhu Y, Yu H, Chen S, Chu Y, Huang H, Zhang J, Li W. Linking genotypes with multiple phenotypes in single-cell CRISPR screens. Genome Biol. 2020;21(19).

  11. Hill AJ, McFaline-Figueroa JL, Starita LM, Gasperini MJ, Matreyek KA, Packer J, Jackson D, Shendure J, Trapnell C. On the design of CRISPR-based single-cell molecular screens. Nat Methods. 2018; 15(4):271–4.

    Article  CAS  Google Scholar

  12. Replogle JM, Norman TM, Xu A, Hussmann JA, Chen J, Cogan JZ, Meer EJ, Terry JM, Riordan DP, Srinivas N, Fiddes IT, Arthur JG, Alvarado LJ, Pfeiffer KA, Mikkelsen TS, Weissman JS, Adamson B. Combinatorial single-cell CRISPR screens by direct guide RNA capture and targeted sequencing. Nat Biotechnol. 2020; 38(8):954–61.

    Article  CAS  Google Scholar

  13. Candes E, Fan Y, Janson L, Lv J. Panning for gold: ‘model-X’ knockoffs for high dimensional controlled variable selection. J R Stat Soc Ser B Stat Methodol. 2018; 80(3):551–77.

    Article  Google Scholar

  14. Morris JA, Daniloski Z, Domingo J, Barry T, Ziosi M, Glinos DA, Hao S, Mimitou E, Smibert P, Roeder K, et al.Discovery of target genes and pathways of blood trait loci using pooled crispr screens and single cell rna sequencing. bioRxiv. 2021.

  15. Love MI, Huber W, Anders S. Moderated estimation of fold change and dispersion for RNA-seq data with DESeq2. Genome Biol. 2014; 15:550.

    Article  Google Scholar

  16. Qiu X, Hill A, Packer J, Lin D, Ma Y-A, Trapnell C. Single-cell mRNA quantification and differential analysis with Census. Nat Methods. 2017; 14(3):309–15.

    Article  CAS  Google Scholar

  17. Hafemeister C, Satija R. Normalization and variance stabilization of single-cell RNA-seq data using regularized negative binomial regression. Genome Biol. 2019; 20(1):1–15.

    Article  Google Scholar

  18. Ardlie KG, Deluca DS, Segrè AV, Sullivan TJ, Young TR, Gelfand ET, Trowbridge CA, Maller JB, Tukiainen T, et al. The Genotype-Tissue Expression (GTEx) pilot analysis: multitissue gene regulation in humans. Science. 2015; 348(6235):648–60.

    Article  Google Scholar

  19. Andersson R, Gebhard C, Miguel-Escalada I, Hoof I, Bornholdt J, Boyd M, Chen Y, Zhao X, Schmidl C, Suzuki T, Ntini E, Arner E, Valen E, Li K, Schwarzfischer L, Glatz D, Raithel J, Lilje B, Rapin N, Bagger FO, Jørgensen M, Andersen PR, Bertin N, Rackham O, Burroughs AM, Baillie JK, Ishizu Y, Shimizu Y, Furuhata E, Maeda S, Negishi Y, Mungall CJ, Meehan TF, Lassmann T, Itoh M, Kawaji H, Kondo N, Kawai J, Lennartsson A, Daub CO, Heutink P, Hume DA, Jensen TH, Suzuki H, Hayashizaki Y, Müller F, Forrest ARR, Carninci P, Rehli M, Sandelin A. An atlas of active enhancers across human cell types and tissues. Nature. 2014; 507(7493):455–61.

    Article  CAS  Google Scholar

  20. Zamanighomi M, Jain SS, Ito T, Pal D, Daley TP, Sellers WR. GEMINI: a variational Bayesian approach to identify genetic interactions from combinatorial CRISPR screens. Genome Biol. 2019; 20(1):1–10.

    Article  Google Scholar

  21. Norman TM, Horlbeck MA, Replogle JM, Alex YG, Xu A, Jost M, Gilbert LA, Weissman JS. Exploring genetic interaction manifolds constructed from rich single-cell phenotypes. Science. 2019; 365(6455):786–93.

    Article  CAS  Google Scholar

  22. Zhang L, Janson L. Floodgate : inference for model-free variable importance. arXiv. 2020:1–67.

  23. Przybyla L, Gilbert LA. A new era in functional genomics screens. Nat Rev Genet. 2021:1–15.

  24. Datlinger P, Rendeiro AF, Boenke T, Senekowitsch M, Krausgruber T, Barreca D, Bock C. Ultra-high-throughput single-cell rna sequencing and perturbation screening with combinatorial fluidic indexing. Nat Methods. 2021; 18(6):635–42.

    Article  CAS  Google Scholar

  25. Pierce SE, Granja JM, Greenleaf WJ. High-throughput single-cell chromatin accessibility CRISPR screens enable unbiased identification of regulatory networks in cancer. Nat Commun. 2021;12(2969).

  26. Liu M, Katsevich E, Janson L, Ramdas A. Fast and Powerful Conditional Randomization Testing via Distillation. Biometrika. 2021;:asab039.

  27. Finner H, Roters M. On the false discovery rate and expected type I errors. Biom J. 2001; 43(8):985–1005.

    Article  Google Scholar

  28. Towns J, Cockerill T, Dahan M, Foster I, Gaither K, Grimshaw A, Hazlewood V, Lathrop S, Lifka D, Peterson GD, Roskies R, Scott J, Wilkins-Diehr N. XSEDE: accelerating scientific discovery. Comput Sci Eng. 2014; 16(05):62–74.

    Article  Google Scholar

  29. Nystrom NA, Levine MJ, Roskies RZ, Scott JR. Bridges: a uniquely flexible HPC resource for new communities and data analytics. New York: ACM; 2015. pp. 1–8.

  30. Dunham I, Kundaje A, Aldred SF, Collins PJ, Davis CA, Doyle F, Epstein CB, Frietze S, Harrow J, Kaul R, Khatun J, et al. An integrated encyclopedia of DNA elements in the human genome. Nature. 2012; 489(7414):57–74.

    Article  CAS  Google Scholar

  31. Rao SSP, Huntley MH, Durand NC, Stamenova EK, Bochkov ID, Robinson JT, Sanborn AL, Machol I, Omer AD, Lander ES, Aiden EL. A 3D map of the human genome at kilobase resolution reveals principles of chromatin looping. Cell. 2014; 159(7):1665–80.

    Article  CAS  Google Scholar

  32. Fishilevich S, Nudel R, Rappaport N, Hadar R, Plaschkes I, Iny Stein T, Rosen N, Kohn A, Twik M, Safran M, Lancet D, Cohen D. GeneHancer: genome-wide integration of enhancers and target genes in GeneCards. Database: J Biol Databases Curation. 2017; 2017:1–17.

    Article  Google Scholar

  33. Barry T, Wang X, Morris JA, Roeder K, Katsevich E. Sceptre improves calibration and sensitivity in single-cell crispr screen analysis. Github. 2021.

Download references

We are indebted to Molly Gasperini, Jacob Tome, and Andrew Hill for clarifying several aspects of their data analysis [9] and to the Shendure lab for providing extensive feedback on an earlier draft of this paper. We thank Shiqi Xie for providing guidance on using the Xie et al. 2019 data and Wei Li for a helpful discussion on scMAGeCK. Finally, we thank Tom Norman, Atray Dixit, and Wesley Tansey for useful discussions on single-cell CRISPR screens. This work was supported, in part, by National Institute of Mental Health (NIMH) grant R01MH123184 as well as SFARI Grant 575547. Part of the data analysis used the Extreme Science and Engineering Discovery Environment (XSEDE) [28], which is supported by National Science Foundation grant number ACI-1548562. Specifically, it used the Bridges system [29], which is supported by NSF award number ACI-1445606, at the Pittsburgh Supercomputing Center (PSC).

Peer review information

Review history

The review history is available as Additional file 2.

Author information

Authors and Affiliations

Authors’ contributions

GK and KR identified the problem, conceived the research, and provided supervision. GK developed the method with input from TB and KR. TB and GK implemented the method with assistance from JM. TB, XW, and GK performed the analyses. JM provided guidance on interpretation and communication of results. TB and GK wrote the manuscript with input from all authors. The authors read and approved the final manuscript.

Authors’ information

Twitter handle: @EugeneKatsevich (Eugene Katsevich)

Corresponding author

Correspondence to Eugene Katsevich.

Ethics declarations

Ethics approval and consent to participate

Ethical approval not applicable.

Competing interests

The authors declare that they have no competing financial interests.

Additional information

Publisher’s Note

Supplementary Information

Additional file 1

Supplementary figures and tables

Additional file 2

Review history

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Barry, T., Wang, X., Morris, J.A. et al. SCEPTRE improves calibration and sensitivity in single-cell CRISPR screen analysis. Genome Biol 22, 344 (2021).

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI:


Organic White Truffle Olive Oil

Size | 1.69 fl oz

Regular Price
Sale Price
Regular Price
Sold Out
Unit Price

Shipping calculated at checkout.
Pour on the luxury with this white truffle olive oil from the truffle experts at Tartuflanghe. It’s made from the ultra-rare white truffles that only grow in the northwestern Piedmont region, also known as the Alba or Piedmont truffle. They are harvested in the late fall months and can only be foraged, never cultivated, making their discovery something of a natural miracle. These precious nuggets are combined with certified organic extra-virgin olive oil to make this fragrant, flavorful finishing oil.

There are three commonly harvested types of truffle, each with its own unique characteristics. Black winter truffles are earthy and pungent, while summer truffles are more delicate, with a sweet, nutty profile. White truffles are prized for their deeply savory flavor, like aged cheese.

The family-run Tartuflanghe has specialized in all things truffle for nearly 50 years. In 1975, chef Beppe Montanaro and his wife, Domenica, founded the company to celebrate their home’s most prized delicacy. (The company’s name is a play on words, combining the Italian for truffle, tartufo, with Langhe, where they are based.) Today, they are the stewards of 50 acres of lush woodland in the Piedmont region. Their truffles are still harvested in the old-fashioned way, with specially trained dogs who sniff out the fragrant delicacies underground. They’re dug and sorted by hand to ensure the highest quality with the least impact on the land. In their state-of-the-art solar-powered facility, Tartuflanghe is constantly innovating new ways to showcase truffles and make their unique flavor accessible to all.
This white truffle olive oil is fragrant, savory, and smooth, with notes of wild herbs. Drizzle it as a finishing touch over hot or cold dishes such as risotto, meat, fish, eggs, pasta, and fresh cheeses. Do not cook, as prolonged heat will degrade the natural truffle essence.
extra virgin olive oil*, white truffle infusion* 17% (extra virgin olive oil*, white truffle (Tuber magnatum Pico)* 1%), freeze-dried white truffle (Tuber magnatum Pico)* 0.35% (like 1.75% of fresh truffle), natural flavor. *Organic
Size: 1.69 fl oz


What sword is used for seppuku?

The most well-known use of the wakizashi is for the purpose of Seppuku, suicide by disembowelment. “Seppuku” or “harakiri” both literally mean “belly cutting”. The blade used for seppuku would usually be a tanto of ko-wakizashi.

Did Masamune make katanas?

1264–1343), was a medieval Japanese blacksmith who is widely recognized as Japan’s greatest swordsmith. He created swords and daggers, known in Japanese as tachi and tantō respectively, in the Sōshū school. For this reason, his only existing works are katana and tantō. No exact dates are known for Masamune’s life.

Has the Honjo Masamune sword been found?

This Japanese Relic Disappeared After WWII and Has Never Been Found. In the late 13th century CE, there was a great swordsmith in Japan, Goro Nyudo Masamune. His swords were considered to be unmatched in quality and even benevolent in nature. The most famous of the swords that he created is known as the Honjo Masamune.

Is Katana the most powerful blade?

The Japanese katana is one of the most well-known and sought-after swords in the world. Here are five reasons why the katana is such a powerful sword. #1) It’s Made of the Highest Quality Steel. The katana is made of the highest quality steel on the planet.

Has anyone survived seppuku?

Having once survived seppuku, Shinsengumi Captain, Harada Sanosuke died on this day, July 6 1868 from gunfire wounds suffered during the Battle of Ueno. Harada Sanosuke was born in in 1840 in Matsuyama, (Ehime Prefecture, pictured) to a low ranking samurai serving the retainers of the Tokugawa Matsudaira clan.

What are the 3 samurai swords called?

Kissaki was the Samurai sword point that determined the sword quality. Japanese swords changed over time, but the three main Samurai sword types were: Katana, Wakizashi and Tanto. The most powerful Samurai, Shogun, used the Katana and Wakizashi swords.

Who is the fake Masamune?

Gasou meeting as fake Masamune with Aki In Chapter 18, at night near a park where Aki Adagaki was pondering about Masamune Makabe asking if she remembers about the nickname ‘Piggy’ and Neko Fujinomiya’s words in hospital, she remembers that the last time she had loved a boy named Masamune in childhood thinking that his …

Where is Masamune sword?

After a donor obtained the sword, he gave the national treasure to the Kyoto National Museum where it belongs. Much like the Shimazu sword, the Honjo Masamune may reappear sometime in the future.

Are there any Muramasa blades left?

In spite of these unfortunate incidents, Tokugawa Ieyasu and his generation seemed to greatly appreciate Muramasa weapons. Ieyasu himself owned two swords forged by Muramasa and left them to his family; as of 2013, the Owari-Tokugawa family still holds one of the two as an heirloom.

Are samurai swords illegal?

What was the deadliest sword?

The claymore was a deadly weapon and a devastating tool on the battlefield. With their average length falling to around 130cm, the claymore offered a mid-ranged combat style and the combined length, dual handed wielding, and weight meant that the claymore could easily sever limbs or even decapitate with a single blow.

How big is the blade on a katana?

The Standard Katana blade is approximately 72cm Blade and 27cm Handle, we use our standard size on all custom Katana swords orders unless requested otherwise. if you want to change the size according to your preference, there is additional payment of $90 for custom size and it takes longer to make than usual.

What kind of character is Kuroh Yatogami?

Kuroh is a quiet, serious and proper gentleman who is also a stubborn and hot headed individual who appears tough and completely no-nonsense on the surface. He is very determined to accomplish his goals, whatever they may be, but despite so Kuroh is willing to set them aside for the finer things in life, such as genuine companionship.

What kind of sword does Yato no kami white have?

Yatō-no-Kami – White Night. The blade is now curved to resemble a wide katana blade, the sword now shines with a yellow aura, and the top two slots on the blade are illuminated yellow. It retains the Noble Yato’s cross guard.

What does a Yato do to a katana?

Being a Katana, while equipped, Yato always reduces its wielder’s Defense and Resistance by 1, while increasing their Speed by 1.


When all movement becomes a common decision.
When the mind's precision is translated to the body language.
When the symbiosis between Music and Dance create the total cohesion.

Bólero is a new creation by Miquel G. Font following the visual patron founded with his previous creation, Exode, which was distributed to several dance companies around Europe. With very hypnotical visuals on stage and his specific body language with a high level physical and musical precision, together with the impact of the master piece by Maurice Ravel, Bolero casts all participants of PAR in Dance on stage to run a histaminical march in a constant crescendo.

Choreography by Miquel G. Font
Music: Maurice Ravel
Costume design: Marta Muiños
Make up: Escola Ana Vilamaña
Light design: Miquel G. Font
Dancers: PAR en Dansa 2020/21
Pictures by Josep Guindo
Video Editing: Habemus Corpus - Miquel G. Font
Premiere: October 2020 - Centre Cultural Terrassa


Reasons Why Cultural Foods Are Needed in a Healthy Diet

Healthy eating may be seen as a necessary evil at times.

On the one hand, it’s necessary for optimum health, but it also conjures up images of limitation and self-denial associated with Eurocentrism.

Even in the Caribbean, where I grew up, many nutrition programs are based on the American food pyramid, which then suggests to local populations what good eating looks like.

However, there is no such thing as a one-size-fits-all dietary prescription when it comes to nutrition and good eating. Traditional foods and culinary culture are also deserving of a place at the table.

I’ll explain why cultural foods are important for a healthy diet in this article.

What is meant by cultural foods?

Cultural Food

Traditions, beliefs, and practices of a geographic area, ethnic group, religious organization, or cross-cultural community are represented through cultural cuisine, also known as traditional dishes.

Beliefs regarding how particular meals are cooked or used may be a part of cultural foods. They may also represent the general culture of a group.

These recipes and traditions have been handed down through the generations.

Pizza, pasta, and tomato sauce from Italy, or kimchi, seaweed, and dim sum from Asia, are examples of cultural cuisine that reflect an area.

Alternatively, they may allude to colonial histories, such as the Caribbean’s mix of West African and East Indian culinary traditions.

Cultural cuisines are frequently at the heart of our identities and family relationships, and they may play a role in religious festivals.

Cultural foods must be completely incorporated into the Western framework.

Cultural foods are part of a healthy diet, but the message isn’t always clear, and it’s frequently ignored.

Dietary Recommendations for Americans from the United States Department of Agriculture (USDA) is one of the gold standards for nutrition guidelines in the West. Meeting people where they are, including their traditional foodways, is encouraged.

In addition to healthy eating, the Canadian Culinary Guide stresses the significance of culture and food traditions.

However, there is still much work to be done in the area of dietetics to guarantee cultural competency, which is defined as the effective and appropriate treatment of individuals without bias, prejudice, or preconceptions.

Cultural requirements and dietary habits were recognized throughout my dietitian training, but there was little enthusiasm or practical implementation. In other cases, healthcare practitioners have limited access to institutional resources.

What does it mean to eat healthily?

Cultural Food

Healthy eating is informally described as getting a range of nutrients from dairy, protein foods, grains, fruits, and vegetables, or the five food categories as they’re called in the United States.

The primary message is that each food category contains vitamins and minerals that are necessary for optimum health. A healthy plate includes half nonstarchy vegetables, one-quarter protein, and one-quarter grains, according to the USDA’s MyPlate, which replaced the food pyramid.

The Caribbean, on the other hand, is a mash-up of six food groups:

  • Staples (starchy, carb-rich meals).

  • Animal foods.

  • Legumes.

  • Fruits.

  • Vegetables.

  • Fats or oils.

Traditional one-pot meals aren’t always easy to divide out on a platter. Instead, all of the food categories are integrated into one meal.

Breadfruit (the mainstay — a starchy fruit with a texture akin to bread once cooked), nonstarchy vegetables like spinach and carrots, and meats like chicken, fish, or pig are all used in the classic one-pot meal known as oil down.

Healthy eating is a lot more flexible than you would think based on the internet.

Food marketing that is focused and effective is frequently the cause of your urge to consume specific meals. The majority of this marketing is done through a Eurocentric perspective that ignores cultural subtlety.

For example, if you Google “healthy eating,” you’ll get a slew of lists and pictures of asparagus, blueberries, and Atlantic salmon, all of which are often seen in the arms or on the tables of white families.

The absence of ethnically varied images and cultural representation conveys an implicit message that local and traditional cuisine may be harmful.

True healthy eating, on the other hand, is a flexible notion that has no defined appearance or ethnicity and does not need the inclusion of particular foods to be counted.

Here are some meals you’ll find on health websites in the West, as well as their traditional counterparts:

  • Callaloo (taro leaves) and spinach, like kale, are healthy vegetables.
  • Quinoa, like rice and beans, is a good source of protein and dietary fiber.
  • Chicken breasts are low in fat and praised as a must-have for a healthy diet, but removing the skin from other sections of the chicken reduces fat content while increasing iron content.
  • Omega-3 fatty acids are abundant in Atlantic salmon, as well as local salmon variants and other fatty fish like sardines.

If kale, quinoa, and Atlantic salmon aren’t accessible in your area, it doesn’t mean your diet is bad.

Contrary to popular belief, a healthy plate does not have to consist of Eurocentric meals, and indigenous cuisine is neither inferior nor nutritionally unsuitable.

Based on food availability, sustainability, and food cultures, healthy eating looks different in various communities and places.

The significance of ethnic cuisines in our daily life

Traditional eating habits and cultural cuisines have a strong link to community and health. They help us connect to our history, promote present-day socializing, and build memories for the future. They also play an important role in dietary success and compliance.

When my mother shows me how to make oil down, a one-pot meal made with breadfruit, taro leaves, pumpkin, coconut milk, and smoked bones, I’m reconnecting with traditional West African culinary customs while also sharing family moments.

Similarly, whenever I make a vegetarian curry meal like dhal (split peas) with turmeric or saffron, I am reminded of East Indian culinary traditions.

These meals may not seem to match the Western idea of nutritious or healthy cuisine to those unfamiliar with them, yet they’re packed with fiber, complex carbohydrates, and veggies.

What role does culture have in what you eat?

Cultural Food

The foods you consume, your religious and spiritual activities, and your outlook on wellness, healing, and healthcare are all influenced by culture.

According to research, your cultural background has a significant impact on your attitudes about particular meals as well as your desire to try new ones. Furthermore, your definition of what constitutes food and what does not is influenced by your society.

As a result, healthy eating must be perceived and understood in a cultural context.

In the United States, for example, supper is likely to be the major meal of the day, whereas lunch is likely to be a light salad or sandwich. In the Caribbean, however, lunch is often the heaviest meal, while supper is typically lighter and resembles breakfast.

We dilute the research and deprive communities of valuable culinary views and experiences when nutrition messaging and advice lack inclusiveness, diversity, and understanding.

Furthermore, a dietitian’s lack of trust and communication with the individuals he or she is serving may lead to health inequalities and poor results.

You’re less likely to follow your dietitian’s advice if you don’t trust them.

So, what’s next?

Even if they aren’t gentrified, promoted on social media, or aligned with the Western worldview, cultural cuisines match the idea of healthy eating.

For many immigrant and non-immigrant families in the United States, these are comfort foods, ways of life, and essential sources of nourishment.

By integrating multiple dietary categories and containing a range of nutrients, these ethnic dishes demonstrate healthy eating:

Ugali is a typical Tanzanian cornmeal dish that is often served with traditional meat and vegetable dishes.

Ema datshi: a spicy stew served with yak cheese and mushrooms, green beans, and potatoes that is popular in Bhutan.

Kalua pork is a classic Hawaiian meal that may be served with grilled fish, eggplant, or taro, among other things.

Schäufele is a roasted pork dish with potato dumplings and sauerkraut or creamed savoy cabbage that is typically served with sauerkraut or creamed savoy cabbage.

Pelau is a Caribbean one-pot meal prepared with caramelized chicken, parboiled rice, pigeon peas, and a variety of vegetables and herbs.

Last but not least

To promote excellent health, healthy eating simply means consuming a variety of nutrient-dense foods.

Healthy eating looks different in various groups and locations, contrary to popular health and wellness messaging. It doesn’t have a distinct appearance or needs the use of certain meals.

Although the American and Canadian dietary food standards promote the inclusion of ethnic foods as part of a balanced diet, nutrition messaging and counseling often lack the competency and inclusiveness necessary to emphasize the significance of cultural foods.


Over 1 in 5 adults is considered inactive across most of the country. This is according to the latest numbers gathered from the Centers for Disease Control and Prevention. Their latest study says that most states are physically inactive, which they define as not participating in any physical activities outside of work over the last month  This could be anything from jogging, to weight lifting, to even mowing the grass, or simple gardening.

So, how do health officials rate the state of New York? According to their findings, we could do a little better. The data says that 25.9% of adults in New York are considered physically inactive. That puts us 18th in the nation as far as inactivity. Mississippi was first (or maybe, last) overall, with 33.2 % of adults considered inactive. The South, as a region, reported the highest level of physical inactivity at 27.5%. Colorado was the most active state, with only 17,7% of adults considered inactive by the CDC's numbers.

We appear to be the least active state among our neighbors. Connecticut reported 22.6% overall, Massachusetts 23.3%, Pennsylvania 24.7%, and Vermont with only 19.6%. According to the CDC, New Jersey wasn't included due to insufficient data.

The findings only measured inactivity over a short period of time. Past surveys have found that while New Yorkers are gaining weight year by year, we still rank as one of the least obese states in the country. Or perhaps, we just aren't quite as fat as some of the other states, where the obesity epidemic as swelled to absolutely alarming proportions?

How about best states to live all together? This could be highly subjective, though according to U.S. News and World Report's rankings of the nation's best states to live in 2021, we were 18th. We're just below our neighbors in New Jersey and Connecticut, who ranked 19th and 20th, respectively. While the Empire State still sits slightly above the middle of the list, many residents continue to leave in droves for warmer climates and less expensive areas to live, according to statistics. According to the estimates from the United States Census Bureau, 126,355 residents left New York between July 2019 and July 2020. It often comes down to; cost of living, poor job growth (especially upstate), taxes, and harsh winters. Now, add the fact that the state was one of the hardest hit areas from COVID in the world, and that's enough to send people packing, according to these estimates.

25 Hudson Valley Locations Featured in Movies

Abandoned Warner Bros. Zoo Discovered by Hikers

Back in the 1970s there was a Warner Bros. zoo and theme park near Greenwood Lake, and its ruins can still be found rotting away in the woods.

KEEP READING: Here are the best places to retire in America

More From WZAD-WCZX The Wolf


The hanged guy tarot was a tarot card that displays that a person was suspended from an income

What’s The Hanged Guy Tarot?

wood with a T-shaped mix. The individual hanging from forest together with his mind downwards views the whole world with an entirely different standpoint. Also, the calm and relaxed expressions on his face show that they have hanged himself voluntarily.

A halo under their mind is expressed as symbolic of understanding, enlightenment, and awareness. Though he’s certain to the tree together with his best feet but their left-foot try bent form the knee and nestled freely behind their best lower body. Their arms make an inverted triangle by twisting all of them and keeping the hands behind their straight back.

The bluish vest worn by him can be considered for facts, whereas his reddish shorts showcase the real human body and passion of individuals. The cards because of the hanged guy is regarded as a card of martyrdom and complete surrender as well as compromise for a significantly better potential future due to the fact people was suspended with time.

Within this article, we are going to discuss the hanged guy which means to understand what you can expect in your life when this cards is chosen.

The Hanged People Tarot Can Tell You A Lot Around Love

What Is The Concept Of Straight Hanged Guy Card?

While checking out tarot in the event the hanged man card was conducted straight, this may be signifies modification, suspension system, give up, reverse, improvement, rebirth, and readjustment. This basically means, this credit means it’s about time for reflection also to acquire lighting before moving on whereas enough time to reject is finished. You could make items proper and move ahead, regardless of what is going on that you experienced.

You are reminded from the hanged people that before going onward you must suspend every little thing or it is carried out by the world. You may not always get such a convenient energy.

This cards proves the old saying hat have you right here will not get there’

But the pauses for this sort may be voluntarily or unwillingly. You might begin sensing that it is time and energy to hold on tight things or incorporate brake system before they escape your own regulation if you believe in intuitions.

However, if you’re uninformed and don’t understand the signs and symptoms of instinct you will then be stopped by the market by putting some obstacles in the form of illnesses, malfunctions and regular impediments. You should be aware of these pauses when you feel some hurdles that you experienced or you should be dropped by the world and you will struggle to dismiss them.

If whenever checking out tarot you’ve got the hanged people card, it indicates that the recreation and jobs is ceased abruptly and all of a sudden. This kind of a condition, you should not pertain added force to force they ahead of time as per your objectives.

In this case, you will want to simply take a pause and surrender with the scenario and take it as a chance to re-evaluate and reconsider the path you used to be progressing. You will not be able to see just what could happen along with you unless you let them incorporate energy.

This way, you will be welcomed of the hanged man to start the arms to allowed these pauses and surrender to them even in the event these are typically against your own objectives. You should link yourself by using these brand-new viewpoints by steering clear of their program working arrangements.

Though while doing so, it’ll be most inconvenient so that you can put your important activities on hold nonetheless it is worthwhile for you personally. This is the way of the world that will help you in observing the newest opinions and causing you to prepared your advancements that will take place in yourself into the upcoming time.

You’ll have to deal with other hurdles within way should you decide withstand or press the impediments you’re facing. Therefore, you need to prevent your time and efforts and allow the chances to get to you in an exceedingly effortless and smooth manner.

Sometimes, the hanged man also represents the constraints or jams you’re feeling in your lifetime. You could be thinking about the issues that is holding your up such a posture or not allowing you to move forward. On one side, the Hanged guy was promoting you to allowed affairs embark on their and surrender rather than resisting them or invest more inside project to obtain the desired outcomes.

Deja una respuesta


What You Should Do When He Pulls Away and Comes Back – 7 Pros Expose How To Carry Out This Example

“A active, radiant, goal-oriented woman is so far more attractive than a woman whom waits around for one to confirm the girl life.”

Enjoying some body try a danger.

You exposure your own center and put your rely upon another. The dating world is full of getting yourself online until you ultimately come across people that is worth your fancy and trust. Really sometimes a journey to reach that host to devotion. A journey filled up with lumps and changes. Often the bump are a feeling of him taking aside and then realize that he comes home to you.

Becoming in the receiving end of someone taking aside leaves us experience insecure and causes us to lose believe.

Perhaps he’s started busy with perform, perhaps he doesn’t return calls or texts as fast as he used to. We convince one slow facts lower and tell your self that it could become normal for 1 partner to make time to plan through his or her feelings to become confident that he desires move ahead into the connection.

If their taking out has actually left your questioning your personal attitude, it’s vital that you correspond with your partner how you are sense.

Sit back along and determine the “why”. If their factors include powerful while discover your believe him, however inspire one to commit to openly communicating your emotions with honesty because to maneuver forth with each other.

But, what if their thinking for pulling out nevertheless leaves your mislead and experience insecure? Take a moment to evaluate how you feel. Could you be delighted that he is additional present in yourself? Does he possess traits you are searching for in a permanent mate? Would you nevertheless believe him?

If you learn that you are answering “no” to those along with other concerns, then it’s time and energy to let your go.

You might be a delightful woman which deserves to be with a man just who respects both you and fulfills your specific requires. Allow your self time and energy to grieve this union and progress to bigger and much better activities.

When every day life is on overload, issues where you work mounting up, life’s changes happening, pulling away from a relationship is likely to be an all-natural reaction to not knowing how to manage pressure and tension. Your beloved may need area through the distraction of a relationship, so she or he might come back to they with attitude and quality.

Keeping away from getting someone’s distance also actually will also help not purchasing into a single facts of exactly why this is certainly happening.

Consequently, it gives some perspective into precisely what the different try sense and convinced. Introspectively, it permits us to explore something occurring for the reason that person’s lifetime that’s causing this attitude.

It also allows us to be mindful in how these behaviors are affecting us and how to respond to it. Exercising good self-awareness into your own needs will help you understand the needs of others and how we meet them both.

Once enthusiast returns, invite him/her into dialogue with you that feels not harmful to both of you to understand more about with each other.

Establishing the level through depersonalization on the scenario, mindfulness, and self-awareness can produce a safe planet to understand more about exactly what that event is like for your relative and also for you too.

Whenever a past admiration methods back into our lives the typically since there is some aspect of the commitment that stays unresolved.

Before speaking about what to do, first review as to how the partnership initially concluded.

  • Was it a lighthearted, relaxed relationship that just fizzled?
  • divorce dating websites

  • Was it acquiring big and each other ghosted on?
  • Got the partnership big with regards to concluded, if yes, what triggered the partnership to get rid of? Infidelity on either of areas?
  • Did it just see difficult plus one or you both chose to stop?
  • Or happened to be you merely maybe not a fit for just one another?

Deja una respuesta


How to communicate with family and loved ones throughout the holiday season

According to a study by Virginia Tech, effective communication is an important characteristic of strong, healthy families. Press here to listen to a podcast by speech instructor, Kimberly Stankovich, and discover the greatest gift you can give to someone during the holiday season.

Worrying about a holiday visit is sometimes the state of mind that describes those who are forced to be with extended relatives once a year.

Here is a Q & A to help cope with the relational struggles, utilizing suggested interpersonal communication skills taught by speech instructor Kimberly Stankovich at Saddleback College.

What are some tools that can be used to effectively communicate with others throughout the holidays?

“The skills used to communicate with loved ones should be practiced on a daily basis. However, the people or in-laws that are seen once a year can possibly be tolerated during one turkey meal,” said Stankovich. “It’s a matter of making a choice and realizing that emotions and feelings are stronger during this time.”

“Knowing how to use “assertion” is valuable in communication and is a learned skill that takes some time to get right and one way is to exchange the word “but” for the word “and” in a sentence,”  Stankovich said.

Instead, Stankovich suggests that for instance, one could say, ‘ I want to go to Aunt Hilda’s and I want to study for finals,’ rather than, ‘I want to go to Aunt Hilda’s, but I have finals.’

“It’s [a formulated sentence that] creates equal feelings between two people,” Stankovich said. “My want and your want are on the same plain.”

Also using “I” statements rather than “you” statements can deviate from making the other person feel judged. For example, I feel embarrassed when you call me “chubby” because I want to feel loved by my family and it makes me feel inferior.

“You are in control of how you feel and by using ‘I’ statements you are taking ownership of your own feelings and wants by handling it in an assertive way,” Stankovich said.

“Something to keep in mind, is each person is in control of their own emotions and no one can make someone feel or respond in a certain way because it’s each person’s own choice,” Stankovich said.

What is one way to avoid being hurt or angry when someone tends to give you a “wintery” cold shoulder?

Stankovich feels it’s important not to assume the other person is having issues about you. It helps you to slow down and not jump to conclusions. Suspending judgement is something you should keep in mind and try implementing the skill of “Perspective Checking.”

“There are three basic steps to perspective checking,” Srankovich said. “The first step is to describe the behavior of the action or words said by the other person. The second step is to offer two possible and different interpretations of the behavior and third is to request feedback from the person.”

For example if you text someone and this person doesn’t text back right away, you may start thinking the person is upset or not caring. So instead of allowing your mind to come-up with a thousand reasons of misinformation, try using these steps to get your answer and avoid or reduce unnecessary conflict. Remember your “I” statements in the process.

“I sent you two text messages and I didn’t hear back from you as quickly as I usually do. I’m wondering if I did something to upset you or you are just busy with finals. What’s going on?”

Then wait for the response and remember to accept his or her answer and leave it at that. It helps the relationship to not judge the person and this helps the person process what you want or need. The person may not be ready to give a valid answer at that exact moment, but perhaps later when he or she is ready and is more likely to remember that you are a safe person to go to. This skill is known for its relationship-building qualities.

What is the greatest gift you can give someone this holiday season?

“The greatest gift one can give to someone during the holiday season is just be quiet and listen,” Stankovich said.

This is her most favorite skill because people in general are usually rushed and take over a conversation. Being mindful to just sit and listen to someone can be an act of kindness during the holiday season. If you try this, remember to act interested, point out certain words to keep the person’s trust open and repeat part of their sentence. Continue to remain quiet without adding your input or judgement unless they ask for your advice. Respect their request, even if they start to judge you. Remember you will have your chance at another time. This is a gift to them.

“If you can learn to become a more effective listener, I think it’s the one skill that will get you through life,” Stankovich said. “If you have a strained relationship and there is one thing you can change, it would be to listen and everything will start to fall into place.”

If you can say to the person “How was your day?” And the person says “tough” then instead of interjecting and telling them about your day, stop and reply with “tough?” and simply be quiet and listen. And if they criticize you then just say “What else?” Humans like to vent and it may have nothing to do with you,  although sometimes they may take it out on you, but continue to say “what else?” This is the best gift you can give to someone you care about.

What if I try these tools, but I can’t seem to get past the hurt?

Keep in mind that these are skills that are taught out of a textbook for those taking class, Speech 5. These skills take practice and the intentions are meant to be helpful.

“There are some folks out there that probably need professional help or medication and that’s OK,” Stankovich said. “There are some concerns and life issues that go way beyond the scope of an introductory human level communications course and we are just scratching the surface.”


Hypothesis Testing: Upper, Lower, and Two Tailed Tests

Hypothesis testing is a statistical procedure that helps to evaluate the two mutually exclusive statements about the population. It helps to know which of the statement is best according to the sample data. Test of hypothesis is based on the information and investigator belief about the parameters of population. The testing process involves two competing hypothesis, first one is null hypothesis and the second one is alternative hypothesis.

In the testing procedure critical values indicates the acceptance and rejection region to make the decisions. For convenience, you can give an account to the critical values calculator that allows you to determine the critical values of any tail.

Procedure of Hypothesis:

The procedure of hypothesis testing is based on the ideas; firstly, we need to state the hypothesis as null or alternative. Select the random samples on the base of population of interest and summary statistics. After that we can determine whether the sample data is supportive for null or alternative hypothesis or not. The procedure of testing is summarized into simple steps and they’re:

Step # 1: Defining the Hypothesis:

In the first step of statistical hypothesis testing, setup the hypothesis and choose the significance level Alpha, which is denoted by α. The significance level is an important factor in statistical hypothesis test. If you know the level of confidence, then simply give a try to the left and right critical value calculator to calculate the critical values of different distributions.

Step # 2: Test Selection:

Selecting the appropriate test statistic for the distribution is very important step of testing. The test statistic is said to be a single number, which is used to summarize the sampling information.  Z-statistic is the example of the test statistic, it is calculated by using the standard formula of z-test:

If the size of the sample is small, in this situation we use t-statistic. In statistical testing, critical value is point on the distribution, which is compared with the test statistic to check whether the null hypothesis is accepted or rejected. By using the t & z critical value table, you can find the critical values of the distribution. For ease, you can also use the critical value calculator to the critical value of the t, z, f, and chi-square distribution.

Step # 3: Making Decisions:

Make a decision for your hypothesis. The decision rule is type of statement that specifies factors that helps to reject the null hypothesis. The decision rule is based on specific values of test statistic. The decision for a particular test depends on three factors and they’re: alternative hypothesis, test statistic, and level of significance.

Hypothesis testing is an important for any business to make the decision. A critical value plays a vital role business that specifies the acceptance and rejection region. Give an account to the left and right critical value calculator that calculates the critical values with its left and right tail.

Step # 4: Computing Results:

It is important to calculate the test statistic and it is considered as the random variable that is calculated from the sample data. It can be used to specify whether to support the null hypothesis or not.

Step # 5: Conclusion:

The last step of the test is making the conclusion about the hypothesis. The final decision is made by comparing the test statistic with the decision rule. In the final conclusion, the null hypothesis is rejected or accepted. The hypothesis is rejected if the hypothesis is true and the hypothesis is accepted when the sample data is not very unlikely.

The null hypothesis is represented by H0 and alternative hypothesis is represented by HA. Critical values in statistical test are considered as a main factor and it helps to check the validity of the hypothesis. There values are complex to calculate. So, use the critical value formula or critical value calculator that evaluates the critical values of one and two tailed test.

Ending Words:

A hypothesis is said to be the rule that helps to specifies whether the claim about the population is accepted or rejected. It depends on the evidence generated by the sample data. The test examines the opposing hypothesis, the first one is null hypothesis and the second one is alternative hypothesis. This might be difficult to calculate but using an online critical value calculator make easier to calculate the critical values of the distributions.