<p>Although you have two times of testing, you really just have two binary variables and you'd like to know if they are associated, there are no repeated measures here. You'd like to know if the value of one binary variable depends on the value of the other binary variable. I'll call them A,B and X,Y.</p>
<p>If there is no relationship between A,B and X,Y, then you expect the ratio of X:Y to be the same for A as it is for B (this is your null hypothesis). You can examine your data by building a 2x2 contingency table with cells AX, AY, BX, and BY.</p>
<p>You can test the null hypothesis described with a <a href="https://en.wikipedia.org/wiki/Chi-squared_test" rel="nofollow noreferrer">chi-square test for independence</a>, or <a href="https://en.wikipedia.org/wiki/Fisher%27s_exact_test" rel="nofollow noreferrer">Fisher's exact test</a> if the sample size is fairly small.</p>

CC BY-SA 4.0
2021-01-06T21:02:46.080Z
Thank you, Bryan!
Max Moser
CC BY-SA 4.0
2021-01-06T21:17:40.837Z
Out of curiosity, is a 2x3 contingency table similarly possible?
Max Moser
CC BY-SA 4.0
2021-01-06T22:18:17.410Z
@MaxMoser Yes, but the analysis can get more complicated depending on your research question. I would recommend collaborating with a statistician or someone in your field who is comfortable with statistics.
Bryan Krause
CC BY-SA 4.0
2021-01-08T01:36:18.497Z
Do you have other information about the participants as well though? You might want to consider a logistic regression scenario where 'rule use at t1' is just one of the predictors, alongside other relevant things you also know like age
steveLangsford
CC BY-SA 4.0
2021-01-06T19:13:07.927Z
2021-01-06T19:13:07.927Z
Bryan Krause
<p>I am designing a correlational study experiment to test children on their performance on a task at <span class="math-container">$t_1$</span> and then at <span class="math-container">$t_2$</span> a year later, specifically using the balance-scale paradigm (Siegler, 1981). I'm not sure which statistical tests will be appropriate to run.</p>
<p>I want to find out if the early use of a sophisticated decision rule at <span class="math-container">$t_1$</span> is predictive of children using even more sophisticated rules in <span class="math-container">$t_2$</span>. Namely, is a child who can deploy a complex decision rule quicker than most of her peers at <span class="math-container">$t_1$</span> more likely to use even more complex decision rules at <span class="math-container">$t_2$</span>? I will compare these results with the <span class="math-container">$t_1$</span> vs <span class="math-container">$t_2$</span> results of children who failed to deploy that more complicated decision rule at <span class="math-container">$t_1$</span>. These two decision rules will be operationalised as non-continuous binary variables.</p>
<p>What kind of statistical testing would be most appropriate here?</p>
<hr>
<p><strong>References</strong></p>
<p>Siegler, R. S. (1981). Developmental sequences within and between concepts. Monographs of the Society for Research in Child Development, 46(2), 84</p>

<developmental-psychology><statistics>
What's the most appropriate statistical analysis to run for a correlational study?
Max Moser
# What's the most appropriate statistical analysis to run for a correlational study?

(Asked by: username_0 on 2021-01-05)

I am designing a correlational study experiment to test children on their performance on a task at $t\_1$ and then at $t\_2$ a year later, specifically using the balance-scale paradigm (Siegler, 1981). I'm not sure which statistical tests will be appropriate to run.

I want to find out if the early use of a sophisticated decision rule at $t\_1$ is predictive of children using even more sophisticated rules in $t\_2$. Namely, is a child who can deploy a complex decision rule quicker than most of her peers at $t\_1$ more likely to use even more complex decision rules at $t\_2$? I will compare these results with the $t\_1$ vs $t\_2$ results of children who failed to deploy that more complicated decision rule at $t\_1$. These two decision rules will be operationalised as non-continuous binary variables.

What kind of statistical testing would be most appropriate here?

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**References**

Siegler, R. S. (1981). Developmental sequences within and between concepts. Monographs of the Society for Research in Child Development, 46(2), 84

**Tags:** developmental-psychology, statistics


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## 1 answers

### Answer by username_1 on 2021-01-06. Score: 3 | Accepted answer

Although you have two times of testing, you really just have two binary variables and you'd like to know if they are associated, there are no repeated measures here. You'd like to know if the value of one binary variable depends on the value of the other binary variable. I'll call them A,B and X,Y.

If there is no relationship between A,B and X,Y, then you expect the ratio of X:Y to be the same for A as it is for B (this is your null hypothesis). You can examine your data by building a 2x2 contingency table with cells AX, AY, BX, and BY.

You can test the null hypothesis described with a [chi-square test for independence](https://en.wikipedia.org/wiki/Chi-squared_test), or [Fisher's exact test](https://en.wikipedia.org/wiki/Fisher%27s_exact_test) if the sample size is fairly small.

> **Comments:**
> **username_0**: Thank you, Bryan!  
> **username_0**: Out of curiosity, is a 2x3 contingency table similarly possible?  
> **username_1**: @MaxMoser Yes, but the analysis can get more complicated depending on your research question. I would recommend collaborating with a statistician or someone in your field who is comfortable with statistics.  
> **username_2**: Do you have other information about the participants as well though? You might want to consider a logistic regression scenario where 'rule use at t1' is just one of the predictors, alongside other relevant things you also know like age  

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