I have completed my data analysis and got "statistically significant results" which is consistent with my hypothesis. However, a student in statistics told me this is a premature conclusion. Why? Is there anything else needed to be included in my report?
Hypothesis testing versus parameter estimation

Typically, hypotheses are framed in a binary way. I'll put directional hypotheses to one side, as they don't change the issue much. It is common, at least in psychology, to talk about hypotheses such as: the difference between group means is or is not zero; the correlation is or is not zero; the regression coefficient is or is not zero; the r-square is or is not zero. In all these cases, there is a null hypothesis of no effect, and an alternative hypothesis of an effect.

This binary thinking is generally not what we are most interested in. Once you think about your research question, you will almost always find that you are actually interested in estimating parameters. You are interested in the actual difference between group means, or the size of the correlation, or the size of the regression coefficient, or the amount of variance explained.

Of course, when we get a sample of data, the sample estimate of a parameter is not the same as the population parameter. So we need a way of quantifying our uncertainty about what the value of the parameter might be. From a frequentist perspective, confidence intervals provide a means of doing, although Bayesian purists might argue that they don't strictly permit the inference you might want to make. From a Bayesian perspective, credible intervals on posterior densities provide a more direct means of quantifying your uncertainty about the value of a population parameter.

Parameters / effect sizes

Moving away from the binary hypothesis testing approach forces you to think in a continuous way. For example, what size difference in group means would be theoretically interesting? How would you map difference between group means onto subjective language or practical implications? Standardised measures of effect along with contextual norms are one way of building a language for quantifying what different parameter values mean. Such measures are often labelled "effect sizes" (e.g., Cohen's d, r, $R^2$, etc.). However, it is perfectly reasonable, and often preferable, to talk about the importance of an effect using unstandardised measures (e.g., the difference in group means on meaningful unstandardised variables such as  income levels, life expectancy, etc.).

There's a huge literature in psychology (and other fields) critiquing a focus on p-values, null hypothesis significance testing, and so on (see this Google Scholar search). This literature often recommends reporting effect sizes with confidence intervals as a resolution (e.g., APA Task force by Wilkinson, 1999). 

Steps for moving away from binary hypothesis testing

If you are thinking about adopting this thinking, I think there are progressively more sophisticated approaches you can take:


Approach 1a. Report the point estimate of your sample effect (e.g., group mean differences) in both raw and standardised terms. When you report your results discuss what such a magnitude would mean for theory and practice. 
Approach 1b. Add to 1a, at least at a very basic level, some sense of the uncertainty around your parameter estimate based on your sample size.
Approach 2. Also report confidence intervals on effect sizes and incorporate this uncertainty into your thinking about the plausible values of the parameter of interest.
Approach 3. Report Bayesian credible intervals, and examine the implications of various assumptions on that credible interval, such as choice of prior, the data generating process implied by your model, and so on.


Among many possible references, you'll see Andrew Gelman talk a lot about these issues on his blog and in his research.

References


Nickerson, R. S. (2000). Null hypothesis significance testing: a review of an old and continuing controversy. Psychological methods, 5(2), 241.
Wilkinson, L. (1999). Statistical methods in psychology journals: guidelines and explanations. American psychologist, 54(8), 594. PDF

