Sample Size

Sample Size Calculation for Dependent Samples *t-*tests are not as simple as sample size calculation for the independent samples *t*-test. While the sample size requirement is smaller because the two samples are related or correlated, the calculation is somewhat complicated. In order to calculate the minimum sample size for the dependent samples *t*-test being used in your Master’s thesis, Ph.D. thesis, Master’s dissertation, or Ph.D. dissertation, you are going to need some information or have a good idea of values for key pieces of information.

Aligning theoretical framework, gathering articles, synthesizing gaps, articulating a clear methodology and data plan, and writing about the theoretical and practical implications of your research are part of our comprehensive dissertation editing services.

- Bring dissertation editing expertise to chapters 1-5 in timely manner.
- Track all changes, then work with you to bring about scholarly writing.
- Ongoing support to address committee feedback, reducing revisions.

For the purposes of this example, I will refer to a Jacob Cohen book, *Statistical Power Analysis for the Behavioral Sciences.* We are going to define power analysis for the dependent samples *t-*test as the sample size necessary to…

- Achieve a Power of 0.80
- Detect a reasonable difference between the groups with a medium effect size of 0.50
- Detect a significant difference between the groups at a 0.05 level of significance

Important to understand is that each of the four items mentioned (Sample Size, Power, Effect Size, and Level of Significance) are a function on one another, meaning that changing any one of these things is going to change the value of the other three. So we have determined values for Power (0.80), Effect Size (0.50), and Level of Significance (0.05), and we are trying to figure out how many people we need to actually achieve all of these values. Get help with your thesis power analysis or dissertation power analysis by scheduling a free 30 minute consultation using the calendar on this page.

Before, we found the sample size for an independent samples *t-*test by looking at a simple table. This time, the groups are related and we need to take that into account in our sample size calculation. Before we continue, however, I would like to tell you the good news… The sample size requirements for the independent samples *t-*test are much larger than that of the dependent samples *t-*test. If you have calculated the independent samples *t-*test sample size and power analysis for your dissertation or thesis, can obtain that many pairs of participants, and are not under a lot of pressure from your college or university to justify the sample size, then…

Since we have established that we are conducting a dependent samples *t-*test, and are assuming the scores for the pairs are related or correlated, we need to know the degree to which they are correlated. Since this is an a priori power analysis for a dissertation or thesis, we could not possibly know the exact correlation between pairs in the sample we are going to obtain and must estimate the degree to which these pairs are going to be correlated.

If this is a dissertation or thesis following other research designs and there is empirical research information available, then look for a correlation coefficient from some of these other studies. For instance, if four of the studies you have read found a strong correlation (0.90) between childhood obesity prior to dieting and after dieting, then we can assume that we are going to find the same thing in our study. We would assume that the correlation would be 0.90. Get help with your thesis power analysis or dissertation power analysis by scheduling a free 30 minute consultation using the calendar on this page.

Here it is in all of its mathematical glory…

n= n_(.10)/(100d^(2 ) )+ 1

<!–>**n= ****n**.10100**d****2 **+ 1<!–>

where, **n _{.10}** = 1571 and is the necessary sample size for the given

d= d_(4^’ )/√(1-r)

where

= the medium effect size of 0.50 and

*r *= 0.40

is the estimation of the correlation within the pairs.

This yields **d = **0.645 = 0.05/√ (1 – 0.40).

**OR**

Just tell them you need 39 pairs of participants or scores. Better yet, get professional help with your thesis or dissertation power analysis by scheduling a free 30 minute consultation using the calendar on this page. Let us give you a customized power analysis for your Master’s thesis, Ph.D. thesis, Master’s dissertation, or Ph.D. dissertation.

We work with graduate students every day and know what it takes to get your research approved.

- Address committee feedback
- Roadmap to completion
- Understand your needs and timeframe