# Sample Size Justification

Posted December 7, 2012

Students typically struggle with sample size justification, in part because there are 2 types.  One type is based on the population and the second based on a power analysis.  Sample size based on a population is generally not used in dissertations.  It not used in dissertations because the requirement would too exhaustive to stratify the population in terms of geography and the size requirement would be too great.
The sample size based on a power analysis is used in dissertation and is a required section in your method chapter (and is needed for IRB or URR).  A power analysis essentially says that the researcher has a 80% chance of finding differences or relationships among the variables if they actually do exist.  Sample size based on a power analysis uses the type of statistical analysis you are using such as an ANCOVA, multiple regression, Pearson correlation, etc), the alpha (typically .05), and a small, medium or large effect size.  Effect size has both theoretical and practical considerations.  At a theoretical level, the researcher needs to review other studies that examined the same type of constructs or the same instruments, then see what effect size was found.  If the effect size is not presented, it can be calculated from the means and standard deviations, one-way ANOVAs, frequency counts, correlations, mean gain scores, unstandardized regression coefficients, full sample standard deviations, chi-squares, phi-coefficients, cell frequencies, t-tests, or proportions.  The practical aspect of justifying the sample size is money and time needed to collect data.  For example, if you’re running a multiple regression with 3 predictor variables AND the effect size is small, you’ll need an N=547!   This is in comparison to a regression at a medium effect size with a desired N=76 or a large effect size with an N=34.   Sample size can be calculated by using a free G*Power analysis program or you can purchase a sample size write-up with references from our website by signing on for our Basic Membership for \$29.00.

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