How to Calculate Effect Size for

Dissertation Students & Researchers

Effect Size Calculation Basics

In general, you need to know the effect size you hope to achieve to calculate statistical power. Effect size can be measured as the standardized difference between two means, or as the correlation between the independent variable classification and the individual scores on the dependent variable, referred to as the effect size correlation. Effect sizes are generally defined as small (d = .2), medium (d = .5), and large (d = .8).
 

Cohen's d

Cohen defined d as the difference between the means, M1 - M2, divided by the standard deviation of either group. For example, the groups in your study could refer to the experimental and control groups. The standard deviation of either group in your study can be used when the variances of the two groups are homogeneous. If you need help determining if the variances of the groups in your study are homogenous you can request help with calculating effect size. Cohen's d can be computed using these two standard deviations. Calculate Your Effect Size Today

Sample Effect Size Calculation

Several formulas could be used to calculate effect size. The magnitude of d, according to Cohen, is d = M₁ - M₂ / Ö [( s₁² + s ₂²) / 2]. d = M₁ - M₂ / s where s = Ö [å (X - M)² / N]. In this case X is the raw score, M is the mean, and N is the number of cases. These are basic formulas. If it is unclear or if you have more than two groups in your study, we can help you figure out the effect size for your study. In addition, the calculation of effect size depends on the statistical test you plan to use. Effect size calculation varies depending on whether you plan to use ANOVA, t test, regression or correlation. Cohen’s effect size measures are well known in research and can be classified as small, medium or large.
 

ANOVA Effect Size
 

ANOVA can help you assess the null hypothesis that all means in your design or groups are equivalent. For ANOVA, the effect size index f is used. You can compute the effect size index from the group means. While there is a formula for this calculation, it is somewhat complicated so we do not present that information here. Suppose you want to compare 10 groups and you want to achieve a medium effect size (f = .25).), alpha of .05. and power of .95? You can use this information to calculate the critical F-value and total sample size needed. Using this information you would need a total sample size of 390.

If this is unclear or difficult to understand, let us help you determine the effect size of your study, using this specific statistical test.
 

T-test for Means Effect Size
 

T-tests are used to compare independent sample means. The null hypothesis in this case assumes that the two groups are equal. Calculating the effect size can help you determine the total sample size do you need to achieve a t statistic equal to or larger than a critical value. For this test, the effect size symbol is d.
For example if you know that there are 70 people in each of your groups and that you want to achieve a d of .50 (medium effect size), you can use this information to calculate the critical t-value and statistical power.

If this is unclear, let us help you determine the effect size of your study, using this specific statistical test.
 

T-test for Correlations Effect Size
 

T-tests are used to evaluate the null hypothesis that a product moment correlation in the population is zero (r = 0). For this test, the effect size symbol is r. If you know your desired effect size you can calculate statistical power and needed sample size. For example, if you want to know how many participants you need in your study for a medium effect size (r = .30) with an alpha of .05. and power of .95, you can use this information to find your answer. Using this information you could determine that you need 111 participants in your study and the critical t-value.

If this is unclear, let us help you determine the effect size of your study, using this specific statistical test.

Chi-Square Test Effect Size

Whether you are using the goodness of fit test or contingency test, calculating effect size is important. For this test, the effect size symbol is w. In either case, you may be comparing 2 distributions over a certain number of categories. Once you know your effect size, you can use this information to calculate the number of people needed and the critical chi-square value. If you want to know how many participants you need in your study for a small effect size (w = .10) with an alpha of .05 and power of .95, you can use this information to find your answer. Using this information you would need 2184 participants in your study.

		symbol		small	medium	large
	Chi-Square Test		w	0.10	0.30	0.50

If this is unclear, let us help you determine the effect size of your study, using this specific statistical test.

Regression Effect Size

For this test, the effect size symbol f² is used. Effect size for regression reflects the f variance accounted for by some source in the population (PVs) relative to the residual variance proportion (PVe). Here f² = PVs/PVe

symbol

small

medium

large

F-Test (MCR)

f2

0.02

0.15

0.35

If this is unclear, let us help you determine the effect size of your study, using this specific statistical test. As we’ve demonstrated, effect size is a critical component in any power analysis or sample size calculation.