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.
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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
= M_{1}  M_{2} / Ö [(
s_{1}² +
s _{2}²) / 2]. d =
M_{1}  M_{2}
/ 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 Fvalue and total sample size
needed. Using this information you would need a total sample size of 390.


Index

small 
medium 
large 



FTest (ANOVA) 
f

0.10 
0.25 
0.40 
If this is unclear or difficult to understand,
let us help
you determine the effect size of your study, using this specific statistical
test.
Ttest for Means Effect Size
Ttests 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 tvalue and statistical power.


symbol

small 
medium 
large 



tTest on Means

d 
0.20 
0.50 
0.80 
If this is unclear,
let us help you determine the effect
size of your study, using this specific statistical test.
Ttest for Correlations Effect Size
Ttests 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 tvalue.


symbol 
small 
medium 
large 


tTest
on Correlations 
r 
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.
ChiSquare 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 chisquare 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 

ChiSquare 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 f^{2} 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 f^{2}
= PVs/PVe
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.
