Question

. A research team wants to see if youth participation in cultural and sports activities may be related to higher values of self-esteem. A group of 100 youths who do participate in such activities were found to have a mean self-esteem of 53.8 (with a standard deviation of 5.1). For the general population of youths, the mean score on the same self-esteem measure is 50, and the standard deviation is 5.9).

Use this information to calculate and interpret the effect size for the mean difference between participating youths and the general youth population.

Answer 1

Solution

Back-up Theory

Effect size: for two-sample t-test

Cohen's d = mean difference /standard deviation ……………………..........………………………. (1)

= D/s

where

D = (X_1bar – X_2bar)

s = (s₁² + s₂²)/2 is the pooled standard deviation

X_1bar and X_2bar are the two sample means and

s₁² + s₂² are the two sample standard deviations.

Interpretation of Effect Size .......................................................................................................... (2)

It provides a system for telling us precisely how large the effects we see in our data really are.

It measures the sizes of differences.

Magnitude of d     Evaluation     …………………………………………....................……………… (3)

0 < d < 0.2                      Small effect

0.2 < d < 0.8                   Medium effect

d > 0.8                            Large effect

Now to work out the solution,

X1bar	53.8
X2bar	50
s1	5.1
s2	5.9
s12	26.01
s22	34.81
s2	30.41
s	5.5145
D	3.8
d	0.6891

Thus, effect size = 0.69 Answer 1

Interpretation

Vide (2),

Effect size tells us how large or small the observed difference is.

Vide (3),

The observed difference of 3.8 is medium effect. Answer 2

DONE