Question

A researcher working in a Human Resources department was interested in gender and sales figures so he conducted a t-test. The mean for males was 66.25 and the mean for females was 78.24, with both groups having a standard deviation of 7. What is the effect size using Cohen’s d?

Answer 1

M1 = mean of males = 66.25

M2 = mean of females = 78.24

sd1 = standard deviation of males = 7

sd2 = standard deviation of females = 7

sd = pooled standard deviation

Cohen's d = 1.71286

Effect size using Cohen's d = 1.71286

Answer 2

Given:

• Mean for males (${\bar{X}}_1$) = 66.25

• Mean for females (${\bar{X}}_2$) = 78.24

• Standard deviation for both groups ($s_1=s_2$) = 7

Step 1: Compute the Mean Difference

$$\text{Mean Difference}={\bar{X}}_2-{\bar{X}}_1=78.24-66.25=11.99$$

Step 2: Calculate the Pooled Standard Deviation

Since both groups have equal standard deviations ($s_1=s_2=7$):

$$s_{\text{pooled}}=s=7$$

$$s_{\text{pooled}}=\sqrt{\frac{(n_1-1)s_1^2+(n_2-1)s_2^2}{n_1+n_2-2}}$$

Step 3: Compute Cohen’s d

$$d=\frac{\text{Mean Difference}}{s_{\text{pooled}}}=\frac{11.99}{7}\approx 1.71$$

Interpretation of Effect Size:

• Cohen’s d ≈ 1.71

• Large effect (Cohen’s benchmarks: 0.2 = small, 0.5 = medium, 0.8 = large).

• 
  

Answer:

The effect size (Cohen’s d) is 1.71, indicating a large difference in sales figures between genders.

Answer 3

Given:

• Mean for males (${\bar{X}}_1$) = 66.25

• Mean for females (${\bar{X}}_2$) = 78.24

• Standard deviation for both groups ($s_1=s_2$) = 7

Step 1: Compute the Mean Difference

$$\text{Mean Difference}={\bar{X}}_2-{\bar{X}}_1=78.24-66.25=11.99$$

Step 2: Calculate the Pooled Standard Deviation

Since both groups have equal standard deviations ($s_1=s_2=7$):

$$s_{\text{pooled}}=s=7$$

$$s_{\text{pooled}}=\sqrt{\frac{(n_1-1)s_1^2+(n_2-1)s_2^2}{n_1+n_2-2}}$$

Step 3: Compute Cohen’s d

$$d=\frac{\text{Mean Difference}}{s_{\text{pooled}}}=\frac{11.99}{7}\approx 1.71$$

Interpretation of Effect Size:

• Cohen’s d ≈ 1.71

• Large effect (Cohen’s benchmarks: 0.2 = small, 0.5 = medium, 0.8 = large).

• 
  

Answer:

The effect size (Cohen’s d) is 1.71, indicating a large difference in sales figures between genders.