Question

a researcher wants to investigate whether there is a difference in the aerobic capacity between two different exercise programs. group 1 participates in a running program, and group 2 participates in a cycling program. after 8 weeks, the aerobic capacity is measured for both groups. below are the sample data:
group 1 (running program): sample size ($n_1$) = 3, sample mean ($overline{x}_1$) = 40, sample variance ($s_1^2$) = 4
group 2 (cycling program): sample size ($n_2$) = 4, sample mean ($overline{x}_2$) = 45, sample variance ($s_2^2$) = 9.
question 3:
what is the effect size d?
1.89
-1.89
0.71
-0.71

Explanation:

Step1: Calculate the pooled standard deviation

The formula for the pooled standard deviation \(s_p\) is \(s_p=\sqrt{\frac{(n_1 - 1)s_1^2+(n_2 - 1)s_2^2}{n_1 + n_2-2}}\)
Substitute \(n_1 = 3\), \(s_1^2=4\), \(n_2 = 4\), \(s_2^2 = 9\) into the formula:

$$
LATEXBLOCK0
$$

Step2: Calculate the effect size \(d\)

The formula for the effect size \(d\) (Cohen's \(d\)) for two - independent - samples is \(d=\frac{\bar{X}_1-\bar{X}_2}{s_p}\)
Substitute \(\bar{X}_1 = 40\), \(\bar{X}_2 = 45\), \(s_p\approx2.6458\) into the formula:

$$ d=\frac{40 - 45}{2.6458}=\frac{- 5}{2.6458}\approx - 1.89 $$

Answer:

-1.89