1. Learn
    2. /
  2. Courses
    3. /
  3. Inferential Statistics

Exercise

Comparing two means (2)

In the previous exercise we used the primary formula to calculate the standard error when comparing two means. There is however an alternative approach to calculating the standard error when we can assume that the variability across both groups is the same. This is called the pooled standard deviation from which we can then calculate the standard error.

The formula for the pooled standard deviation is the following:

$$s = \sqrt{\frac{{(n_1 - 1) * s_1^2 + (n_2 - 1) * s_2^2}}{n_1 + n_2 - 2}}$$

From this formula, we can then calculate the standard error using the following formula:

$$se = s * \sqrt{\frac{1}{n_1} + \frac{1}{n_2}}$$

Instructions

100 XP
  • Consider our previous example with the average number of hours that people do sport. This time we assume that the standard deviation for males and females is equal. The standard deviation for both groups now is 2.8. Calculate the pooled standard deviation and put it in a variable called pooled. The sample sizes were respectively 100 and 150
  • Calculate the standard error and put it in a variable called se