Consider a study in which the population variance estimate based on treatment group of 14 participants is 8, and the population variance estimate based on a control group of 17 individuals is 9. Compute the pooled estimate of population variance.
To compute the pooled estimate of population variance, you need to combine the variance estimates from the treatment and control groups. The pooled estimate takes into account the sample sizes of each group.
The formula for the pooled estimate of variance is:
Sp² = ((n1-1) * s1² + (n2-1) * s2²) / (n1 + n2 - 2)
Where:
- Sp²: Pooled estimate of population variance
- n1: Sample size of the treatment group
- s1²: Variance estimate of the treatment group
- n2: Sample size of the control group
- s2²: Variance estimate of the control group
In your example:
- n1 (treatment group) = 14
- s1² (treatment group variance estimate) = 8
- n2 (control group) = 17
- s2² (control group variance estimate) = 9
Now, let's plug these values into the formula:
Sp² = ((14-1) * 8 + (17-1) * 9) / (14 + 17 - 2)
= (13 * 8 + 16 * 9) / 29
= (104 + 144) / 29
= 248 / 29
Therefore, the pooled estimate of population variance is approximately 8.551.
Note: The pooled estimate of population variance is commonly used in statistical tests and analysis, such as the t-test, to evaluate the significance of differences between groups.