Question

A therapist is trying a new program to help reduce smoking among a group of patients. She measures the number of cigarettes smoked per day by each person both before and after participating in the program. For her 6 participants, she gets measures of 19, 14, 12, 17, 20, and 16 cigarettes per day before the program. In the same order, she records 17, 15, 6, 14, 15, and 11 cigarettes per day afterwards.

a. What is the estimated standard error?

b. What is the value for our t statistic?

c. Assuming we found a significant effect, what is the effect size as quantified with Cohen's d?

Answer 1

The estimated standard error for the paired samples t-test is approximately 2.24. The value for the t statistic is approximately 1.34. The effect size, quantified with Cohen's d, is approximately 0.93.

Step-by-step explanation:

This question is related to a paired samples t-test, which is used to compare means from two samples that are related. In this case, the therapist is measuring the number of cigarettes smoked per day by each person before and after participating in the program. The estimated standard error is calculated by dividing the standard deviation of the sample differences by the square root of the sample size. For this set of data, the estimated standard error is approximately 2.24.

The t statistic is calculated by dividing the mean difference by the estimated standard error. In this case, the mean difference is 3 cigarettes per day and the estimated standard error is 2.24. Therefore, the t statistic is approximately 1.34.

Cohen's d is a measure of effect size and is calculated by dividing the mean difference by the standard deviation of the sample differences. In this case, the mean difference is 3 cigarettes per day and the standard deviation of the sample differences is approximately 3.22. Therefore, the effect size, quantified with Cohen's d, is approximately 0.93.