Matched Group Means Test

Matched Group Means Test

Compare sample mean from two groups of matched cases.

Matched cases = pre and post test data on sample people, or data on cases that are not independent of each other.

Example of matched cases:

pre and post weight from a sample of people in an exercise program (pre = before starting program, post = after entering program)

pre and post anxiety of a sample of stats students (pre = first day of class, post = last day of class)

* physician and patient satisfaction with their interaction (not independent)
* husband and wives assessment of hours they both spend doing housework.


For a matched means test, DV = continuous, IV = categorical


The IV in a matched group means test is the matching variable(s) or group variable. There are only two matched groups in this formula.

df = n - 1

t calc = (mean difference - null value)/ (std dev of difference/ sq rt of n)

CI = mean difference +/- two tailed t crit (std dev of difference/ sq rt of n)

See board for t calc and confidence interval formula.

Must compute the difference in scores for each case before computing the mean difference.

Example 1.

I think physician and patients will have different satisfaction with their interaction with each other.

Ho: There is no difference in satisfaction scores between patients and physicians.

H1: There is a difference in satisfaction scores between patients and physicians.

Alpha = .05

See board for mathematical hypotheses and diagram.
Satisfaction Scores 1-5, higher score means more satisfied (Note: this isn't really continuous, but some disciplines cheat like this a lot)

Ph Pt Difference
5 4 1
4 4 0
4 2 2
4 4 0
5 4 1
3 3 0
4 1 3
4 2 2
3 3 0
4 1 3

n =10, mean difference = 1.2, standard deviation of the difference = 1.23

df = 10-1 = 9, t crit = 2.26

see board for t-calculation

t calc = 3.08

Reject null. There is a difference in satisfaction scores between patients and physicians. Physicians are more satisfied with the physician - patient interaction than are patients.

Confidence Interval = 1.2 +/- (2.26*.39) = .32-2.08

We are 95% confident that the difference in satisfaction between physicians and patients is somewhere between .32 and 2.08 (on a 5 point scale).

Reject null, because 0 is not in the interval.

Example 2. In Class Exercise

Below is the data on what husbands and wives reported as the number of times the husband washed the dishes in the last week. We think that husbands overestimate the number of times that they washed the dishes when compared to what wives' report.

Alpha = .10
H W Difference
7 0 7
2 2 0
4 0 4
3 2 1
10 4 6
8 4 4
14 14 0

Mean Difference 3.14
Std Dev of Difference 2.85



Example 3. In Class Exercise

The anxiety level among students who take statistics generally declines by the end of the semester.

Alpha = .05