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. 

DV = continuous,  IV = categorical*

*Can use a continuous IV but must recode it into categories.  Example,  could use income, but need to recode into a few income categories.

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.

 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.

The anxiety level among students who take SOC 301 generally declines by the end of the semester.

Alpha = .05

Null Hypothesis:  Anxiety scores among students who take SOC 301 do not change or increase across the semester.

Research Hypothesis: Anxiety scores among students who take SOC 301 tend to decline by the end of the semester.

One tailed test, on left (expect negative difference scores)

Average change from post-semester to pre-semester anxiety scores = -4.2, s = 4.80, n = 10

t calc = -2.77, p = .02

Reject null. p is less than alpha.  We would be wrong approximately 2% of the time if we took repeated samples from this population.

Interpretation: Anxiety scores among students who take SOC 301 tend to decline by the end of the semester. ON a scale of 1-10, the average drop  in anxiety is just over 4 points by the end of the semester. 

Take Home 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

Null:  Husbands and wives equally estimate the number of times that husbands wash dishes per week, or husbands underestimate when compared to their wives.   Mean Husbands < or = Mean Wives

Research Hypothesis:  Husbands overestimate the number of times that they washed the dishes when compared to what wives' report. Mean Husbands > Mean Wives

t crit =  +1.44

t calc = (3.14 - 0) / (2.85/sq rt 7) = 3.14 / (2.85/2.65) = 3.14/1.08 = 2.91

Reject null.  T calc is bigger than t crit.

Interpretation: Husbands overestimate the number of times that they washed the dishes when compared to what wives' report.  Husbands estimate that they washed the dishes on average 3.14 more times than wives report that their husbands washed the dishes.