7.1.6 - Paired Hotelling's T-Square
7.1.6 - Paired Hotelling's T-SquarePaired Samples occur in a number of different situations. For example:
- Pairs of similar individuals are selected from a population. These are selected in such a way that the two members of each pair are more similar to one another than they are to different observations in the dataset. Under this setting, one treatment may be applied to a randomly selected member of each pair, while the other treatment is applied to the remaining member.
- For a single sample of individuals, measurements may be taken both before and after treatment. For example, the mineral content of six bones is measured before and after one year of diet and exercise treatments.
- Cat eye experiment: At the University of Georgia an experiment was conducted to test the effect of a treatment for glaucoma. In this experiment, a treatment for glaucoma is applied to a randomly selected eye of each cat, while the remaining eye received a placebo. Many measurements were taken on each eye including pressure, dilation, etc.
The example that we are going to consider in this lesson involves spouse data. In this case, we have husband and wife pairs.
Example 7-6: Spouse Data
A sample of husband and wife pairs are asked to respond to each of the following questions:
- What is the level of passionate love you feel for your partner?
- What is the level of passionate love your partner feels for you?
- What is the level of companionate love you feel for your partner?
- What is the level of companionate love your partner feels for you?
A total of 30 married couples were questioned. Responses were recorded on a five-point scale. Responses included the following values:
- None at all
- Very little
- Some
- A great deal
- Tremendous amount
We will try to address two separate questions from these data.
- Do the husbands respond to the questions in the same way as their wives?
- Do the husbands and wives accurately perceive the responses of their spouses?
We shall address Question 1 first...