INFERENTIAL STATISTICS FOR DECISION MAKING

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Chapter 12 questions and problems
1. Can the repeated-measures ANOVA technique in can be used to analyze a design with only one independent variable?  Explain your answer in detail.
2. Is Tukey HSD test appropriate for data analyzed with a repeated-measures ANOVA?  Explain your answer in detail.
Data Set 12-1
Subjects X1 X2 X3 
1 0 3 5 8
2 3 4 6 13
 3 7 11 21
3. Calculate SStot using data set 12-1. Show all of your work.
4. Calculate SStreat using data set 12-1. Show all of your work.
5. Developmental psychologists study children at different ages. In this study, the children were tested three times, at ages 5, 6 and 7. At each age, they worked a set of 25 problems. Each problem was a measure of the child’s understanding of the concept of conservation (the concept that quantity remains the same despite changes in shape). The scores below represent percentage correct on the set of 25 problems. Calculate a repeated-measures ANOVA, Tukey HSD tests, and write an interpretation.
Child Data Set
Age
Child 5 6 7
1 4 12 68
2 12 24 80
3 20 16 88
4 20 20 84

Sample Solution

Answer

The answer is a) a nominal scale variable.

Explanation

A nominal scale variable is a type of variable that classifies observations into categories that have no inherent order. The possible responses to the question “How many Blu-ray players made by other manufacturers have you used?” are 0, 1, 2, 3, and so on. These categories have no inherent order, so the variable is nominal.

Nominal Scale Variables

Nominal scale variables are the simplest type of scale. They are used to classify observations into categories that have no inherent order. For example, gender, eye color, and blood type are all nominal scale variables.

Ordinal Scale Variables

Ordinal scale variables are a type of scale that classifies observations into categories that have order. However, the distances between the categories are not meaningful. For example, the categories “good,” “fair,” and “poor” are ordinal scale variables.

Interval Scale Variables

Interval scale variables are a type of scale that classifies observations into categories that have order and the distances between the categories are meaningful. For example, temperature measured in degrees Celsius is an interval scale variable.

Ratio Scale Variables

Ratio scale variables are a type of scale that classifies observations into categories that have order, the distances between the categories are meaningful, and there is a true zero point. For example, length measured in meters is a ratio scale variable.

In the Scenario

The possible responses to the question “How many Blu-ray players made by other manufacturers have you used?” are 0, 1, 2, 3, and so on. These categories have no inherent order, so the variable is nominal. Therefore, the answer is a) a nominal scale variable.

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