Week 22

Question 1

“Dependent-groups” analysis is another name for within-subjects analysis.

a) true
b) false

Answer 1

a) true

Explanation … “Dependent-groups” analysis is a general name for a situation in which there is some sort of connection between the individuals that appear in the various experimental groups of a study. The connection may be that it is the same individuals appearing over and over in the study or it might be a more general connection (for instance twins or triplets, or individuals from the same family). In any case, the connection between the individuals in the different groups allows a unique matching of their observations across the design and this, in turn, allows us to calculate the subject means that are the basis of a within-subjects approach. Dependent-groups analysis is to be contrasted with “independent-groups” analysis where no matching of observations is possible. For t-tests the same difference was denoted by the names “dependent-samples” t-test (also called “paired-samples” or “matched-pairs” t-tests) and ”independent-samples” t-test.

Question 2

In an ANOVA conducted on some dataset; changing from a between-subjects analysis to a within-subjects analysis will not change the numerator of any F-test conducted.

a) true
b) false

Answer 2

a) true

Explanation … ANOVA always results in one or more F-tests and the numerator (the term in the top) of each F-ratio is always an estimate of the effect of some treatment on the mean. But in going from a between-subjects analysis to a within-subjects analysis the only difference is error handling and since within-group errors appear exclusively in the bottom of any F-ratio the numerator is unchanged. Overall, then, a within-subjects analysis does not seek to change MSTreatment, it works instead to reduce the MSError terms that appear in the bottoms of any F-ratios that will be calculated and, in this way, increase power.

Question 3

The between-subjects SSError in a 1-way within-subjects ANOVA is calculated from the squares of differences between the cell means and the grand mean.

a) true
b) false

Answer 3

b) false

Explanation … The distinctive part of a within-subjects ANOVA is an attempt to quantify and isolate stable differences between individuals. It is these differences that should appear in the between-subjects SSError. The technique ANOVA uses to get at these differences is to form subject means (the mean score for a subject across the whole design) and then to keep track of how they differ from the grand mean. It is these differences, not the differences between cell means and the grand mean, that are squared then summed to form the between-subjects SSError.

Question 4

How many observations are there a 2-way, completely within-subjects ANOVA with n = 5, a = 2, and b = 4?

a) 5
b) 8
c) 10
d) 40

Answer 4

d) 40

Explanation … This is a question about the total number of observations, N, in a design. In a 2  4 design there are 8 cells and, if this is a balanced design (as you should always assume unless told otherwise) there are n = 5 observations in each cell. Thus N = 5  8 = 40 observations. This sort of question – about how many observations there are in total in a design – doesn’t depend on whether or not the design contains between-subjects variables or within-subjects variables.

Question 5

5) How many participants are there in a 2-way, completely within-subjects ANOVA with n = 5, a = 2, and b = 4?
a) 5
b) 8
c) 10
d) 40

Answer 5

a) 5

Explanation … The design in this question is the same as in the previous question, but you are asked about the number of participants in the design rather than the total number of observations. There are still 8 cells, but because this is a completely within-subjects design the same participants occur again and again in every cell. Thus, in this design, the number of participants is equal to n, the number of observations per cell. Since n = 5, there are 5 participants in the design.