Hearing Aids

Score is a continuous response, List and Subject are discrete factors, so this is a two-way ANOVA problem. More specifically, this is a Randomized Block design with List as the factor and Subject as a blocking variable.

Step 1: Graphs
Graph > Boxplot > with Groups, Graph variable= Score, Categorical variable= Subject

Graph > Boxplot > with Groups, Graph variable= Score, Categorical variable= List

Step 2: Summary Statistics
Stat > Basic Statistics > Display Descriptive Statistics, Variable= Score, By variables= List

List n Mean Std

1 24 32.75 7.41

2 24 29.67 8.06

3 24 25.25 8.32

4 24 25.58 7.78

List	n	Mean	Std
1	24	32.75	7.41
2	24	29.67	8.06
3	24	25.25	8.32
4	24	25.58	7.78

Because Subject is the blocking variable one would normally not include a table of summary statistics.

Step 3: Interaction
Stat > ANOVA > Interactions Plot, Response= Score, Factors= List Subject

There seems to be interaction between Lists and Subjects
A test is not possible because every factor-level combination appears only once (no repeated measures design)

Step 4: Test
Stat > ANOVA > Twoway, Response=Score, Row Factor= Subject, Column factor= List, Graphs > Residual vs. Fits and Normal plot

Test for List:

1) a=0.05
2) H₀: a₁ = .. =a₄=0 (no difference in the mean scores of different lists)
3) H_a: a_i≠0 for some i (some differences in the mean scores of different lists)
4) p-value= 0.000 < a
5) We reject H₀, there are some differences in the mean scores of the lists

Step 5: Multiple Comparison
Stat > ANOVA > Oneway, Response= Score, Factor= Lists, Comparisons > Check Tukey

3 4 2 1

_________

_____

There are some significant differences between list 1 and lists 3 and 4.