Exam 12: Analysis of Variance

Calculate the F ratio on the following sets of scores. Group 1 Group 2 Group 3 5 7 10 3 6 10 3 6 9 2 4 10

Between variability results from the accumulated differences between each sample mean and the total mean.

When doing an ANOVA with one degree of freedom between groups, then

The between SS plus the within SS equals the total SS.

When doing an F ratio on a three-group design, 5 subjects in each group, the within degrees of freedom will equal

A factorial ANOVA must have a minimum of

When doing an F ratio, subtracting the number of groups from the total number of subjects yields the

The greater the value of the MS between groups,

Total variability results from the accumulated differences between each individual score and the total mean.

A significant F ratio can only occur when the between variability is less than the within variability.

The mean square (MS) is always equal to (when based on SS/df)

With a sample mean of 10, the MS must equal 100.

Questions below are based on the following: (This is similar to an item in the text at the back of chapter 12 but WITH A DIFFERENT DATA SET). A researcher is interested in whether a certain amphetamine drug will affect the retention of learned behavior among rats as a function of how much time is allowed to elapse between the training and the retention test. Four groups, ten subjects in each group, were randomly selected from a colony of Sprague-Dawley rats. All the rats were given the same amount of training on a simple maze. Groups A and C were given the amphetamine, whereas Groups B and D were given a placebo. Groups A and B were tested for retention immediately following the training, whereas Groups C and D were tested 4 hours later. The retention measure consisted of a scaled score based on how many correct responses the rats would exhibit while running the maze, the higher the score the higher the retention FACTOR A Amphetamine Group A Placebo Group B 15 13 9 9 9 12 Immediate 11 7 Test 10 7 6 8 10 10 12 9 14 5 7 11 FACTOR B Group C Group D 1 8 5 6 Delayed 2 9 Test 4 4 5 4 6 5 5 6 2 6 6 6 1 7 -Calculate the means for each of the four groups (If you graph them you will discover that the two graph lines are not parallel).

Questions below are based on the following: (This is similar to an item in the text at the back of chapter 12 but WITH A DIFFERENT DATA SET). A researcher is interested in whether a certain amphetamine drug will affect the retention of learned behavior among rats as a function of how much time is allowed to elapse between the training and the retention test. Four groups, ten subjects in each group, were randomly selected from a colony of Sprague-Dawley rats. All the rats were given the same amount of training on a simple maze. Groups A and C were given the amphetamine, whereas Groups B and D were given a placebo. Groups A and B were tested for retention immediately following the training, whereas Groups C and D were tested 4 hours later. The retention measure consisted of a scaled score based on how many correct responses the rats would exhibit while running the maze, the higher the score the higher the retention FACTOR A Amphetamine Group A Placebo Group B 15 13 9 9 9 12 Immediate 11 7 Test 10 7 6 8 10 10 12 9 14 5 7 11 FACTOR B Group C Group D 1 8 5 6 Delayed 2 9 Test 4 4 5 4 6 5 5 6 2 6 6 6 1 7 -Calculate the F ratio for the interaction

Dividing the sum of squares (SS) by the degrees of freedom (df), yields the

An F ratio of 10 means that the MS within is 10 times larger than the MS between.

When analyzing a significant ANOVA, in order to establish precisely where the sample differences may have occurred, we may

The sums of squares components relate such that SS total is equal to

Doing successive t tests within the context of a single experiment

The alternative hypothesis for the F ratio is that the sample means