Exam 12: Analysis of Variance

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 -Is the column F ratio significant?

The F ratio may be used to assess differences between (among)

In a factorial ANOVA, the row variability, column variability and rxc variability, are all components of the

In order to calculate an F ratio, there must be

A factorial ANOVA may show the significance of

The only time the variance becomes equal to the standard deviation is when

For questions below use the data on the following page: A researcher is interested in establishing whether memory is a function of both IQ and time of testing. A random sample of 40 university students was selected and each student was given an IQ test. Half of the students scored above 115 and were assigned to the high IQ category. The students were than all given a series of paragraphs to read, followed by a memory test on the content of what had been read. Half the students took the memory test immediately after reading the material, while the other half waited an hour before testing. The results were as follows (high scores indicating better memory retention): -Was the row independent variable manipulated or assigned?

The F ratio may compare two or more sample means.

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 columns 215

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 rows

The greater the sum of squares within groups

For questions below use the data on the following page: A researcher is interested in establishing whether memory is a function of both IQ and time of testing. A random sample of 40 university students was selected and each student was given an IQ test. Half of the students scored above 115 and were assigned to the high IQ category. The students were than all given a series of paragraphs to read, followed by a memory test on the content of what had been read. Half the students took the memory test immediately after reading the material, while the other half waited an hour before testing. The results were as follows (high scores indicating better memory retention): -Find the MS within.

Three groups of subjects were randomly selected, 10 subjects in each group. The SS between was 668.47, and the SS within was 923.40. a. Calculate the F ratio b. Should Ho be rejected? If rejected, state the probability of alpha error.

Dividing the MS between by the MS within, yields the

The sums of squares components relates such that SS between is equal to

Once an F ratio is found to be significant, then

For questions below use the data on the following page: A researcher is interested in establishing whether memory is a function of both IQ and time of testing. A random sample of 40 university students was selected and each student was given an IQ test. Half of the students scored above 115 and were assigned to the high IQ category. The students were than all given a series of paragraphs to read, followed by a memory test on the content of what had been read. Half the students took the memory test immediately after reading the material, while the other half waited an hour before testing. The results were as follows (high scores indicating better memory retention): -Find the MS for rows.

Four groups of subjects were randomly selected, and subjected to different experimental treatments. Their scores were: Group 1 Group 2 Group 3 Group 4 5 7 8 15 4 5 7 14 3 6 6 18 6 8 8 12 a. Calculate the F ratio b. Should Ho be rejected ? If rejected, state the probability of alpha error.

The factorial ANOVA is only applied when

The greater the value of the F ratio,