Question

The following partial ANOVA table is taken from the article ” Perception of Spatial Incongruity ” (J. Nerv. Ment. Dis., 1961: 222) in which the abilities of three different groups to identify a perceptual incongruity were assessed and compared. All individuals in the experiment had been hospitalized to undergo psychiatric treatment. There were 21 individuals in the depressive group, 32 individuals in the functional ”other ” group, and 21 individuals in the brain-damaged group. Complete the ANOVA table and carry out the F test at level α = 0.01.

               

Answer 1

Solution 

Complete the ANOVA table and carry out the F test at level α = 0.01.

Test the null hypothesis :

We have H_0 : There is no significance difference between means of groups. with alternative hypothesis

Since H_a : at least one mean is different from others.

                   

There were 21 individuals in the depressive group, denoted by n_1 = 21

There were 32 individuals in the functional ”other” group, denoted by n_2 = 32

There were 21 individuals in the brain-damaged group, denoted by n_3 = 21

Then, k = 3, n = n_1 + n_2 + n_3 = 21 + 32 + 21 = 74

We have, SST r = (3 − 1)M ST r = 2 × 76.09 = 152.18

Then , SSE = SST − SST r = 1123.14 − 152.18 = 970.96

Since, MSE = (SSE/n − I )= 13.3008

The test statistic for the data can be calculated as : f = (MSTr/MSE) = 5.72

                   

The critical value of test statistic at α = 0.01 with (2, 71) degrees of freedom is

F_(0.01,2,71) = 4.92

The probability value of test statistic is p-value = P (F ≥ F_(0.01,2,71)) = 0.005

Since, p-value < 0.01, we fail to accept the null hypothesis and conclude that there is significant difference in at least one mean of groups.