A psychologist was looking at the effects of an intervention on depression level

Question

A psychologist was looking at the effects of an intervention on depression levels. Three groups were used: waiting list control, treatment and post treatment (a group who had had the treatment 6 months before). The change in depression levels over the time of the treatment was recorded (although bear in mind only the treatment group actually got any treatment during this time). The R output is below. Based on this output, what should the researcher conclude? Levene's Test for Homogeneity of Variance (center = "median") One-way analysis of means (not assuming equal variances) data: tumour and usage F = 4.345, num df = 2.00, denom df = 26.436, p-value = .023 Explain how each number in the above output from question III was computed. That is, for each number in the output provide, its formula and the numbers to be plugged into the formula

Explanation / Answer

Levene’s Test is meant to test if the variances of the treatment groups are same. It’s analogous to ANOVA where means of treatment groups are compared.

Levene’s Test

H0: variances of all the 3 groups equal

Ha: variances of at least one pair of groups is different

Table numbers interpretations:

df: for groups we have df=2 since there are 3 groups so n-1=3-1=2

For residuals it should be n-1-k

Mean sq= total sum of sq/df i.e. 529.4/2=264.7

And same is the case for residuals

F=MSgroup/MSresidual= 264.7/51.8=5.11

By F-table

P-value=0.023

At 5% level we reject

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