Question

Here are data from an experiment comparing memory of people given lists of 20 items to remember. Four groups of subjects were asked to remember words, faces, pictures, or colors. Instead of giving you all the data, for each group I just give you the mean number of items recalled and the sum of squares. Sum of Squares 205.7 231.2 Group Words Faces Size 20 24 Mean 9.5 12.1 10.2 8.1 Pictures 19 211.8 Colors 21 224.1 1. Find the grand mean. Remember that the sum of all the scores in any group equals the group mean times the size of the group. M 10.051 2. Find the sum of squares for the differences among groups. SStreatment =187.19 3. Find the residual sum of squares. SSresidual 872.8 4. Find the total sum of squares of the outcome SStotal 105.9 Calculate the effect size, or proportion of explained variance n2=0.176 5. 6-7. Convert both sums of squares to mean squares. The degrees of freedom are dftreatment = k - 1 3 and dfresidual En - k = 80. MSresidual MStreatment 8. Calculate the F statistic for deciding whether the group means differ. F = 9. The critical value (with a 5%) is Ferit = 2.72. What do you conclude? (Don't just write null or alternative.) Focus tes)

Can you solve 6-9 please

Answer 1

Solution:

Part 6-7)

We have:

df_treatment = 3

df_residual = 80

SS_treatment = 187.19

SS_residual =872.8

Thus

MS_treatment = SS_treatment / df_treatment

MS_treatment =   187.19 / 3

MS_treatment = 62.40

MS_residual = SS_residual / df_residual

MS_residual = 872.8 / 80

MS_residual = 10.91

Part 8) F statistic:

F = MS_treatment / MS_residual   

F = 62.40 / 10.91

F = 5.72

Part 9) F critical value = 2.72

Since F test statistic value = 5.72 > F critical value = 2.72, we reject null hypothesis.

Thus answer is:

Reject null