Question

A researcher wanted to examine if the type of music one listens to while studying affects memory performance. She randomly selected five samples of participants and assigned each of them to one of five experimental conditions - listening to classical music, jazz, R&R, R&B or Hip hop. Each sample had 14 subjects (n = 14). All participants were asked to memorize a list of words while listening to one of the five types of music tested. At the end, all participants took a memory test. One-factor ANOVA for independent samples was conducted to test if there is a significant effect of music type on memory performance. The results of the analysis are shown in the following ANOVA summary table.

                          

                                           Source       SS         df        MS             

                           Between Treatments     48       ____     ____    F = 3.00  

                           Within Treatments      ____     ____     ____    

                           Total                        ____     ____

          A. Fill in all missing values in the ANOVA summary table. Show your work (i.e., all computational steps for finding the missing values). Hint: start with the df values and figure out the rest by solving simple equations with one unknown (i.e., refer to the computational formulas for df, MS & F statistic).

       

           B. Do the data indicate a significant effect of type music on memory performance (assume p < .05)? Use the outcomes of one-factor ANOVA summarized in the table to test this research question.

Answer 1

A)

We will fill ANOVA table

As we can see that there are 5 treatments in total

So df for between treatments will be 5-1 = 4

Then $\small MS_{Between \ treatments} = \frac{SS_{Between \ treatments}}{4} = \frac{48}{4} = 12$

And we know that F statistic is given by:

$\small F = \frac{MS_{Between \ treatments}}{MS_{within \ treatments}} = 3$

So $\small MS_{within \ treatments} = \frac{12}{3} = 4$

and we know that df for within treatments is given by:

Total subjects = 14*5 = 70

so total df = 70-1 = 69

and we know that

df_total = df_between + df_within

69 = 4 + df_within

df_within = 69-4 = 65

So

$\small SS_{within \ treatments} = MS_{within \ treatments} * df_{within} = 4*65 = 260$

So the final ANOVA table is :

Source	SS	df	MS	F
Between Treatments	48	4	12	3
Within Treatments	260	65	4
Total	308	69

B)

Here now we need to find the p value corresponding this F statistic

$\small P \ Value = P(F_{4, 65} > 3) = 1 - P(F_{4, 65} \leq 3) = 1 - 0.9753645 = 0.02463552$

where this p value is calculated in R

code is attached :

> pf(3, 4, 65) [1] 0.9753645

Here as we can see that p value = 0.02463552 <

a = 0,05

which implies that we have enough evidence to reject null hypothesis.

i.e., Here 5 type of music are different at level of significance.

a = 0,05

Do hit the like button if you like the solution.