Question

Jeremy wants to know if some scary movies are more frightening than others. He takes a group of students and randomly assigns them to watch one of three popular scary movies (Jaws, Alien, or Psycho), and counts the number of times each person screams during the movie. Is there a significant difference in the number of screams when comparing these movies? Set α = .05. Jaws Alien Psycho ∑▒〖X_1=〗 103 ∑▒〖X_2=〗 149 ∑▒〖X_3=〗 79 ∑▒〖X_1^2=〗 1162 ∑▒〖X_2^2=〗 2178 ∑▒〖X_3^2=〗 569 n_1= 11 n_2= 11 n_3= 11

State the null and alternative hypotheses in words.

Set up the criteria for making a decision. That is, find the critical value(s).

Calculate the appropriate test statistic and complete the table below. Show your work.

Source	SS	df	MS	F
Between (Group)
Within (Error)
Total

1. Evaluate the null: (circle one)      REJECT         FAIL TO REJECT         

2. Based on your result, would it be appropriate to do a post-hoc test?

                       

(Circle One)                Yes                              No

6. Calculate and interpret eta-squared.   

Answer 1

	1	2	3	Total
	103	149	79	331
	1162	2178	569	3909
n	11	11	11	33

ANOVA

This is ANOVA - Single Factor. We first need to find the and . They are 'Total variance' and 'Variance in between the treatments' respectively.

We want to test whether the mean scream times is same or not for all the movies.

We know

=

Grand total = 331 Sum of individual squares = 3909

= 588.9697

=

Note: We have to separately sum for all the treatment.

= = 3550.091

= 230.061

Df (Bet) = k -1 ………..where k = no. of treatments

= 2

358.909

Df (res) = n – k

= 30

Source	SS	df	MS (SS / df)	F  (MSB / MSE)
Between (Group)	230.0606	2	115.0303	9.6150
Within (Error)	358.9091	30	11.9636
Total	588.9697	32

State the null and alternative hypotheses in words.

Null: All the movies are scary on the same mean level. (mean screams times are same).

Alternative: At least one of the movies is scary on a different mean level. (At least one mean scream times is different)

Set up the criteria for making a decision. That is, find the critical value(s).

α = .05

C.V. =

=

= 3.3158 .......................found using f-dist tables with df1 = 2 df2= 30 and p =0.05

Calculate the appropriate test statistic and complete the table below. Show your work.

Source	SS	df	MS (SS / df)	F  (MSB / MSE)
Between (Group)	230.0606	2	115.0303	9.6150
Within (Error)	358.9091	30	11.9636
Total	588.9697	32

Test Stat = F = 9.6150

Since F-stat > C.V.

Evaluate the null: (circle one)      REJECT      

Based on your result, would it be appropriate to do a post-hoc test?

We are rejecting the hypothesis which is to conclude at least one of the movies is scary on a different mean level. To check which pairs have significance difference, a post -hoc test can be conducted.

(Circle One)                Yes   

Calculate and interpret eta-squared.   

Eta-squared helps to determine the proportion of variance of treatments out of the total variance that is measure effect size.

This tells us how much dependent variables explain the variation in the data.

That means that 39.06% of variance is expalined by the different dependent variables (movies).