ONE-WAY ANOVA

Posted: August 27th, 2021

HOMEWORK #7: ONE-WAY ANOVA

Problem 1

Question 1

Number of levels in the factor of interest (k) = 3

Total number of participants (N) = 15

Question 2: The critical F-Value

Degrees of Freedom = N – K = 12

F-Critical = 3.49

Question 3

Source	SS	df	MS	F
Between	81.12	2	40.56	2.311
Within	35.10	2	17.55
Total	116.22	12

P <0.05

Question 4: Reject or retain HO: F-calculated < F-Critical, that is, 2.311 < 3.49, hence reject H0.

Problem 2

Question 1

Number of levels in the factor of interest (k) = 4

Total number of participants (N) = 16

Question 2

The critical F-Value

Degrees of Freedom = N – K = 12

F-Critical = 3.49

Question 3

Source	SS	df	MS	F
Between	6.33	3	2.11	0.345
Within	20.16	3	6.71
Total	26.49	12

P <0.05

Question 4: Reject or retain HO: F-calculated < F-Critical, that is, 0.345 < 3.49, hence reject H0.

HOMEWORK #7: ONE-WAY ANOVA

Problem 1

Question 1: Was there a significant main effect on TV watching?  – Yes.

Question 2: Was there a significant main effect on the number of books? – No.

Question 3: Was there a significant interaction? – Yes

Question 4: Overall TV exposure led to higher levels of hyperactivity than no TV exposure. True – TV exposure has a five score than No TV exposure that has a score of 3. More, it is statistically significant at a 5% significance level.

Question 5: The impact of TV watching depended on several books. True – Interaction between TV watching and a number of books is statistically significant at a 5% significance level.

Question 6: Overall, children with a highnumber of books and children with a low number of books had similar hyperactivity scores. – False – the Eta-squared for the Number of books and Interaction are not the same, although exhibit slight difference.

Question 7: Children with a high amount of books had higher hyperactivity scores if they were in the TV exposure group than children with a high amount of books in the no TV exposure group. True – High books vs. TV exposure has a score of 5, while high books have No TV exposure has a score of 3.

Question 8: Overall, children with a higher number of books had lower hyperactivity scores than children with fewer books. True – High books score 5 while low books score is 17.

Question 9: TV exposure and no TV exposure resulted in similar levels of hyperactivity. False – TV exposure score is 5 while no TV exposure score is 3.

Question 10: TV watching had the most significant impact on variance in children’s hyperactivity.

Problem 2

Question 1: Was there a significant main effect on the age group?  – No.

Question 2: Was there a significant main effect of advertisement? – No.

P<0.05 F-cal = 2.64 and F – Critical = 3.49; F –cal < F -Crit

Question 3: Was there a significant interaction? – No.

P<0.05 F-cal = 2.94 and F – Critical = 3.49; F –cal < F -Crit

Question 4:The impact of Facebook ads did NOT depend on age group. False– It is statistically significant at a 5% significance level.

Question 5:Overall, Gen Z and Baby Boomers were equally likely to wear masks. False- there no statistically significant evidence to show equal interaction.

Question 6: Instagram ads were equally effective with both age groups. False – Instagram has a likelihood score of 25, and there is no statistical evidence of an effect on age group.

Question 7: Overall, everyone was likely to wear masks as a result of radio ads. True – radio ads have a likelihood score of 10, and advertisement is statistically significant at p<0.05.

Question 8: The impact of radio ads was dependent on the age group. False – there is no statistical evidence demonstrating this dependence at p<0.05.

Question 9:Overall, the type of ad DID impact the likelihood of wearing a mask. False – there is no statistical evidence showing this at a p-value <0.05.

Question 10:age group had the highest impact on variance in the likelihood of wearing a mask because of a high Eta-squared value of 0.22