Question

Background

The 2016 US Presidential Election brought considerable attention to the phenomenon of “fake news”: entirely fabricated and often partisan content that is presented as factual. Researchers evaluated one mechanism that may contribute to the believability of fake news: fluency via prior exposure. Using an actual fake news headline presented as it was seen on Facebook (Kid Rock launches campaign to run for U.S. Senate in 2018), the researchers hypothesized that previous exposure to the fake news story would increase perceptions of accuracy. Subjects were pre-screened to determine in which of 3 groups they belonged: 1) no previous exposure to the fake news story, 2) previous exposure to the fake news story and had not heard that the story was, in fact, fake, or 3) previous exposure to the fake news story but had heard that the story was, in fact, fake. They recorded perception of the accuracy of the news story (ranging from 1 (definitely false) to 6 (definitely true)).

Please complete all empty boxes in the tables below.

Data

	No exposure (Group A)	Previous exposure, not informed it was fake (Group B)	Previous exposure, informed it was fake (Group C)
	1	3	6
	1	6	6
	2	6	6
	4	4	5
	1	5	5
	4	4	4
	3	5	3
	2	6	4
	1	6	6
	6	3	3
	5	3	6
Mean
St. Dev	1.79	1.29	1.22
n
N

One-way ANOVA (please show your work!)

Source of variability	df	SS	MS	F		h2
Between-groups		31.09
Within-groups (error)		63.64
Total		94.73
Critical F-value (obtain from F table)
Is the ANOVA significant? Y or N

Post-hoc results using the Tukey test

Comparison	p-value	Significant? Y or N
Group A versus Group B	.0095
Group A versus Group C	.0033
Group B versus Group C	.6156

Full interpretation of the results

Describe ANOVA results. Describe post-hoc results (if applicable). Describe differences between groups. Interpret effect size.

Answer 1

Anova: Single Factor
SUMMARY
Groups	Count	Sum	Average	Variance
A	11	30	2.727273	3.218182
B	11	51	4.636364	1.654545
C	11	54	4.909091	1.490909
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	31.09091	2	15.54545	7.328571	0.002561	3.31583
Within Groups	63.63636	30	2.121212
Total	94.72727	32

η² = Treatment Sum of Squares
           Total Sum of Square

= 31.09091/94.63636 = 0.3285

Critical F-value (obtain from F table)		3.3158
Is the ANOVA significant? Y or N

Yes, Anova is significant as TS > critical value

Comparison	p-value	Significant? Y or N
Group A versus Group B	.0095	Y
Group A versus Group C	.0033	Y
Group B versus Group C	.6156	N