Question

An investigator conducts an experiment involving the effects of background information on jurors’ decision making. All participants watch a video of a trial in which a woman is accused of shoplifting. Before viewing the video, each participant is given a background sheet with information about the accused woman. Each participant is randomly assigned to one of three conditions. Participants in group 1 are given a background sheet that states that the woman has previously been convicted of shoplifting three times. Participants in group 2 are given a background sheet that includes an explicit statement that the woman has no criminal record at all. Participants in group 3 are given a background sheet that includes no information about any prior criminal history one way or the other. After watching the video, each participant rates the likely guilt of the woman, ranging from 1 (completely innocent) to 10 (completely guilty). Is there an effect of background information on perceived guilt? Analyze the data using JASP, SPSS, or an online calculator, and answer the following questions

1. By hand, perform a planned comparison (a = 0.05) between group 1 (criminal record) condition and group 2 (no criminal record) condition. State the null and alternative hypotheses, calculate tobt by hand (show your work!), report |tcrit| (including df), and your decision about the null hypothesis.

2. By hand, calculate and interpret the effect size, omega-squared, for the omnibus F test.

guilty rating	group
9	1
7	1
5	1
10	1
8	1
4	2
2	2
5	2
4	2
1	2
4	3
6	3
8	3
3	3
3	3

Answer 1

1. The hypothesis being tested is:

H0: µ1 = µ2

H1: µ1 ≠ µ2

The p-value is 0.0036.

Since the p-value (0.0036) is less than the significance level (0.05), we can reject the null hypothesis.

Therefore, we can conclude that µ1 ≠ µ2.

group 1	group 2
7.80	3.20	mean
1.92	1.64	std. dev.
5	5	n
	8	df
	4.600	difference (group 1 - group 2)
	3.200	pooled variance
	1.789	pooled std. dev.
	1.131	standard error of difference
	0	hypothesized difference
	4.066	t
	.0036	p-value (two-tailed)

2.

2.57	effect size
0.67	omega-squared