Question

A study by Staub, 1970, was concerned with the effects of instructions to young children and their subsequent attempts to help another child (apparently) in distress. Twenty-four first-grade students were randomly assigned to one of three groups. The first group was labeled as indirect responsibility (IR). Students in the IR group were informed that another child was alone in an adjoining room and had been warned not to climb up on a chair. The second group was labeled direct responsibility one (DR1). Students in the DR1 group were told the same story as in the IR condition, but was also told that they were left in charge and to take care of anything that happened. The students were given a simple task, and the researcher left the room. The students then heard a loud crash in the adjoining room followed by a minute of sobbing and crying. Students in the third group, direct responsibility two (DR2), had the same instructions as the DR1 group, but the sounds of distress also included calls for help. Ratings from 1 (no help) to 5 (went to the adjoining room) were given to each student by an observer sitting behind a one-way mirror. The ratings are given below.

1. Perform a one-way ANOVA in SPSS with α = .05 and answer the following questions.

IR	DR1	DR2
3	5	4
4	4	4
2	5	3
1	4	3
1	5	4
2	5	2
1	4	5
1	3	3

PART A: The ANOVA is based on three assumptions. Describe the three assumptions in detail.

PART B: State the null hypothesis in words.

Answer 1

Here we have data:

IR	DR1	DR2
3	5	4
4	4	4
2	5	3
1	4	3
1	5	4
2	5	2
1	4	5
1	3	3

We use Excel to calculation :

Anova: Single Factor
SUMMARY
Groups	Count	Sum	Average	Variance
Column 1	8	15	1.875	1.267857143
Column 2	8	35	4.375	0.553571429
Column 3	8	28	3.5	0.857142857
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	25.75	2	12.875	14.42	0.00011448	3.4668
Within Groups	18.75	21	0.892857143
Total	44.5	23

Three assumptions:

1) The one-way ANOVA is considered a robust test against the normality assumption. This means that it tolerates violations to its normality assumption rather well.

2) There are two tests that you can run that are applicable when the assumption of homogeneity of variances has been violated: (1) Welch or (2) Brown and Forsythe test.

3) A lack of independence of cases has been stated as the most serious assumption to fail.

Hypothesis:

H_o: μ_IR = μ_DR1 = μ_DR2

H_a: At least one of the treatment mean is different from others.

Reject the null hypothesis.

Here we have sufficient evidence to reject the null hypothesis, because F-observed value (14.42) is grater than F-critical value (3.4668).