Question

Problem Set 2: The One-way ANOVA

Research Scenario: As part of a new prevention program, a clinical psychologist wants to see whether feelings of alienation differ as a function of immigration status in a local high school. She divides volunteer students into three categories: first-generation immigrants, second-generation immigrants, and non-immigrants. She then administers an instrument assessing feelings of alienation, where higher scores indicate stronger feelings of alienation from peers, adults, and society in general. Is there a difference in alienation scores among these three groups?

Using this table, enter the data into a new SPSS data file and run a one-way ANOVA to test whether there is a difference in feelings of alienation among the three groups. Create a boxplot to show the difference in alienation scores among the three groups.

Data: First generation immigrants: 35,39,34,37,36,23,39

Second generation immigrants : 26,37,28,29,36,25,18

Third generation immigrants: 29,22,17,25,19,30,16

1. Paste SPSS output. (7 pts)

2. Write an APA-style Results section based on your analysis. Include your boxplot as an APA-style figure as demonstrated in the APA writing presentation. (Results = 8 pts; Graph = 5 pts) Please answer this part! Very important! Thank you!

Answer 1

Solution:

Here, we have to use one way analysis of variance or ANOVA F test for checking the given claim or hypothesis. The null and alternative hypotheses for this test are given as below:

Null hypothesis: H₀: There is no any significant difference in the average alienation scores among three groups.

Alternative hypothesis: H_a: There is a significant difference in the average alienation scores among three groups.

We assume level of significance = α = 0.05 = 5%

The required box plot and ANOVA table by using SPSS are given as below:

Box plots are given as below:

From above box plots, it is observed that there is a significant difference in the average alienation scores among three groups.

The descriptive statistics and ANOVA table is given as below:

Descriptives
Alienation score
	N	Mean	Std. Deviation	Std. Error	95% Confidence Interval for Mean		Minimum	Maximum
					Lower Bound	Upper Bound
First generation immigrants	7	34.7143	5.49892	2.07840	29.6286	39.7999	23.00	39.00
Second generation immigrants	7	28.4286	6.55381	2.47711	22.3673	34.4898	18.00	37.00
Third generation immigrants	7	22.5714	5.62308	2.12533	17.3709	27.7719	16.00	30.00
Total	21	28.5714	7.56684	1.65122	25.1270	32.0158	16.00	39.00

ANOVA
Alienation score
	Sum of Squares	df	Mean Square	F	Sig.
Between Groups	516.286	2	258.143	7.389	.005
Within Groups	628.857	18	34.937
Total	1145.143	20

From above ANOVA, the p-value is given as 0.005 which is less than alpha value 0.05, so we reject the null hypothesis.

There is a sufficient evidence to conclude that there is a significant difference in the average alienation scores among three groups.