Question

The following five independent random samples are obtained from five normally distributed populations with equal variances. The dependent variable is the number of bank transactions in 1 month, and the groups are five different banks.

Group 1	Group 2	Group 3	Group 4	Group 5
16	16	2	5	7
5	10	9	8	12
11	7	11	1	14
23	12	13	5	16
18	7	10	8	11
12	4	13	11	9
12	23	9	9	19
19	13	9	9	24

Use SPSS to conduct a one-factor ANOVA to determine if the group means are equal using alpha = .05. Test the assumptions, plot the group means, consider an effect size, interpret the results, and write an APA style summary.

Answer 1

ANOVA The number of bank transactions Sum of Squares Between Groups 31 4.400 Within Groups B46.000 Total 1160.400 4 Mean Square 78.600 24.171 3.252023 Explore Case Processing Summary Cases Valid Missing Percent Percent 100.0% 0.0% Total Percent 40 100.0% The numberor bank transactions Tests of Normality Kolmogorov-Smirnova Statistic Siger The number of bank .128 099 transactions a. Lilliefors Significance Correction Shapiro-Wilk Statistics of 960 Sig. 164

The number of bank transactions Histogram Mean = 11.3 Std. Dev. = 5.455 N = 40 Frequency The number of bank transactions

Average bank transactions 14.5 11.5 9.5 Group 1 Group 2 Group 3 Group 4 Group 5

After performing the analysis in SPSS, we found that there is significant difference in groups of mean because the p-value or sig. Value in one way factor ANOVA is 0.023 which is less than the level of significance 0.05 therefore we reject the null hypothesis and conclude that there is significant difference in means of the groups.

Yhe normality assumption is fulfilled by the data as the test for normality test like shapiro wilk and kolmogorov smirnov p-value insignificant i.e. 0.164 and 0.099 respectively which is greater than 0.05 therefore we fail to reject the null hypothesis and conclude that the data is normally distributed.

The group means are found in group1 is 14.5, group2 11.5, group3, 9.5, group4, 7 and group5, 14. The groups mean are also plotted in the bar graph. The highest mean is found in group1 whereas the lowest in group4.

The effect size is found from the ANOVA table between the group is 4 and within the group is 35.