Question

Interpreting ANOVA

(Please use the attached document, bold the questions, and include your answers in non-bolded font).

An Industrial Organizational psychologist is interested in examining the relative effectiveness of three leadership styles on worker productivity. A sample of N = 15 assembly line workers is obtained. These individuals are randomly assignment to each of the three leadership conditions: Authoritarian, Democratic, and Delegative. The number of units workers produced in a 10-hour shift is recorded. The data are as follows:

ANOVA

Productivity

	Sum of Squares	df	Mean Square	F	Sig.
Between Groups	329.200	2	164.600	159.290	.000
Within Groups	12.400	12	1.003
Total	341.600	14

Multiple Comparisons

Productivity

Tukey HSD

					95% Confidence Interval
(I) Leadership	(J) Leadership	Mean Difference (I-J)	Std. Error	Sig.	Lower Bound	Upper Bound
Authoritative	Democratic	-10.40000*	.64291	.000	-12.1152	-8.6848
	Delegative	-9.40000*	.64291	.000	-11.1152 -	7.6848
Democratic	Authoritative	10.40000*	.64291	.000	8.6848	12.1152
	Delegative	1.00000	.64291	.301	-.7152	2.7152
Delegative	Authoritative	9.40000*	.64291	.000	7.6848	11.1152
	Democratic	-1.00000	.64291	.301	-2.7152	.7152

*The mean difference is significant at the 0.05 level.

a. Why is the one-way ANOVA, rather than the independent samples t test, appropriate for this study?

b. Study the table and comment on whether the means for the three leadership styles differ significantly. In other words, does leadership style influence worker productivity? Explain.

c. In terms of these data, discuss why it is appropriate to conduct post hoc tests after the initial analysis of variance? Under what circumstances would it be inappropriate to conduct post hoc tests after performing a one-way ANOVA?

d. Discuss what these post hoc tests tell you that you could not determine from the initial analysis of variance. e. Using the information in the tables above, write an APA style results section.

Answer 1

1. Independent t test is used when there are means of two groups to compare. ( for example, males and females). One way ANOVA is used for more than two groups. In this study, there are means of three types of leadership to compare: authoritative, democratic and delegative. That would make them three groups.

2. According to the results of one way ANOVA, the F value computed (i.e. 159.290) is significant at .000 level. The means of the three leadership styles differ at 0.05 level of significance. This shows that leadership style influence worker productivity.

3. Post hoc tests are conducted when the means of more than two groups are compared. In this study, there are three types of leadership to compare. Post hoc tests would be inappropriate when there are less than three groups to compare.

4. The initial analysis of variance will only provide a difference among all the three groups. Post hoc test results show the comparison of mean of each group with the mean of other groups.

5. Table 1 shows the results of one way ANOVA. The F value computed was 159.290 which was found to be statistically significant at 0.05 level. Thus, the results accept the hypothesis that the leadership style influences the worker productivity.

Table 2 shows the results of Post hoc test followed by one way ANOVA. Tukey HSD results compare the means of three leadership styles. The mean difference between Authoritative and Democratic leadership was found to be statistically significant at 0.05 level. The mean difference was -10.4000 which indicates that Democratic leadership influences the worker productivity more than the Authoritative leadership. The mean difference between delegative leadership and Authoritative leadership was 9.4000 which was found to be significant at 0.05 level. This shows that delegative leadership influences worker productivity more than the autocratic leadership. The differences between the means of delegative leadership and democratic leadership were not statistically significant.