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.
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