In: Psychology
Interpreting ANOVA
(Please use the attached document, bold the questions, and include your answers in nonbolded 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 10hour 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 (IJ) 
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 oneway 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 oneway 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.
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.