1. At this point we know the following about male and female salaries.
a. Male and female overall average salaries are not equal in the population.
b. Male and female overall average compas are equal in the population, but males are a bit more spread out.
c. The male and female salary range are almost the same, as is their age and service.
d. Average performance ratings per gender are equal.
Let's look at some other factors that might influence pay - education(degree) and performance ratings.
Last week, we found that average performance ratings do not differ between males and females in the population.
Now we need to see if they differ among the grades. Is the average performace rating the same for all grades?
(Assume variances are equal across the grades for this ANOVA.)
You can use these columns to place grade Perf Ratings if desired.
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D |
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F |
| Null Hypothesis: |
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| Alt. Hypothesis: |
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Interpretation:
What is the p-value:
Is P-value < 0.05?
Do we REJ or Not reject the null?
If the null hypothesis was rejected, what is the effect size value (eta squared):
Meaning of effect size measure:
What does that decision mean in terms of our equal pay question:
2 While it appears that average salaries per each grade differ, we need to test this assumption.
Is the average salary the same for each of the grade levels? (Assume equal variance, and use the analysis toolpak function ANOVA.)
Use the input table to the right to list salaries under each grade level.
If desired, place salaries per grade in these columns
What is the p-value:
Is P-value < 0.05?
Do you reject or not reject the null hypothesis:
If the null hypothesis was rejected, what is the effect size value (eta squared):
Meaning of effect size measure:
Interpretation:
The table and analysis below demonstrate a 2-way ANOVA with replication. Please interpret the results.
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BA |
MA |
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Ho: Average compas by gender are equal |
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| Male |
1.017 |
1.157 |
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Ha: Average compas by gender are not equal |
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0.87 |
0.979 |
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Ho: Average compas are equal for each degree |
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1.052 |
1.134 |
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Ha: Average compas are not equal for each degree |
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1.175 |
1.149 |
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Ho: Interaction is not significant |
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1.043 |
1.043 |
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Ha: Interaction is significant |
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1.074 |
1.134 |
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1.02 |
1 |
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Perform analysis: |
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0.903 |
1.122 |
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0.982 |
0.903 |
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Anova: Two-Factor With Replication |
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1.086 |
1.052 |
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1.075 |
1.14 |
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SUMMARY |
BA |
MA |
Total |
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1.052 |
1.087 |
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Male |
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| Female |
1.096 |
1.05 |
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Count |
12 |
12 |
24 |
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1.025 |
1.161 |
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Sum |
12.35 |
12.9 |
25.25 |
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1 |
1.096 |
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Average |
1.029 |
1.075 |
1.052 |
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0.956 |
1 |
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Variance |
0.007 |
0.007 |
0.007 |
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1 |
1.041 |
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1.043 |
1.043 |
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Female |
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1.043 |
1.119 |
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Count |
12 |
12 |
24 |
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1.21 |
1.043 |
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Sum |
12.79 |
12.79 |
25.58 |
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1.187 |
1 |
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Average |
1.066 |
1.066 |
1.066 |
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1.043 |
0.956 |
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Variance |
0.006 |
0.004 |
0.005 |
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1.043 |
1.129 |
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1.145 |
1.149 |
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Total |
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Count |
24 |
24 |
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Sum |
25.14 |
25.69 |
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Average |
1.048 |
1.07 |
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Variance |
0.006 |
0.005 |
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ANOVA |
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Source of Variation |
SS |
df |
MS |
F |
P-value |
F crit |
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Sample |
0.002 |
1 |
0.002 |
0.383 |
0.539 |
4.062 |
(This is the row variable or gender.) |
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Columns |
0.006 |
1 |
0.006 |
1.06 |
0.309 |
4.062 |
(This is the column variable or Degree.) |
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Interaction |
0.006 |
1 |
0.006 |
1.091 |
0.302 |
4.062 |
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Within |
0.259 |
44 |
0.006 |
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Total |
0.274 |
47 |
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Interpretation:
For Ho: Average compas by gender are equal Ha: Average compas by gender are not equal
What is the p-value:
Is P-value < 0.05?
Do you reject or not reject the null hypothesis:
If the null hypothesis was rejected, what is the effect size value (eta squared):
Meaning of effect size measure:
For Ho: Average compas are equal for all degrees Ha: Average compas are not equal for all grades
What is the p-value:
Is P-value < 0.05?
Do you reject or not reject the null hypothesis:
If the null hypothesis was rejected, what is the effect size value (eta squared):
Meaning of effect size measure:
For: Ho: Interaction is not significant Ha: Interaction is significant
What is the p-value:
Is P-value < 0.05?
Do you reject or not reject the null hypothesis:
If the null hypothesis was rejected, what is the effect size value (eta squared):
Meaning of effect size measure:
What do these decisions mean in terms of our equal pay question:
4 Many companies consider the grade midpoint to be the "market rate" - what is needed to hire a new employee.
Does the company, on average, pay its existing employees at or above the market rate?
What is the p-value:
Is P-value < 0.05?
What else needs to be checked on a 1-tail in order to reject the null?
Do we REJ or Not reject the null?
If the null hypothesis was rejected, what is the effect size value: NA
Meaning of effect size measure: NA
Interpretation:
5. Using the results up thru this week, what are your conclusions about gender equal pay for equal work at this point?