ANOVA and Paired T-test
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.
A B C D E F
Null Hypothesis:
Alt. Hypothesis:
Place B17 in Outcome range box.
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:
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.
Null Hypothesis: If desired, place salaries per grade in these columns
Alt. Hypothesis: A B C D E F
Place B55 in Outcome range box.
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.
BA MA Ho: Average compas by gender are equal
Male 1.017 1.157 Ha: Average compas by gender are not equal
0.870 0.979 Ho: Average compas are equal for each degree
1.052 1.134 Ha: Average compas are not equal for each degree
1.175 1.149 Ho: Interaction is not significant
1.043 1.043 Ha: Interaction is significant
1.074 1.134
1.020 1.000 Perform analysis:
0.903 1.122
0.982 0.903 Anova: Two-Factor With Replication
1.086 1.052
1.075 1.140 SUMMARY BA MA Total
1.052 1.087 Male
Female 1.096 1.050 Count 12 12 24
1.025 1.161 Sum 12.349 12.9 25.249
1.000 1.096 Average 1.02908333 1.075 1.052042
0.956 1.000 Variance 0.00668645 0.00652 0.006866
1.000 1.041
1.043 1.043 Female
1.043 1.119 Count 12 12 24
1.210 1.043 Sum 12.791 12.787 25.578
1.187 1.000 Average 1.06591667 1.065583 1.06575
1.043 0.956 Variance 0.00610245 0.004213 0.004933
1.043 1.129
1.145 1.149 Total
Count 24 24
Sum 25.14 25.687
Average 1.0475 1.070292
Variance 0.00647035 0.005156
ANOVA
Source of Variation SS df MS F P-value F crit
Sample 0.00225502 1 0.002255 0.383482 0.538939 4.061706 (This is the row variable or gender.)
Columns 0.00623352 1 0.006234 1.060054 0.30883 4.061706 (This is the column variable or Degree.)
Interaction 0.00641719 1 0.006417 1.091288 0.301892 4.061706
Within 0.25873675 44 0.00588
Total 0.27364248 47
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:
Place data values in these columns
Many companies consider the grade midpoint to be the "market rate" - what is needed to hire a new employee. Salary Midpoint
Does the company, on average, pay its existing employees at or above the market rate?
Null Hypothesis:
Alt. Hypothesis:
Statistical test to use:
Place the cursor in B160 for test.