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Week 3
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.
<1 point>
1
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:
<1 point>
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.
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:
<1 point>
3
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
<1 point>
4
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.
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:
<2 points>
5.
Using the results up thru this week, what are your conclusions
about gender equal pay for equal work at this point?
ScoreWeek 3ANOVA and Paired T-test.docx

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