# Week 3 ANOVA and Paired T-test At this point we know the following about male and female salaries.

August 31, 2017

Question
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Week 3

ANOVA and Paired T-test

At this point we know the following about male and female salaries.
Male and female overall average salaries are not equal in the population.
a.
Male and female overall average compas are equal in the population, but males are a bit more spread out.
b.
The male and female salary range are almost the same, as is their age and service.
c.
Average performance ratings per gender are equal.
d.
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 what is the effect size
If the null hypothesis was rejected, or Not reject the null?
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:
Alt. Hypothesis:

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):

If desired, place salaries per grade in these columns
A
B
C
D
E

F

Meaning of effect size measure:
Interpretation:
3

<1 point>

The table and analysis below demonstrate a 2-way ANOVA with replication. Please interpret the results.

Male

Female

BA
1.017
0.870
1.052
1.175
1.043
1.074
1.020
0.903
0.982
1.086
1.075
1.052
1.096
1.025
1.000
0.956
1.000
1.043
1.043
1.210
1.187
1.043
1.043
1.145

MA
1.157
0.979
1.134
1.149
1.043
1.134
1.000
1.122
0.903
1.052
1.140
1.087
1.050
1.161
1.096
1.000
1.041
1.043
1.119
1.043
1.000
0.956
1.129
1.149

Ho: Average compas by gender are equal
Ha: Average compas by gender are not equal
Ho: Average compas are equal for each degree
Ha: Average compas are not equal for each degree
Ho: Interaction is not significant
Ha: Interaction is significant
Perform analysis:
Anova: Two-Factor With Replication
SUMMARY BA

MA

Total

Male

Count
Sum
Average
Variance

12
12
24
12.349
12.9
25.249
1.029083333
1.075 1.0520417
0.006686447 0.0065198 0.006866

Female

Count
Sum
Average
Variance

12
12
24
12.791
12.787
25.578
1.065916667 1.0655833 1.06575
0.006102447 0.0042128 0.0049334

Total

Count
Sum
Average
Variance

24
24
25.14
25.687
1.0475 1.0702917
0.006470348 0.0051561

ANOVA
Source of Variation SS

df

MS

Sample
0.002255021
Columns 0.006233521
Interaction 0.006417188
Within
0.25873675

1
1
1
44

Total

F

P-value

F crit

0.002255 0.3834821 0.538939 4.0617065 (This is the row variab
0.0062335 1.060054 0.3088296 4.0617065 (This is the column va
0.0064172 1.0912878 0.3018915 4.0617065
0.0058804

47

0.273642479

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:

<1 point>

4

Many companies consider the grade midpoint to be the "market rate" – what is needed to hire a new employee.

Place data values in thes
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?

ble or gender.)
ariable or Degree.)

ese columns

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