Posted: August 12th, 2015

ANOVA and Paired T-test

Score:    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    1.029083333    1.075    1.052041667
0.956    1.000        Variance    0.006686447    0.006519818    0.006866042
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    1.065916667    1.065583333    1.06575
1.043    0.956        Variance    0.006102447    0.004212811    0.004933413
1.043    1.129
1.145    1.149        Total
Count    24    24
Sum    25.14    25.687
Average    1.0475    1.070291667
Variance    0.006470348    0.005156129

ANOVA
Source of Variation    SS    df    MS    F    P-value    F crit
Sample    0.002255021    1    0.002255021    0.383482117    0.538938951    4.06170646      (This is the row variable or gender.)
Columns    0.006233521    1    0.006233521    1.060053961    0.308829563    4.06170646      (This is the column variable or Degree.)
Interaction    0.006417188    1    0.006417188    1.091287766    0.301891506    4.06170646
Within    0.25873675    44    0.005880381

Total    0.273642479    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?