Problem Set Week 3 three ANOVA and Paired T-test

Problem Set Week 3 three 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.

Male and female overall average compas are equal in the population, but males are a bit more spread out.

The male and female salary range are almost the same, as is their age and service.

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.)

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:

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):

Meaning of effect size measure:

Interpretation:

3

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

BA

MA

Male

1.017

1.157

0.870

0.979

1.052

1.134

1.175

1.149

1.043

1.043

1.074

1.134

1.020

1.000

0.903

1.122

0.982

0.903

1.086

1.052

1.075

1.140

1.052

1.087

Female

1.096

1.050

1.025

1.161

1.000

1.096

0.956

1.000

1.000

1.041

1.043

1.043

1.043

1.119

1.210

1.043

1.187

1.000

1.043

0.956

1.043

1.129

1.145

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

12

12

24

Sum

12.349

12.9

25.249

Average

1.02908333

1.075

1.052042

Variance

0.00668645

0.00652

0.006866

Female

Count

12

12

24

Sum

12.791

12.787

25.578

Average

1.06591667

1.065583

1.06575

Variance

0.00610245

0.004213

0.004933

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:

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?

Null Hypothesis:

Alt. Hypothesis:

Statistical test to use:

Place the cursor in B160 for test.

Place data values in these columns

Salary

Midpoint

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:

Meaning of effect size measure:

Interpretation:

5.  

Using the results up thru this week, what are your conclusions about gender equal pay for equal work at this point?