# ANOVA and Paired T-test – GradSchoolPapers.com

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?