Week 3 Paired T-test and ANOVA

For this week’s work, again be sure to state the null and alternate hypotheses and use alpha = 0.05 for our decision value in the reject or do not reject decision on the null hypothesis.

1. Many companies consider the grade midpoint to be the “market rate” – the salary needed to hire a new employee.

Does the company, on average, pay its existing employees at or above the market rate? Salary Midpoint Diff

Use the data columns at the right to set up the paired data set for the analysis.

Null Hypothesis

Alt Hypothesis

Statistical test to use:

What is the p-value:

Is P-value < 0.05 (one tail test) or 0.25 (two tail test)?

Do we REJ or Not reject the null?

If the null hypothesis was rejected, what is the effect size value:

If calculated, what is the meaning of effect size measure:

Interpretation of test results:

Let’s look at some other factors that might influence pay – education(degree) and performance ratings.

2. 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.)

The rating values sorted by grade have been placed in columns I – N for you.

Null Hypothesis: Ho: means equal for all grades

Alt. Hypothesis: Ha: at least one mean is unequal

Place B17 in Outcome range box.

Interpretation of test results:

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:

3. 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?

Use the input table to the right to list salaries under each grade level.

(Assume equal variance, and use the analysis toolpak function ANOVA.)

Null Hypothesis:

Alt. Hypothesis:

Place B51 in Outcome range box.

Interpretation of test results:

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):

If calculated, what is the meaning of effect size measure:

Interpretation:

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

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:

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 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:

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 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:

For: Ho: Interaction is not significant Ha: Interaction is significant

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:

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