# BUS308 -3 WEEK

**monv32**

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 | 1.02908333 | 1.075 | 1.052042 | ||||||||||

0.956 | 1.000 | Variance | 0.00668645 | 0.00652 | 0.006866 | ||||||||||

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 | 1.06591667 | 1.065583 | 1.06575 | ||||||||||

1.043 | 0.956 | Variance | 0.00610245 | 0.004213 | 0.004933 | ||||||||||

1.043 | 1.129 | ||||||||||||||

1.145 | 1.149 | 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: | |||||||||||||||

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. | |||||||||||||||

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