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.