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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? 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): 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 Replica±on 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 1.0520417 0.956 1.000 Variance 0.006686447 0.0065198 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 1.065916667 1.0655833 1.06575 1.043 0.956 Variance 0.006102447 0.0042128 0.0049334 1.043 1.129 1.145 1.149 Total Count 24 24 Sum 25.14 25.687 Average 1.0475 1.0702917 Variance 0.006470348 0.0051561 ANOVA Source of Varia SS df MS F P-value F crit Sample 0.002255021 1 0.002255 0.3834821 0.538939 4.0617065 (This is the row variab Columns 0.006233521 1 0.0062335 1.060054 0.3088296 4.0617065 (This is the column va Interac±on 0.006417188 1 0.0064172 1.0912878 0.3018915 4.0617065 Within 0.25873675 44 0.0058804 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: 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: 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: Meaning of effect size measure: What do these decisions mean in terms of our equal pay question: Place data values in the <1 point> 4 Many companies consider the grade midpoint to be the "market rate" - what is needed to hire a new employee. Salary Midpoint If the null hypothesis was rejected, what is the effect size value (eta squared): If the null hypothesis was rejected, what is the effect size value (eta squared): If the null hypothesis was rejected, what is the effect size value (eta squared):

ID Salary Compa Midpoint Age Service Gender Raise 1 56.5 0.992 57 34 85 8 0 5.7 2 28.3 0.913 31 52 80 7 0 3.9 3 34 1.097 31 30 75 5 1 3.6 4 64.5 1.132 57 42 100 16 0 5.5 5 46.6 0.971 48 36 90 16 0 5.7 6 75.6 1.129 67 36 70 12 0 4.5 7 41.6 1.040 40 32 100 8 1 5.7 8 24.6 1.070 23 32 90 9 1 5.8 9 74.6 1.114 67 49 100 10 0 4 10 24 1.044 23 30 80 7 1 4.7 11 24.3 1.055 23 41 100 19 1 4.8 12 57.9 1.015 57 52 95 22 0 4.5 13 41.9 1.047 40 30 100 2 1 4.7 14 24.5 1.066 23 32 90 12 1 6 15 23.1 1.005 23 32 80 8 1 4.9 16 41.1 1.027 40 44 90 4 0 5.7 17 71.8 1.259 57 27 55 3 1 3 18 34.2 1.104 31 31 80 11 1 5.6 19 23.8 1.036 23 32 85 1 0 4.6 20 34.3 1.106 31 44 70 16 1 4.8 21 78.5 1.171 67 43 95 13 0 6.3 22 54.9 1.143 48 48 65 6 1 3.8 23 23.3 1.015 23 36 65 6 1 3.3 24 55.9 1.165 48 30 75 9 1 3.8 25 23.7 1.029 23 41 70 4 0 4 26 23.8 1.036 23 22 95 2 1 6.2 27 38.7 0.967 40 35 80 7 0 3.9 28 76.7 1.145 67 44 95 9 1 4.4 29 75.9 1.133 67 52 95 5 0 5.4 30 48.5 1.011 48 45 90 18 0 4.3 31 22.3 0.970 23 29 60 4 1 3.9 32 27 0.871 31 25 95 4 0 5.6 33 61.4 1.077 57 35 90 9 0 5.5 34 27.8 0.898 31 26 80 2 0 4.9 35 22.8 0.992 23 23 90 4 1 5.3 36 24.7 1.075 23 27 75 3 1 4.3 37 23.3 1.014 23 22 95 2 1 6.2 38 56.8 0.997 57 45 95 11 0 4.5 Performance Rating

39 36.1 1.165 31 27 90 6 1 5.5 40 24 1.045 23 24 90 2 0 6.3 41 47.3 1.182 40 25 80 5 0 4.3 42 21.9 0.950 23 32 100 8 1 5.7 43 75.6 1.128 67 42 95 20 1 5.5 44 57.2 1.003 57 45 90 16 0 5.2 45 53.1 1.107 48 36 95 8 1 5.2 46 58.1 1.019 57 39 75 20 0 3.9 47 61 1.071 57 37 95 5 0 5.5 48 64.6 1.134 57 34 90 11 1 5.3 49 66.3 1.163 57 41 95 21 0 6.6 50 57.5 1.008 57 38 80 12 0 4.6