# ANOVA and Paired T-test

Week 3 ANOVA and Paired T-test SEE DATA BELOW IN CELL 142 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 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: 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: 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 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: The ongoing question that the weekly assignments will focus on is: Are males and females paid the same for equal work (under the Equal Pay Act)? Note: to simplfy the analysis, we will assume that jobs within each grade comprise equal work. The column labels in the table mean: ID – Employee sample number Salary – Salary in thousands Age – Age in years Performance Rating – Appraisal rating (Employee evaluation score) Service – Years of service (rounded) Gender: 0 = male, 1 = female Midpoint – salary grade midpoint Raise – percent of last raise Grade – job/pay grade Degree (0= BSBA 1 = MS) Gender1 (Male or Female) Compa – salary divided by midpoint 5. Using the results up thru this week, what are your conclusions about gender equal pay for equal work at this point? See comments at the right of the data set. ID Salary Compa Midpoint Age Performance Rating Service Gender Raise Degree Gender1 Grade 8 23 1.000 23 32 90 9 1 5.8 0 F A 10 22 0.956 23 30 80 7 1 4.7 0 F A 11 23 1.000 23 41 100 19 1 4.8 0 F A 14 24 1.043 23 32 90 12 1 6 0 F A 15 24 1.043 23 32 80 8 1 4.9 0 F A 23 23 1.000 23 36 65 6 1 3.3 1 F A 26 24 1.043 23 22 95 2 1 6.2 1 F A 31 24 1.043 23 29 60 4 1 3.9 0 F A 35 24 1.043 23 23 90 4 1 5.3 1 F A 36 23 1.000 23 27 75 3 1 4.3 1 F A 37 22 0.956 23 22 95 2 1 6.2 1 F A 42 24 1.043 23 32 100 8 1 5.7 0 F A 3 34 1.096 31 30 75 5 1 3.6 0 F B 18 36 1.161 31 31 80 11 1 5.6 1 F B 20 34 1.096 31 44 70 16 1 4.8 1 F B 39 35 1.129 31 27 90 6 1 5.5 1 F B 7 41 1.025 40 32 100 8 1 5.7 0 F C 13 42 1.050 40 30 100 2 1 4.7 1 F C 22 57 1.187 48 48 65 6 1 3.8 0 F D 24 50 1.041 48 30 75 9 1 3.8 1 F D 45 55 1.145 48 36 95 8 1 5.2 0 F D 17 69 1.210 57 27 55 3 1 3 0 F E 48 65 1.140 57 34 90 11 1 5.3 1 F E 28 75 1.119 67 44 95 9 1 4.4 1 F F 43 77 1.149 67 42 95 20 1 5.5 1 F F 19 24 1.043 23 32 85 1 0 4.6 1 M A 25 24 1.043 23 41 70 4 0 4 0 M A 40 25 1.086 23 24 90 2 0 6.3 0 M A 2 27 0.870 31 52 80 7 0 3.9 0 M B 32 28 0.903 31 25 95 4 0 5.6 0 M B 34 28 0.903 31 26 80 2 0 4.9 1 M B 16 47 1.175 40 44 90 4 0 5.7 0 M C 27 40 1.000 40 35 80 7 0 3.9 1 M C 41 43 1.075 40 25 80 5 0 4.3 0 M C 5 47 0.979 48 36 90 16 0 5.7 1 M D 30 49 1.020 48 45 90 18 0 4.3 0 M D 1 58 1.017 57 34 85 8 0 5.7 0 M E 4 66 1.157 57 42 100 16 0 5.5 1 M E 12 60 1.052 57 52 95 22 0 4.5 0 M E 33 64 1.122 57 35 90 9 0 5.5 1 M E 38 56 0.982 57 45 95 11 0 4.5 0 M E 44 60 1.052 57 45 90 16 0 5.2 1 M E 46 65 1.140 57 39 75 20 0 3.9 1 M E 47 62 1.087 57 37 95 5 0 5.5 1 M E 49 60 1.052 57 41 95 21 0 6.6 0 M E 50 66 1.157 57 38 80 12 0 4.6 0 M E 6 76 1.134 67 36 70 12 0 4.5 1 M F 9 77 1.149 67 49 100 10 0 4 1 M F 21 76 1.134 67 43 95 13 0 6.3 1 M F 29 72 1.074 67 52 95 5 0 5.4 0 M F

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