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equal_pay___student_rev_4_3_2.xls
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Data

ID Sal Compa Mid Age EES SER G Raise Deg Gen1 Gr
1 58 1.017 57 34 85 8 0 5.7 0 M E 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)?
2 27 0.870 31 52 80 7 0 3.9 0 M B Note: to simplfy the analysis, we will assume that jobs within each grade comprise equal work.
3 34 1.096 31 30 75 5 1 3.6 1 F B
4 66 1.157 57 42 100 16 0 5.5 1 M E The column labels in the table mean:
5 47 0.979 48 36 90 16 0 5.7 1 M D ID – Employee sample number Sal – Salary in thousands
6 76 1.134 67 36 70 12 0 4.5 1 M F Age – Age in years EES – Appraisal rating (Employee evaluation score)
7 41 1.025 40 32 100 8 1 5.7 1 F C SER – Years of service G – Gender (0 = male, 1 = female)
8 23 1.000 23 32 90 9 1 5.8 1 F A Mid – salary grade midpoint Raise – percent of last raise
9 77 1.149 67 49 100 10 0 4 1 M F Grade – job/pay grade Deg (0= BS\BA 1 = MS)
10 22 0.956 23 30 80 7 1 4.7 1 F A Gen1 (Male or Female) Compa - salary divided by midpoint, a measure of salary that removes the impact of grade
11 23 1.000 23 41 100 19 1 4.8 1 F A
12 60 1.052 57 52 95 22 0 4.5 0 M E This data should be treated as a sample of employees taken from a company that has about 1,000
13 42 1.050 40 30 100 2 1 4.7 0 F C employees using a random sampling approach.
14 24 1.043 23 32 90 12 1 6 1 F A
15 24 1.043 23 32 80 8 1 4.9 1 F A
16 47 1.175 40 44 90 4 0 5.7 0 M C Mac Users: The homework in this course assumes students have Windows Excel, and
17 69 1.210 57 27 55 3 1 3 1 F E can load the Analysis ToolPak into their version of Excel.
18 36 1.161 31 31 80 11 1 5.6 0 F B The analysis tool pak has been removed from Excel for Windows, but a free third-party
19 24 1.043 23 32 85 1 0 4.6 1 M A tool that can be used (found on an answers Microsoft site) is:
20 34 1.096 31 44 70 16 1 4.8 0 F B http://www.analystsoft.com/en/products/statplusmacle
21 76 1.134 67 43 95 13 0 6.3 1 M F Like the Microsoft site, I make cannot guarantee the program, but do know that
22 57 1.187 48 48 65 6 1 3.8 1 F D Statplus is a respected statistical package. You may use other approaches or tools
23 23 1.000 23 36 65 6 1 3.3 0 F A as desired to complete the assignments.
24 50 1.041 48 30 75 9 1 3.8 0 F D
25 24 1.043 23 41 70 4 0 4 0 M A
26 24 1.043 23 22 95 2 1 6.2 0 F A
27 40 1.000 40 35 80 7 0 3.9 1 M C
28 75 1.119 67 44 95 9 1 4.4 0 F F
29 72 1.074 67 52 95 5 0 5.4 0 M F
30 49 1.020 48 45 90 18 0 4.3 0 M D
31 24 1.043 23 29 60 4 1 3.9 1 F A
32 28 0.903 31 25 95 4 0 5.6 0 M B
33 64 1.122 57 35 90 9 0 5.5 1 M E
34 28 0.903 31 26 80 2 0 4.9 1 M B
35 24 1.043 23 23 90 4 1 5.3 0 F A
36 23 1.000 23 27 75 3 1 4.3 0 F A
37 22 0.956 23 22 95 2 1 6.2 0 F A
38 56 0.982 57 45 95 11 0 4.5 0 M E
39 35 1.129 31 27 90 6 1 5.5 0 F B
40 25 1.086 23 24 90 2 0 6.3 0 M A
41 43 1.075 40 25 80 5 0 4.3 0 M C
42 24 1.043 23 32 100 8 1 5.7 1 F A
43 77 1.149 67 42 95 20 1 5.5 0 F F
44 60 1.052 57 45 90 16 0 5.2 1 M E
45 55 1.145 48 36 95 8 1 5.2 1 F D
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
48 65 1.140 57 34 90 11 1 5.3 1 F 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

Week 3

Week 3 Testing multiple means with ANOVA <Note: use right click on row numbers to insert rows to perform analysis below any question>
For questions 3 and 4 below, be sure to list the null and alternate hypothesis statements. Use .05 for your significance level in making your decisions.
For full credit, you need to also show the statistical outcomes - either the Excel test result or the calculations you performed.
1.      Based on the sample data, can the average(mean) salary in the population be the same for each of the grade levels? (Assume equal variance, and use the analysis toolpak function ANOVA.)
Set up the input table/range to use as follows: Put all of the salary values for each grade under the appropriate grade label.
Be sure to incllude the null and alternate hypothesis along with the statistical test and result.
A B C D E F Note: Assume equal variances for all grades.
2.      The table and analysis below demonstrate a 2-way ANOVA with replication. Please interpret the results.
Grade
Gender A B C D E F
M 24 27 40 47 56 76 The salary values were randomly picked for each cell.
25 28 47 49 66 77
F 22 34 41 50 65 75
24 36 42 57 69 77
Ho: Average salaries are equal for all grades
Ha: Average salaries are not equal for all grades
Ho: Average salaries by gender are equal
Ha: Average salaries by gender are not equal
Ho: Interaction is not significant
Ha: Interaction is significant
Perform analysis:
Anova: Two-Factor With Replication
SUMMARY A B C D E F Total
M
Count 2 2 2 2 2 2 12
Sum 49 55 87 96 122 153 562
Average 24.5 27.5 43.5 48 61 76.5 46.8333333333
Variance 0.5 0.5 24.5 2 50 0.5 364.5151515152
F
Count 2 2 2 2 2 2 12
Sum 46 70 83 107 134 152 592
Average 23 35 41.5 53.5 67 76 49.3333333333
Variance 2 2 0.5 24.5 8 2 367.3333333333
Total
Count 4 4 4 4 4 4
Sum 95 125 170 203 256 305
Average 23.75 31.25 42.5 50.75 64 76.25
Variance 1.5833333333 19.5833333333 9.6666666667 18.9166666667 31.3333333333 0.9166666667
ANOVA
Source of Variation SS df MS F P-value F crit
Sample 37.5 1 37.5 3.8461538462 0.0734833371 4.7472253467
Columns 7841.8333333333 5 1568.3666666667 160.8581196581 0.0000000001 3.1058752391 Note: a number with an E after it (E9 or E-6, for example)
Interaction 91.5 5 18.3 1.8769230769 0.1723082608 3.1058752391 means we move the decimal point that number of places.
Within 117 12 9.75 For example, 1.2E4 becomes 12000; while 4.56E-5 becomes 0.0000456
Total 8087.8333333333 23
Do we reject or not reject each of the null hypotheses? What do your conclusions mean about the population values being tested?
Interpretation:
3.    Using our sample results, can we say that the compa values in the population are equal by grade and/or gender, and are independent of each factor?
Grade Be sure to include the null and alternate hypothesis along with the statistical test and result.
Gender A B C D E F <Randomly pick compas to fill each cell - for exampe, a compa
M for the intersection of M and A might be 1.043.>
<If desired, you can use the compa values that relate to the
F salary values used in question 2 for a more direct comparison of the two
outcomes.>
Conduct and show the results of a 2-way ANOVA with replication using the completed table above. The results should look something like those in question 2.
Interpret the results. Are the average compas for each gender (listed as sample) equal? For each grade? Do grade and gender interaction impact compa values?
4.   Pick any other variable you are interested in and do a simple 2-way ANOVA without replication. Why did you pick this variable and what do the results show?
Variable name: Be sure to include the null and alternate hypothesis along with the statistical test and result.
Gender A B C D E F
M Hint: use mean values in the boxes.
F
5.   Using the results for this week, What are your conclusions about gender equal pay for equal work at this point?