Statistics for Managers Assignment

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Data

ID Sal Compa Mid Age EES SR 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
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
13 42 1.050 40 30 100 2 1 4.7 0 F C
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
17 69 1.210 57 27 55 3 1 3 1 F E
18 36 1.161 31 31 80 11 1 5.6 0 F B
19 24 1.043 23 32 85 1 0 4.6 1 M A
20 34 1.096 31 44 70 16 1 4.8 0 F B
21 76 1.134 67 43 95 13 0 6.3 1 M F
22 57 1.187 48 48 65 6 1 3.8 1 F D
23 23 1.000 23 36 65 6 1 3.3 0 F A
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 1

Week 1. Describing the data.
1. Using the Excel Analysis ToolPak function descriptive statistics, generate descriptive statistics for the salary data.
Which variables does this function not work properly for, even though we have some excel generated results?
2. Sort the data by Gen or Gen 1 (into males and females) and find the mean and standard deviation for each gender for the following variables:
sal, compa, age, sr and raise. Use the descriptive stats function for one gender and the Fx functions (average and stdev) for the other.
3.   What is the probability distribution table for a:
a.       Randomly selected person being a male in a specific grade?
b.      Randomly selected person being in a specific grade?
4. Find:
a. The z score for each male salary, based on only the male salaries.
b. The z score for each female salary, based on only the female salaries.
5. Repeat question 4 for compa for each gender.
6.      What conclusions can you make about the issue of male and female pay equality? Are all of the results consistent? If not, why not?

Week 2

Week 2 Testing means
1 Is either the male or female salary equal to the overall mean salary? (Two hypotheses tests - 1 sample tests)
2 Are the male and female salaries statistically equal to each other?
3 Are the male and female compas equal to each other?
4. If the salary and compa mean tests in questions 3 and 4 provide different equality results,
which would be more appropriate to use in answering the question about salary equity? Why?
5. What other information would you like to know to answer the question about salary equity between the genders? Why?

Week 3

Week 3
1.      Is the average salary 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.
A B C D E F
2.      The factorial ANOVA with only 2 variables can be done with the Analysis ToolPak function 2-Way ANOVA with replication. Set up a data input table like the following:
Grade
Gender A B C D E F
M
F
For each empty cell randomly pick a male or female salary from each grade.
Interpret the results. Are the average salaries for each gender (listed as sample) equal?
Are the average salaries for each grade (listed as column) equal?
3.   Repeat question 2 for the compa values.
Grade
Gender A B C D E F
M
F
For each empty cell randomly pick a male or female salary from each grade.
Interpret the results. Are the average compas for each gender (listed as sample) equal?
Are the average compas for each grade (listed as column) equal?
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?
5.   What are your conclusions about salary equity now?

Week 4

Week 4 Confidence Intervals and Chi Square (CHs 11 - 12) Q1 Q2
Let's look at some other factors that might influence pay. Gr Deg Gen1 Sal
A 0 F 34
1.      Is the probability of having a graduate degree independent of the grade the employee is in? A 0 F 41
C 0 F 77
2.      Construct a 95% confidence interval on the mean service for each gender? Do they intersect? C 0 F 55
D 1 M 77
3.      Are males and females distributed across grades in a similar pattern? D 1 M 60
4.      Do 95% confidence intervals on the mean length of service for each gender intersect?
5.      How do you interpret these results in light of our equity question?

Week 5

Week 5 Correlation and Regression
1.      Create a correlation table for the variables in our data set. (Use analysis ToolPak function Correlation.)
2.   Create a multiple regression equation (using the Analysis ToolPak function Regression) to predict either salary or compa using the mid
(a substitute variable for grade level), age, ees, sr, raise, and deg variables. (Note: since salary and compa are different ways of
expressing an employee’s salary, we do not want to have both used in the same regression.)
3.  Based on all of your results to date, is gender a factor in the pay practices of this company? Why or why not?
4.      In looking at equal pay issues across an entire company, which is a better variable to use – compa or salary? Why?
5.      Why did the single factor tests and analysis (such as t and single factor ANOVA tests on salary equality) not provide a complete answer to our salary equality question?
What outcomes in your life or work might benefit from a multiple regression examination rather than a simpler one varable test?