Week 4 Problem set

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Week4ProblemSet.xlsx
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Data

ID Salary Compa-ratio Midpoint Age Performance Rating Service Gender Raise Degree Gender1 Grade Do not manipuilate Data set on this page, copy to another page to make changes
1 62.5 1.096 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 27.8 0.897 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 35.9 1.158 31 30 75 5 1 3.6 1 F B
4 65.4 1.147 57 42 100 16 0 5.5 1 M E The column labels in the table mean:
5 49.1 1.023 48 36 90 16 0 5.7 1 M D ID – Employee sample number Salary – Salary in thousands
6 75.6 1.129 67 36 70 12 0 4.5 1 M F Age – Age in years Performance Rating - Appraisal rating (employee evaluation score)
7 40.2 1.005 40 32 100 8 1 5.7 1 F C Service – Years of service (rounded) Gender – 0 = male, 1 = female
8 23.3 1.013 23 32 90 9 1 5.8 1 F A Midpoint – salary grade midpoint Raise – percent of last raise
9 78.5 1.171 67 49 100 10 0 4 1 M F Grade – job/pay grade Degree (0= BS\BA 1 = MS)
10 22.9 0.997 23 30 80 7 1 4.7 1 F A Gender1 (Male or Female) Compa-ratio - salary divided by midpoint
11 24.2 1.050 23 41 100 19 1 4.8 1 F A
12 64 1.122 57 52 95 22 0 4.5 0 M E
13 40.8 1.021 40 30 100 2 1 4.7 0 F C
14 24.1 1.046 23 32 90 12 1 6 1 F A
15 23.8 1.034 23 32 80 8 1 4.9 1 F A
16 40.9 1.023 40 44 90 4 0 5.7 0 M C
17 66.5 1.167 57 27 55 3 1 3 1 F E
18 35.2 1.136 31 31 80 11 1 5.6 0 F B
19 23.9 1.039 23 32 85 1 0 4.6 1 M A
20 33.5 1.080 31 44 70 16 1 4.8 0 F B
21 74.2 1.107 67 43 95 13 0 6.3 1 M F
22 55.8 1.162 48 48 65 6 1 3.8 1 F D
23 23 1.001 23 36 65 6 1 3.3 0 F A
24 55.9 1.164 48 30 75 9 1 3.8 0 F D
25 25 1.085 23 41 70 4 0 4 0 M A
26 22.6 0.983 23 22 95 2 1 6.2 0 F A
27 46.3 1.157 40 35 80 7 0 3.9 1 M C
28 75.2 1.122 67 44 95 9 1 4.4 0 F F
29 77.8 1.161 67 52 95 5 0 5.4 0 M F
30 45.6 0.949 48 45 90 18 0 4.3 0 M D
31 22.8 0.991 23 29 60 4 1 3.9 1 F A
32 28.7 0.927 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 27.9 0.899 31 26 80 2 0 4.9 1 M B
35 23.8 1.034 23 23 90 4 1 5.3 0 F A
36 22.7 0.987 23 27 75 3 1 4.3 0 F A
37 23.7 1.032 23 22 95 2 1 6.2 0 F A
38 60.7 1.065 57 45 95 11 0 4.5 0 M E
39 36.2 1.169 31 27 90 6 1 5.5 0 F B
40 24.3 1.058 23 24 90 2 0 6.3 0 M A
41 41.4 1.035 40 25 80 5 0 4.3 0 M C
42 23 1.001 23 32 100 8 1 5.7 1 F A
43 75.7 1.130 67 42 95 20 1 5.5 0 F F
44 61 1.071 57 45 90 16 0 5.2 1 M E
45 54.8 1.141 48 36 95 8 1 5.2 1 F D
46 62 1.087 57 39 75 20 0 3.9 1 M E
47 61 1.071 57 37 95 5 0 5.5 1 M E
48 71.6 1.257 57 34 90 11 1 5.3 1 F E
49 60.6 1.063 57 41 95 21 0 6.6 0 M E
50 57.7 1.012 57 38 80 12 0 4.6 0 M E

Week 4

Week 4: Identifying relationships - correlations and regression
To Ensure full credit for each question, you need to show how you got your results. This involves either showing where the data you used is located
or showing the excel formula in each cell. Be sure to copy the appropriate data columns from the data tab to the right for your use this week.
1 What is the correlation between and among the interval/ratio level variables with salary? (Do not include compa-ratio in this question.)
a. Create the correlation table. Use Cell K08 for the Excel test outcome location.
i. What is the data input ranged used for this question:
ii. Create a correlation table in cell K08.
b. Technically, we should perform a hypothesis testing on each correlation to determine
if it is significant or not. However, we can be faithful to the process and save some
time by finding the minimum correlation that would result in a two tail rejection of the null.
We can then compare each correlation to this value, and those exceeding it (in either a
positive or negative direction) can be considered statistically significant.
i. What is the t-value we would use to cut off the two tails? T =
ii. What is the associated correlation value related to this t-value? r =
c. What variable(s) is(are) significantly correlated to salary?
d. Are there any surprises - correlations you though would be significant and are not, or non significant correlations you thought would be?
e. Why does or does not this information help answer our equal pay question?
2 Perform a regression analysis using salary as the dependent variable and the variables used in Q1 along with
our two dummy variables - gender and education. Show the result, and interpret your findings by answering the following questions.
Suggestion: Add the dummy variables values to the right of the last data columns used for Q1.
What is the multiple regression equation predicting/explaining salary using all of our possible variables except compa-ratio?
a. What is the data input ranged used for this question:
b. Step 1: State the appropriate hypothesis statements: Use Cell M34 for the Excel test outcome location.
Ho:
Ha:
Step 2: Significance (Alpha):
Step 3: Test Statistic and test:
Why this test?
Step 4: Decision rule:
Step 5: Conduct the test - place test function in cell M34
Step 6: Conclusion and Interpretation
What is the p-value:
What is your decision: REJ or NOT reject the null?
Why?
What is your conclusion about the factors influencing the population salary values?
c. If we rejected the null hypothesis, we need to test the significance of each of the variable coefficients.
Step 1: State the appropriate coefficient hypothesis statements: (Write a single pair, we will use it for each variable separately.)
Ho:
Ha:
Step 2: Significance (Alpha):
Step 3: Test Statistic and test:
Why this test?
Step 4: Decision rule:
Step 5: Conduct the test
Note, in this case the test has been performed and is part of the Regression output above.
Step 6: Conclusion and Interpretation
Place the t and p-values in the following table
Identify your decision on rejecting the null for each variable. If you reject the null, place the coefficient in the table.
Midpoint Age Perf. Rat. Seniority Raise Gender Degree
t-value:
P-value:
Rejection Decision:
If Null is rejected, what is the variable's coefficient value?
Using the intercept coefficient and only the significant variables, what is the equation?
Salary =
d. Is gender a significant factor in salary?
e. Regardless of statistical significance, who gets paid more with all other things being equal?
f. How do we know?
3 After considering the compa-ratio based results in the lectures and your salary based results, what else would you like to know
before answering our question on equal pay? Why?
4 Between the lecture results and your results, what is your answer to the question
of equal pay for equal work for males and females? Why?
5 What does regression analysis show us about analyzing complex measures?