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 Sal – Salary in thousands
Age – Age in years
EES – Appraisal rating (Employee evaluation score)
SER – Years of service
G – Gender (0 = male, 1 = female)
Mid – salary grade midpoint Raise – percent of last raise
Grade – job/pay grade
Deg (0= BSBA 1 = MS)
Gen1 (Male or Female)
Compa – salary divided by midpoint, a measure of salary that removes the impact of grade
This data should be treated as a sample of employees taken from a company that has about 1,000
employees using a random sampling approach.
Mac Users: The homework in this course assumes students have Windows Excel, and
can load the Analysis ToolPak into their version of Excel.
The analysis tool pak has been removed from Excel for Windows, but a free third-party
tool that can be used (found on an answers Microsoft site) is:
http://www.analystsoft.com/en/products/statplusmacle
Like the Microsoft site, I make cannot guarantee the program, but do know that
Statplus is a respected statistical package. You may use other approaches or tools
as desired to complete the assignments.
Week 1. Describing the data.
<Use right click on the row numbers at the left to insert rows below each question for your results and comments.>
1 Using the Excel Analysis ToolPak function descriptive statistics, generate and show the descriptive statistics for each appropriate variable in the sample data set.
a. For which variables in the data set does this function not work correctly for? Why?
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 either the descriptive stats function or the Fx functions (average and stdev).
3
What is the probability for a:
a.
Randomly selected person being a male in grade E?
b. Randomly selected male being in grade E?
c. Why are the results different?
4
5
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.
c. The z score for each female compa, based on only the female compa values.
d. The z score for each male compa, based on only the male compa values.
e. What do the distributions and spread suggest about male and female salaries?
Why might we want to use compa to measure salaries between males and females?
Based on this sample, what conclusions can you make about the issue of male and female pay equality?
Are all of the results consistent with your conclusion? If not, why not?
W eek 2
Testing means with the t-test
<Note: use right click on row numbers to insert rows to perform analysis below any question>
For questions 2 and 3 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
Below are 2 one-sample t-tests comparing male and female average salaries to the overall sample mean.
Based on our sample, how do you interpret the results and what do these results suggest about the population means for male and female salaries?
Males
Females
Ho: Mean salary = 45
Ho: Mean salary = 45
Ha: Mean salary =/= 45
Ha: Mean salary =/= 45
Note when performing a one sample test with ANOVA, the second variable (Ho) is listed as the same value for every corresponding value in the data set.
t-Test: Two-Sample Assuming Unequal Variances
t-Test: Two-Sample Assuming Unequal Variances
Since the Ho variable has Var = 0, variances are unequal; this test defaults to 1 sample t in this situation
Male
Ho
Female
Ho
Mean
52
45
Mean
38
45
Variance
316
0
Variance
334.6667
0
Observations
25
25
Observations
25
25
Hypothesized Mean Difference 0
Hypothesized Mean Difference
0
df
24
df
24
t Stat
1.968903827
t Stat
-1.91321
P(T<=t) one-tail
0.03030785
P(T<=t) one-tail
0.033862
t Critical one-tail
1.71088208
t Critical one-tail 1.710882
P(T<=t) two-tail
0.060615701
P(T<=t) two-tail
0.067724
t Critical two-tail
2.063898562
t Critical two-tail 2.063899
Conclusion: Do not
Conclusion: Do not
reject Ho; mean
reject Ho; mean
equals 45
equals 45
Males
The way that I interpret the results are that since the p-value =.061 is greater than the alpha = .05 it tells me that there is insufficient evidence to make the claim that the average salary of males is significantly different than the average for all employees.
Females
The way that I interpret the results are that since the p-value =.068 is greater than the alpha = .05 it tells me that there is insufficient evidence to make the claim that the average salary of males is significantly different than the average for all employees.
2
Based on our sample results, perform a 2-sample t-test to see if the population male and female salaries could be equal to each other.
t-Test : Two-sample Assuming equal variances
Male-salay
Female-salary
mean
52
38
Variance
316 334.6667
Observations
25
25
Pooled Variance
325.3333
Hypothesized mean Difference 0
degree of freedom
48
t-Stat
2.744219
0.004253
P(T ? t) one-tail
t Critical one-tail
1.677224
P(T ? t) Two-tail
0.008506
t Critical two-tail
t-Test : Two-sample Assuming Unequal variances
Male-salay emale-salary
F
mean
52
38
Variance
316 334.6667
Observations
25
25
Hypothesized mean Difference
0
degree of freedom
48
t-stat
2.744219
P(T ? t) one-tail
0.004253
t Critical one-tail
1.67724
P(T ? t) Two-tail
0.008506
t Critical two-tail
2.010635
2.010635
Based on the results of the 2-sample t-test the p-value =.008 and being less than alpha which is .05 that tells me that there is sufficient evidence that indicates the average salaries of males and females significantly different.
3
Based on our sample results, can the male and female compas in the population be equal to each other? (Another 2-sample t-test.)
t-Test: Two-Sample Assuming Equal Variances
t-Test: Two-Sample Assuming UnEqual Variances
Male-compa Female-compa
Mean
1.05624
1.06872
Variance
0.007021
0.004948
Observations
25
25
Pooled Variance
0.005984
Hypothesized mean Difference
0
degree of freedom
48
t-Stat
-0.57037
P(T ? t) one-tail
0.285544
t Critical one-tail
1.677224
P(T ? t) Two-tail
0.571088
t Critical two-tail
2.010635
Male-compaemale-compa
F
Mean
1.05624 1.06872
Variance 0.007021 0.004948
Observations
25
25
Hypothesized mean 0
Difference
degree of freedom 48
t-Stat
-0.57037
P(T ? t) one-tail
0.285572
t Critical one-tail
1.677927
P(T ? t) Two-tail
0.571144
t Critical two-tail
2.011741
Based on the sample results the p-value =.571 is greater than the alpha = .05 tells me that there is insufficient
evidence to indicate the average compa’s of males and females are significantly different, which also tells me
that the male and female compass are equal.
4
What other information would you like to know to answer the question about salary equity between the genders? Why?
The other information that would be needed to answer the question is about salary equity between the
genders are, years of service, degree, performance rating, and experience. All of these attributes are important
w hen salaries are negotiated and agreed upon
5
If the salary and compa mean tests in questions 3 and 4 provide different results about male and female salary equality,
w hich would be more appropriate to use in answering the question about salary equity? Why?
What are your conclusions about equal pay at this point?
The mean test in questions 3 & 4 do give different conclusions.
The reason why, is that by using the compa it removes the impact of grade.
In my conclusions the better of the two t-test is the one which compares the comp’s.
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.
Note: Assume equal variances for all grades.
A
B
C
D
E
F
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
The salary values were randomly picked for each cell.
M
24
27
40
47
56
76
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
M
Count
Sum
Average
Variance
B
C
D
E
F
Total
2
49
24.5
0.5
2
55
27.5
0.5
2
87
43.5
24.5
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