# AU Statistical Differences in Pay Between Men and Women Worksheet

ID1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

Salary Compa- Midpoint

ratio

55.6

27.2

35

59.5

48.3

76.7

41.4

21.8

75.8

23.9

23.3

61.2

42.5

23.8

22.8

42.6

65.9

34.6

25.6

34.2

73.1

56.1

22.9

54.6

24.8

22.8

45.5

76

77.5

45.5

24.3

27.5

55.9

27.7

23.5

23.6

22.9

59.5

35.9

23.8

0.976

0.877

1.128

1.044

1.007

1.145

1.035

0.949

1.132

1.040

1.014

1.073

1.063

1.033

0.993

1.066

1.156

1.115

1.114

1.102

1.091

1.169

0.994

1.137

1.080

0.990

1.137

1.134

1.157

0.948

1.058

0.888

0.981

0.895

1.021

1.026

0.996

1.044

1.159

1.036

57

31

31

57

48

67

40

23

67

23

23

57

40

23

23

40

57

31

23

31

67

48

23

48

23

23

40

67

67

48

23

31

57

31

23

23

23

57

31

23

Age

34

52

30

42

36

36

32

32

49

30

41

52

30

32

32

44

27

31

32

44

43

48

36

30

41

22

35

44

52

45

29

25

35

26

23

27

22

45

27

24

Performance Service Gender

Rating

85

80

75

100

90

70

100

90

100

80

100

95

100

90

80

90

55

80

85

70

95

65

65

75

70

95

80

95

95

90

60

95

90

80

90

75

95

95

90

90

8

7

5

16

16

12

8

9

10

7

19

22

2

12

8

4

3

11

1

16

13

6

6

9

4

2

7

9

5

18

4

4

9

2

4

3

2

11

6

2

0

0

1

0

0

0

1

1

0

1

1

0

1

1

1

0

1

1

0

1

0

1

1

1

0

1

0

1

0

0

1

0

0

0

1

1

1

0

1

0

Raise Degree Gender1

5.7

3.9

3.6

5.5

5.7

4.5

5.7

5.8

4

4.7

4.8

4.5

4.7

6

4.9

5.7

3

5.6

4.6

4.8

6.3

3.8

3.3

3.8

4

6.2

3.9

4.4

5.4

4.3

3.9

5.6

5.5

4.9

5.3

4.3

6.2

4.5

5.5

6.3

0

0

1

1

1

1

1

1

1

1

1

0

0

1

1

0

1

0

1

0

1

1

0

0

0

0

1

0

0

0

1

0

1

1

0

0

0

0

0

0

M

M

F

M

M

M

F

F

M

F

F

M

F

F

F

M

F

F

M

F

M

F

F

F

M

F

M

F

M

M

F

M

M

M

F

F

F

M

F

M

41

42

43

44

45

46

47

48

49

50

40.1

23.3

76.1

69.7

52.8

61.5

62.3

70.2

62

59.1

1.003

1.014

1.136

1.222

1.100

1.079

1.093

1.232

1.088

1.036

40

23

67

57

48

57

57

57

57

57

25

32

42

45

36

39

37

34

41

38

80

100

95

90

95

75

95

90

95

80

5

8

20

16

8

20

5

11

21

12

0

1

1

0

1

0

0

1

0

0

4.3

5.7

5.5

5.2

5.2

3.9

5.5

5.3

6.6

4.6

0

1

0

1

1

1

1

1

0

0

M

F

F

M

F

M

M

F

M

M

Grade

E

B

B

E

D

F

C

A

F

A

A

E

C

A

A

C

E

B

A

B

F

D

A

D

A

A

C

F

F

D

A

B

E

B

A

A

A

E

B

A

Do not manipuilate Data set on this page, copy

to another page to make changes

The ongoing question that the weekly assignments will focus on is: Are males and females paid the same

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 scor

Service – Years of service (rounded)

Gender – 0 = male, 1 = female

Midpoint – salary grade midpointRaise – percent of last raise

Grade – job/pay grade

Degree (0= BS\BA 1 = MS)

Gender1 (Male or Female)

Compa-ratio – salary divided by midpoint

C

A

F

E

D

E

E

E

E

E

Week 1: Descriptive Statistics, including Probability

While the lectures will examine our equal pay question from the compa-ratio viewpoint, our weekly assignments will

examining the issue using the salary measure.

The purpose of this assignmnent is two fold:

1. Demonstrate mastery with Excel tools.

2. Develop descriptive statistics to help examine the question.

3. Interpret descriptive outcomes

The first issue in examining salary data to determine if we – as a company – are paying males and females equally for

descriptive statistics to give us something to make a preliminary decision on whether we have an issue or not.

1

Descriptive Statistics: Develop basic descriptive statistics for Salary

The first step in analyzing data sets is to find some summary descriptive statistics for key variables.

Suggestion: Copy the gender1 and salary columns from the Data tab to columns T and U at the right.

Then use Data Sort (by gender1) to get all the male and female salary values grouped together.

a.

Use the Descriptive Statistics function in the Data Analysis tab

to develop the descriptive statistics summary for the overall

group’s overall salary. (Place K19 in output range.)

Highlight the mean, sample standard deviation, and range.

Using Fx (or formula) functions find the following (be sure to show the formula

and not just the value in each cell) asked for salary statistics for each gender:

Male

Female

Mean:

Sample Standard Deviation:

Range:

b.

2

Develop a 5-number summary for the overall, male, and female SALARY variable.

For full credit, show the excel formulas in each cell rather than simply the numerical answer.

Overall Males

Females

Max

3rd Q

Midpoint

1st Q

Min

3

Location Measures: comparing Male and Female midpoints to the overall Salary data range.

For full credit, show the excel formulas in each cell rather than simply the numerical answer.

Male

Using the entire Salary range and the M and F midpoints found in Q2

a. What would each midpoint’s percentile rank be in the overall range?

b. What is the normal curve z value for each midpoint within overall range?

4

Probability Measures: comparing Male and Female midpoints to the overall Salary data range

For full credit, show the excel formulas in each cell rather than simply the numerical answer.

Male

Using the entire Salary range and the M and F midpoints found in Q2, find

a. The Empirical Probability of equaling or exceeding (=>) that value for

b. The Normal curve Prob of => that value for each group

5

Conclusions: What do you make of these results? Be sure to include findings from this week’s lectures a

In comparing the overall, male, and female outcomes, what relationship(s) see, to exist between the data se

What does this suggest about our equal pay for equal work question?

our weekly assignments will focus on

ales and females equally for doing equal work is to develop some

ics for key variables.

s T and U at the right.

Place Excel outcome in Cell K19

ary data range.

merical answer.

Female

Use Excel’s =PERCENTRANK.EXC function

Use Excel’s =STANDARDIZE function

Salary data range

merical answer.

Female

Show the calculation formula = value/50 or =countif(range,”>=”&cell)/50

Use “=1-NORM.S.DIST” function

s from this week’s lectures as well.

to exist between the data sets?

Gender1

F

F

F

F

F

F

F

F

F

F

F

F

F

F

F

F

F

F

F

F

F

F

F

F

F

M

M

M

M

M

M

M

M

M

M

M

M

M

M

M

M

M

M

Salary

35

41.4

21.8

23.9

23.3

42.5

23.8

22.8

65.9

34.6

34.2

56.1

22.9

54.6

22.8

76

24.3

23.5

23.6

22.9

35.9

23.3

76.1

52.8

70.2

55.6

27.2

59.5

48.3

76.7

75.8

61.2

42.6

25.6

73.1

24.8

45.5

77.5

45.5

27.5

55.9

27.7

59.5

M

M

M

M

M

M

M

23.8

40.1

69.7

61.5

62.3

62

59.1

Week 2: Identifying Significant Differences – part 1

To Ensure full credit for each question, you need to show how you got your results. This involves either showing wh

or showing the excel formula in each cell.

Be sure to copy the appropriate data columns from the data tab to

As with our examination of compa-ratio in the lecture, the first question we have about salary between the genders in

What we do, depends upon our findings.

1

As with the compa-ratio lecture example, we want to examine salary variation within the groups – are they

a

What is the data input ranged used for this question:

b

c.

Which is needed for this question: a one- or two-tail hypothesis statement and test ?

Answer:

Why:

Step 1:

Step 2:

Step 3:

Step 4:

Step 5:

Ho:

Ha:

Significance (Alpha):

Test Statistic and test:

Why this test?

Decision rule:

Conduct the test – place test function in cell k10

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 variance in the

population for male and female salaries?

2

Once we know about variance quality, we can move on to means: Are male and female average salaries eq

(Regardless of the outcome of the above F-test, assume equal variances for this test.)

c.

a

What is the data input ranged used for this question:

b

Does this question need a one or two-tail hypothesis statement and test?

Why:

Ho:

Ha:

Significance (Alpha):

Test Statistic and test:

Why this test?

Decision rule:

Conduct the test – place test function in cell K35

Step 1:

Step 2:

Step 3:

Step 4:

Step 5:

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 means in the population for

male and female salaries?

3

Education is often a factor in pay differences.

Do employees with an advanced degree (degree = 1) have higher average salaries?

Note: assume equal variance for the salaries in each degree for this question.

a

What is the data input ranged used for this question:

b

c.

Step 1:

Step 2:

Step 3:

Step 4:

Step 5:

Does this question need a one or two-tail hypothesis statement and test?

Why:

Ho:

Ha:

Significance (Alpha):

Test Statistic and test:

Why this test?

Decision rule:

Conduct the test – place test function in cell K60

Step 6: Conclusion and Interpretation

What is the p-value:

Is the t value in the t-distribution tail indicated by the

arrow in the Ha claim?

What is your decision: REJ or NOT reject the null?

Why?

What is your conclusion about the impact of education on

average salaries?

4

Considering both the compa-ratio information from the lectures and your salary information, what conclus

Why – what statistical results support this conclusion?

lves either showing where the data you used is located

mns from the data tab to the right for your use this week.

between the genders involves equality – are they the same or different?

Use Cell K10 for the Excel test outcome location.

Use Cell K35 for the Excel test outcome location.

Use Cell K60 for the Excel test outcome location.

ormation, what conclusions can you reach about equal pay for equal work?

Week 3: Identifying Significant Differences – part 2

To Ensure full credit for each question, you need to show how you got your results. This involves either showing wh

or showing the excel formula in each cell.

Be sure to copy the appropriate data columns from

1

A good pay program will have different average salaries by grade. Is this the case for our company?

a

What is the data input ranged used for this question:

Note: assume equal variances for each grade, even though this may not be accurate, for purposes of this question.

b.

Step 1:

Step 2:

Step 3:

Step 4:

Step 5:

Ho:

Ha:

Significance (Alpha):

Test Statistic and test:

Why this test?

Decision rule:

Conduct the test – place test function in cell K08

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 means in the

population for grade salaries?

2

If the null hypothesis in question 1 was rejected, which pairs of means differ?

(Use the values from the ANOVA table to complete the follow table.)

Groups

Compared

Mean Diff.

T value used +/- Term

Low

A-B

A-C

A-D

A-E

A-F

B-C

B-D

B-E

B-E

C-D

C-E

C-F

D-E

D-F

E-F

3

One issue in salary is the grade an employee is in – higher grades have higher salaries.

This suggests that one question to ask is if males and females are distributed in a similar pattern across the

a

What is the data input ranged used for this question:

b.

Step 1:

Step 2:

Step 3:

Step 4:

Step 5:

Ho:

Ha:

Significance (Alpha):

Test Statistic and test:

Why this test?

Decision rule:

Conduct the test – place test function in cell K54

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 means in the

population for male and female salaries?

4

What implications do this week’s analysis have for our equal pay question?

Why – what statistical results support this conclusion?

This involves either showing where the data you used is located

he appropriate data columns from the data tab to the right for your use this week.

he case for our company?

Use Cell K08 for the Excel test outcome location.

ate, for purposes of this question.

to

High

Difference

Significant? Why?

Use Cell K54 for the Excel test outcome location.

Place the actual distribution in the table below.

A

B

C

D

Male

Female

E

Place the expected distribution in the table below.

A

B

C

D

E

Male

Female

Data Input Table:

Group name:

List salaries within each grade

A

B

Salary Range Groups

C

D

F

F

nge Groups

E

F

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 wh

or showing the excel formula in each cell.

Be sure to copy the appropriate data columns from the data t

1

What is the correlation between and among the interval/ratio level variables with salary? (Do not include c

a. Create the correlation table.

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 cor

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 wi

our two dummy variables – gender and education. Show the result, and interpret your findings by answerin

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 ex

a.

What is the data input ranged used for this question:

b.

Step 1: State the appropriate hypothesis statements:

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 coeff

Step 1: State the appropriate coefficient hypothesis statements:

(Write a single pair, we

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 a

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,

Midpoint

Age

Perf. Rat. Seniority

Raise

Gender

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 wou

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?

lves either showing where the data you used is located

olumns from the data tab to the right for your use this week.

lary? (Do not include compa-ratio in this question.)

Use Cell K08 for the Excel test outcome location.

, or non significant correlations you thought would be?

es used in Q1 along with

ur findings by answering the following questions.

r possible variables except compa-ratio?

Use Cell M34 for the Excel test outcome location.

ch of the variable coefficients.

Write a single pair, we will use it for each variable separately.)

he Regression output above.

If you reject the null, place the coefficient in the table.

Degree

s the equation?

things being equal?

d results, what else would you like to know