Help with Bus 308

See comments at the right of the data set.

ID

Salary

Compa

Midpoint

Age

Performance Rating

Service

Gender

Raise

Degree

Gender1

Grade

8

23

1.000

23

32

90

9

1

5.8

0

F

A

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)?

10

22

0.956

23

30

80

7

1

4.7

0

F

A

Note: to simplfy the analysis, we will assume that jobs within each grade comprise equal work.

11

23

1.000

23

41

100

19

1

4.8

0

F

A

14

24

1.043

23

32

90

12

1

6

0

F

A

The column labels in the table mean:

15

24

1.043

23

32

80

8

1

4.9

0

F

A

ID – Employee sample number

Salary – Salary in thousands

23

23

1.000

23

36

65

6

1

3.3

1

F

A

Age – Age in years

Performance Rating – Appraisal rating (Employee evaluation score)

26

24

1.043

23

22

95

2

1

6.2

1

F

A

Service – Years of service (rounded)

Gender: 0 = male, 1 = female

31

24

1.043

23

29

60

4

1

3.9

0

F

A

Midpoint – salary grade midpoint

Raise – percent of last raise

35

24

1.043

23

23

90

4

1

5.3

1

F

A

Grade – job/pay grade

Degree (0= BS\BA 1 = MS)

36

23

1.000

23

27

75

3

1

4.3

1

F

A

Gender1 (Male or Female)

Compa - salary divided by midpoint

37

22

0.956

23

22

95

2

1

6.2

1

F

A

42

24

1.043

23

32

100

8

1

5.7

0

F

A

3

34

1.096

31

30

75

5

1

3.6

0

F

B

18

36

1.161

31

31

80

11

1

5.6

1

F

B

20

34

1.096

31

44

70

16

1

4.8

1

F

B

39

35

1.129

31

27

90

6

1

5.5

1

F

B

7

41

1.025

40

32

100

8

1

5.7

0

F

C

13

42

1.050

40

30

100

2

1

4.7

1

F

C

22

57

1.187

48

48

65

6

1

3.8

0

F

D

24

50

1.041

48

30

75

9

1

3.8

1

F

D

45

55

1.145

48

36

95

8

1

5.2

0

F

D

17

69

1.210

57

27

55

3

1

3

0

F

E

48

65

1.140

57

34

90

11

1

5.3

1

F

E

28

75

1.119

67

44

95

9

1

4.4

1

F

F

43

77

1.149

67

42

95

20

1

5.5

1

F

F

19

24

1.043

23

32

85

1

0

4.6

1

M

A

25

24

1.043

23

41

70

4

0

4

0

M

A

40

25

1.086

23

24

90

2

0

6.3

0

M

A

2

27

0.870

31

52

80

7

0

3.9

0

M

B

32

28

0.903

31

25

95

4

0

5.6

0

M

B

34

28

0.903

31

26

80

2

0

4.9

1

M

B

16

47

1.175

40

44

90

4

0

5.7

0

M

C

27

40

1.000

40

35

80

7

0

3.9

1

M

C

41

43

1.075

40

25

80

5

0

4.3

0

M

C

5

47

0.979

48

36

90

16

0

5.7

1

M

D

30

49

1.020

48

45

90

18

0

4.3

0

M

D

1

58

1.017

57

34

85

8

0

5.7

0

M

E

4

66

1.157

57

42

100

16

0

5.5

1

M

E

12

60

1.052

57

52

95

22

0

4.5

0

M

E

33

64

1.122

57

35

90

9

0

5.5

1

M

E

38

56

0.982

57

45

95

11

0

4.5

0

M

E

44

60

1.052

57

45

90

16

0

5.2

1

M

E

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

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

6

76

1.134

67

36

70

12

0

4.5

1

M

F

9

77

1.149

67

49

100

10

0

4

1

M

F

21

76

1.134

67

43

95

13

0

6.3

1

M

F

29

72

1.074

67

52

95

5

0

5.4

0

M

F

Score:

Week 3

ANOVA and Paired T-test

At this point we know the following about male and female salaries.

a.

Male and female overall average salaries are not equal in the population.

b.

Male and female overall average compas are equal in the population, but males are a bit more spread out.

c.

The male and female salary range are almost the same, as is their age and service.

d.

Average performance ratings per gender are equal.

Let's look at some other factors that might influence pay - education(degree) and performance ratings.

<1 point>

1

Last week, we found that average performance ratings do not differ between males and females in the population.

Now we need to see if they differ among the grades. Is the average performace rating the same for all grades?

(Assume variances are equal across the grades for this ANOVA.)

You can use these columns to place grade Perf Ratings if desired.

A

B

C

D

E

F

Null Hypothesis:

Alt. Hypothesis:

Place B17 in Outcome range box.

Interpretation:

What is the p-value:

Is P-value < 0.05?

Do we REJ or Not reject the null?

was rejected, what is the effect size value (eta squared):

If the null hypothesis

Meaning of effect size measure:

What does that decision mean in terms of our equal pay question:

<1 point>

2

While it appears that average salaries per each grade differ, we need to test this assumption.

Is the average salary the same for each of the grade levels? ANOVA.)

(Assume equal variance, and use the analysis toolpak function

Use the input table to the right to list salaries under each grade level.

Null Hypothesis:

If desired, place salaries per grade in these columns

Alt. Hypothesis:

A

B

C

D

E

F

Place B55 in Outcome range box.

What is the p-value:

Is P-value < 0.05?

Do you reject or not reject the null hypothesis:

If the null hypothesis was rejected

Interpretation:

<1 point>

3

The table and analysis below demonstrate a 2-way ANOVA.

with replication. Please interpret the results

BA

MA

Ho: Average compas by gender are equal

Male

1.017

1.157

Ha: Average compas by gender are not equal

0.870

0.979

Ho: Average compas are equal for each degree

1.052

1.134

Ha: Average compas are not equal for each degree

1.175

1.149

Ho: Interaction is not significant

1.043

1.043

Ha: Interaction is significant

1.074

1.134

1.020

1.000

Perform analysis:

0.903

1.122

0.982

0.903

Anova: Two-Factor With Replication

1.086

1.052

1.075

1.140

SUMMARY

BA

MA

Total

1.052

1.087

Male

Female

1.096

1.050

Count

12

12

24

1.025

1.161

Sum

12.349

12.9

25.249

1.000

1.096

Average

1.02908333

1.075

1.052042

0.956

1.000

Variance

0.00668645

0.00652

0.006866

1.000

1.041

1.043

1.043

Female

1.043

1.119

Count

12

12

24

1.210

1.043

Sum

12.791

12.787

25.578

1.187

1.000

Average

1.06591667

1.065583

1.06575

1.043

0.956

Variance

0.00610245

0.004213

0.004933

1.043

1.129

1.145

1.149

Total

Count

24

24

Sum

25.14

25.687

Average

1.0475

1.070292

Variance

0.00647035

0.005156

ANOVA

Source of Variation

SS

df

MS

F

P-value

F crit

0.00225502

1

0.002255

0.383482

0.538939

4.061706

(This is the row variable or gender.)

Columns

0.00623352

1

0.006234

1.060054

0.30883

4.061706

(This is the column variable or Degree.)

Interaction

0.00641719

1

0.006417

1.091288

0.301892

4.061706

Within

0.25873675

44

0.00588

Columns

Total

0.27364248

47

Interpretation:

If the null hypothesis was rejected, what

What is the p-value:

Is P-value < 0.05?

Do you reject or not reject the null hypothesis:

is the effect size value (eta squared):

Meaning of effect size measure:

For Ho: Average compas are equal for all degrees Ha: Average compas are not equal for all grades

What is the p-value:

Is P-value < 0.05?

Do you reject or not reject the null hypothesis:

s the effect size value (eta squared):

If the null hypothesis was rejected, what i

Meaning of effect size measure:

For: Ho: Interaction is not significant

Ha: Interaction is significant

What is the p-value:

Is P-value < 0.05?

Do you reject or not reject the null hypothesis:

ect size value (eta squared):

If the null hypothesis was rejected, what is the eff

Meaning of effect size measure:

What do these decisions mean in terms of our equal pay

n in terms of our equal pay question:

Place data values in these columns

<1 point>

4

Salary

Midpoint

Many companies consider the grade midpoint to be the "market rate" - what is needed to hire a new employee.

Does the company, on average, pay its existing employees at or above the market rate?

Null Hypothesis:

Alt. Hypothesis:

Statistical test to use:

Place the cursor in B160 for test.

What is the p-value:

Is P-value < 0.05?

What else needs to be checked on a 1-tail in order to reject the null?