BUS 308 Weeks 1

5/20/2018 BUS 308 Weeks 1

1/43

See comments at the right of the data set.

ID Salary Compa Midpoint Age Performanc

e Rating

Service Gender Raise

8 23 1.000 23 32 90 9 1 5.8

10 22 0.956 23 30 80 7 1 4.7

11 23 1.000 23 41 100 19 1 4.8

14 24 1.043 23 32 90 12 1 6

15 24 1.043 23 32 80 8 1 4.9

23 23 1.000 23 36 65 6 1 3.3

26 24 1.043 23 22 95 2 1 6.2

31 24 1.043 23 29 60 4 1 3.9

35 24 1.043 23 23 90 4 1 5.3

36 23 1.000 23 27 75 3 1 4.3

37 22 0.956 23 22 95 2 1 6.2

42 24 1.043 23 32 100 8 1 5.7

3 34 1.096 31 30 75 5 1 3.6

18 36 1.161 31 31 80 11 1 5.6

20 34 1.096 31 44 70 16 1 4.8

39 35 1.129 31 27 90 6 1 5.5

7 41 1.025 40 32 100 8 1 5.7

13 42 1.050 40 30 100 2 1 4.7

22 57 1.187 48 48 65 6 1 3.8

24 50 1.041 48 30 75 9 1 3.8

45 55 1.145 48 36 95 8 1 5.2

17 69 1.210 57 27 55 3 1 3

48 65 1.140 57 34 90 11 1 5.3

28 75 1.119 67 44 95 9 1 4.4

43 77 1.149 67 42 95 20 1 5.5

19 24 1.043 23 32 85 1 0 4.6

25 24 1.043 23 41 70 4 0 4

40 25 1.086 23 24 90 2 0 6.3

2 27 0.870 31 52 80 7 0 3.9

32 28 0.903 31 25 95 4 0 5.6

34 28 0.903 31 26 80 2 0 4.9

16 47 1.175 40 44 90 4 0 5.7

27 40 1.000 40 35 80 7 0 3.9

41 43 1.075 40 25 80 5 0 4.3

5 47 0.979 48 36 90 16 0 5.7

30 49 1.020 48 45 90 18 0 4.3

1 58 1.017 57 34 85 8 0 5.7

4 66 1.157 57 42 100 16 0 5.5

12 60 1.052 57 52 95 22 0 4.5

5/20/2018 BUS 308 Weeks 1

2/43

33 64 1.122 57 35 90 9 0 5.5

38 56 0.982 57 45 95 11 0 4.5

44 60 1.052 57 45 90 16 0 5.2

46 65 1.140 57 39 75 20 0 3.9

47 62 1.087 57 37 95 5 0 5.5

49 60 1.052 57 41 95 21 0 6.6

50 66 1.157 57 38 80 12 0 4.6

6 76 1.134 67 36 70 12 0 4.5

9 77 1.149 67 49 100 10 0 4

21 76 1.134 67 43 95 13 0 6.3

29 72 1.074 67 52 95 5 0 5.4

5/20/2018 BUS 308 Weeks 1

3/43

Degree Gender1 Grade

0 F A The ongoing question that the weekly assignments will focus on i

0 F A Note: to simplfy the analysis, we will assume that jobs within each

0 F A

0 F A The column labels in the table mean:

0 F A ID Employee sample number Salary Salary in th

1 F A Age Age in years Performance Rating

1 F A Service Years of service (rounded) Gender: 0 = male, 1

0 F A Midpoint salary grade midpoint Raise percent of la

1 F A Grade job/pay grade Degree (0= BS\BA 1

1 F A Gender1 (Male or Female) Compa - salary divi

1 F A

0 F A

0 F B

1 F B

1 F B

1 F B

0 F C

1 F C

0 F D

1 F D

0 F D

0 F E

1 F E

1 F F

1 F F

1 M A

0 M A

0 M A

0 M B

0 M B

1 M B

0 M C

1 M C

0 M C

1 M D

0 M D

0 M E

1 M E

0 M E

5/20/2018 BUS 308 Weeks 1

4/43

1 M E

0 M E

1 M E

1 M E

1 M E

0 M E

0 M E

1 M F

1 M F

1 M F

0 M F

10

5/20/2018 BUS 308 Weeks 1

5/43

: Are males and females paid the same for equal work (under the Equal Pay Act)?

grade comprise equal work.

usands

Appraisal rating (Employee evaluation score)

= female

t raise

= MS)

ed by midpoint

5/20/2018 BUS 308 Weeks 1

6/43

Week 1. Measurement and Description - chapters 1 and 2

1 Measurement issues. Data, even numerically coded variables, can be one of 4 levels -

nominal, ordinal, interval, or ratio. It is important to identify which level a variable is, as

this impact the kind of analysis we can do with the data. For example, descriptive statistics

such as means can only be done on interval or ratio level data.

Please list under each label, the variables in our data set that belong in each group.

Nominal Ordinal Interval Ratio

Gender ID

Degree Salary

Gender1 Compa

Grade Mid point

Performance

Servics

raise

b. For each variable that you did not call ratio, why did you make that decision?

Ratio scales are the ultimate nirvana when it comes to measurement scales because they tell us abou

No one variable is ratio because no variable values tells about the order among them so they a

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

For salary, compa, age, performance rating, and service; find the mean, standard deviation, an

You can use either the Data Analysis Descriptive Statistics tool or the Fx =average and =stde

(the range must be found using the difference between the =max and =min functions with Fx

Note: Place data to the right, if you use Descriptive statistics, place that to the right as well.

Salary Compa Age Perf. Rat. Service

Overall Mean 45.0 1.0625 35.7 85.9 9.0

Standard Deviation 19.20 0.08 8.25 11.41 5.72

Range 55 0.34 30 45 21

Female Mean 38.0 1.0687 32.5 84.2 7.9


Range 55 0.254 26 45 18

Male Mean 52.0 1.0562 38.9 87.6 10.0


Range 53 0.305 28 30 21

3 What is the probability for a:

a. Randomly selected person being a male in grade E?

5/20/2018 BUS 308 Weeks 1

7/43

b. Randomly selected male being in grade E?

Note part b is the same as given a male, what is probabilty of being in grade E?

c. Why are the results different?

4 For each group (overall, females, and males) find:

a. The value that cuts off the top 1/3 salary in each group.

b. The z score for each value:

c. The normal curve probability of exceeding this score:

d. What is the empirical probability of being at or exceeding this salary value?

e. The value that cuts off the top 1/3 compa in each group.

f. The z score for each value:

g. The normal curve probability of exceeding this score:

h. What is the empirical probability of being at or exceeding this compa value?

i. How do you interpret the relationship between the data sets? What do they mean about our e

Answer: we will find the correlation matrix to find the relationship among the variables.

Equal pay for equal work means the correlation of salaries with the remaining v

5. What conclusions can you make about the issue of male and female pay equality? Are all of t

What is the difference between the sal and compa measures of pay?

The salary male and females are not equal

Yes, all of the result is consistent

The means of salaries and Compa are not equal.

Conclusions from looking at salary results:

looking at the salaries the male and femaly payments are not equal

Conclusions from looking at compa results:

Looking at the Compa result the payments are not equal

Do both salary measures show the same results?

Yes, in both the case we see that the the payments are not equal for the male and female.

Can we make any conclusions about equal pay for equal work yet?

No, because in both the case we see that male and females payments according to salary and c

5/20/2018 BUS 308 Weeks 1

8/43

the order, they tell us the exact value between units

re ratio variables.

ables.

d range for 3 groups: overall sample, Females, and Males.

functions.

functions.

Probability

0.4

5/20/2018 BUS 308 Weeks 1

9/43

0.83

The results are different because population and samples are different for both the cases. In the fir

In the second case among the grade E we choose thos emales who are male.

Overall Female Male

41 24 40

-0.208 -1.094 -0.260

0.583 0.863 0.603

0.583 0.778 0.750

1.025 1.043 1.075

-0.488 -0.366 0.224

0.687 0.643 0.411

0.687 0.643 0.411

ual pay for equal work question?

riable in the data set is high, actually thy are dependent to each other.

he results consistent?

ompa are not equal therefore we canot say that equal pay for equal work

5/20/2018 BUS 308 Weeks 1

10/43

5/20/2018 BUS 308 Weeks 1

11/43

st case male is the population and we are choosing those males who got grade E

5/20/2018 BUS 308 Weeks 1

12/43

Week 2 Testing means

In questions 2 and 3, be sure to include the null and alternate hypotheses you will be te

In the first 3 questions use alpha = 0.05 in making your decisions on rejecting or not re

1 Below are 2 one-sample t-tests comparing male and female average salaries to the ove(Note: a one-sample t-test in Excel can be performed by selecting the 2-sample unequa

Based on our sample, how do you interpret the results and what do these results sugges

Males Females

Ho: Mean salary = 45 Ho: Mean salary = 45

Ha: Mean salary =/= 45 Ha: Mean salary =/= 45

Note: While the results both below are actually from Excel's t-Test: Two-Sample Assu

having no variance in the Ho variable makes the calculations default to the one-sample

Male Ho Female

Mean 52 45 Mean 38

Variance 316 0 Variance 334.667

Observations 25 25 Observations 25

Hypothesized Mean 0 Hypothesized Mean 0

df 24 df 24

t Stat 1.96890383 t Stat -1.9132

P(T

5/20/2018 BUS 308 Weeks 1

13/43

Ho:

Ha:

Test to use:

Place B43 in Outcome range box.

P-value is:

Is P-value < 0.05?

Reject or do not reject Ho:

Meaning of effect size measure:

Interpretation:

b. Since the one and two tail t-test results provided different outcomes, which is the prop

3 Based on our sample data set, can the male and female compas in the population be eq

Ho:Ha:

Statistical test to use:


If the null hypothesis was rejected,

what is the effect size value:

5/20/2018 BUS 308 Weeks 1

14/43

What is the p-value:

Is P-value < 0.05?

Reject or do not reject Ho:


Interpretation:

4 Since performance is often a factor in pay levels, is the average Performance Rating th

Ho:

Ha:

Test to use:


If the null hypothesis was rejected,

what is the effect size value:

5/20/2018 BUS 308 Weeks 1

15/43


Is P-value < 0.05?

Do we REJ or Not reject the null?


Interpretation:

5 If the salary and compa mean tests in questions 2 and 3 provide different results about

which would be more appropriate to use in answering the question about salary equity

What are your conclusions about equal pay at this point?

If the null hypothesis was

rejected, what is the effect size

5/20/2018 BUS 308 Weeks 1

16/43

sting.

ecting the null hypothesis.

all sample mean.l variance t-test and making the second variable = Ho value -- see column S)

t about the population means for male and female average salaries?

ing Unequal Variances,

t-test outcome - we are tricking Excel into doing a one sample test for us.

Ho

45

0

25

d female average salaries could be equal to each other.

statistically equal variances.)

mean equals 45

5/20/2018 BUS 308 Weeks 1

17/43

r/correct apporach to comparing salary equality? Why?

al to each other? (Another 2-sample t-test.)

5/20/2018 BUS 308 Weeks 1

18/43

same for both genders?

5/20/2018 BUS 308 Weeks 1

19/43

ale and female salary equality,

Why?

5/20/2018 BUS 308 Weeks 1

20/43

Q3

Ho Female Male Female

45 34 1.017 1.096

45 41 0.870 1.025

45 23 1.157 1.00045 22 0.979 0.956

45 23 1.134 1.000

45 42 1.149 1.050

45 24 1.052 1.043

45 24 1.175 1.043

45 69 1.043 1.210

45 36 1.134 1.161

45 34 1.043 1.096

45 57 1.000 1.187

45 23 1.074 1.000

45 50 1.020 1.041

45 24 0.903 1.043

45 75 1.122 1.119

45 24 0.903 1.043

45 24 0.982 1.043

45 23 1.086 1.000

45 22 1.075 0.956

45 35 1.052 1.129

45 24 1.140 1.043

45 77 1.087 1.149

45 55 1.052 1.145

45 65 1.157 1.140

5/20/2018 BUS 308 Weeks 1

21/43

Week 3

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

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 Last week, we found that average performance ratings do not differ between males a

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

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

Null Hypothesis:

Alt. Hypothesis:


Interpretation:


Is P-value < 0.05?



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

If the null hypothesis was rejected, what is the effect size

value (eta squared):

5/20/2018 BUS 308 Weeks 1

22/43

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

Is the average salary the same for each of the grade levels? (Assume equal variance,

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

Null Hypothesis:Alt. Hypothesis:



Is P-value < 0.05?

Do you reject or not reject the null hypothesis:


Interpretation:

3 The table and analysis below demonstrate a 2-way ANOVA with replication. Please

BA MA Ho: Average compas by gender are

If the null hypothesis was rejected, what is the effect sizevalue (eta squared):

5/20/2018 BUS 308 Weeks 1

23/43

Male 1.017 1.157 Ha: Average compas by gender are

0.870 0.979 Ho: Average compas are equal for

1.052 1.134 Ho: Average compas are not equal

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

1.052 1.087 Male

Female 1.096 1.050 Count 12 12

1.025 1.161 Sum 12.349 12.9

1.000 1.096 Average 1.02908333 1.075

0.956 1.000 Variance 0.00668645 0.00652

1.000 1.0411.043 1.043 Female

1.043 1.119 Count 12 12

1.210 1.043 Sum 12.791 12.787

1.187 1.000 Average 1.06591667 1.065583

1.043 0.956 Variance 0.00610245 0.004213

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 Variat SS df

Sample 0.00225502 1

Columns 0.00623352 1

Interaction 0.00641719 1

Within 0.25873675 44

Total 0.27364248 47

Interpretation:

Ha: Average compas by gender are


Is P-value < 0.05?

For Ho: Average compas by gender are equal

5/20/2018 BUS 308 Weeks 1

24/43



Ha: Average salaries are not equal

What is the p-value:Is P-value < 0.05?



For: Ho: Interaction is not significan Ha: Interaction is significant




What do these decisions mean in terms of our equal pay question:

4 Many companies consider the grade midpoint to be the "market rate" - what is neede

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

Null Hypothesis:

Alt. Hypothesis:

Statistical test to use:

Place the cursor in B160 for correl.





For Ho: Average salaries are equal for all grades

If the null hypothesis was rejected, what is the effect sizevalue (eta squared):

5/20/2018 BUS 308 Weeks 1

25/43


Is P-value < 0.05?


Meaning of effect size measure: NA

Interpretation:

5. Using the results up thru this week, what are your conclusions about gender equal pa

If the null hypothesis was rejected, what is

the effect size value:Since the effect size was not discussed in this chapter, we do

not have a formula for it - it differs from the non-paired t.

5/20/2018 BUS 308 Weeks 1

26/43

bit more spread out.

d females in the population.

the same for all grades?

A B C D E F

5/20/2018 BUS 308 Weeks 1

27/43

ption.

and use the analysis toolpak function ANOVA.)

A B C D E F

interpret the results.

equal

5/20/2018 BUS 308 Weeks 1

28/43

not equal

ach degree

or each degree

Total

24

25.249

1.052042

0.006866

24

25.578

1.06575

0.004933

MS F P-value F crit

0.002255 0.383482 0.538939 4.061706 (This is the row variable or gender.)

0.006234 1.060054 0.30883 4.061706 (This is the column variable or Degree.)

0.006417 1.091288 0.301892 4.061706

0.00588

not equal

5/20/2018 BUS 308 Weeks 1

29/43

or all grades

to hire a new employee. Midpoint Salary

?

5/20/2018 BUS 308 Weeks 1

30/43

y for equal work at this point?

5/20/2018 BUS 308 Weeks 1

31/43

Week 4 Confidence Intervals and Chi Square (Chs 11 - 12)

For questions 3 and 4 below, be sure to list the null and alternate hypothesis statements. Use .05

For full credit, you need to also show the statistical outcomes - either the Excel test result or the

1 Using our sample data, construct a 95% confidence interval for the popul

Interpret the results. How do they compare with the findings in the week

Mean St error t value Low toMales

Females

5/20/2018 BUS 308 Weeks 1

32/43

EXPECTED

M Grad

Fem Grad

Male Und

Female Und

Interpretation:

What is the value of the chi square statistic:

What is the p-value associated with this value:

Is the p-value

5/20/2018 BUS 308 Weeks 1

33/43

What does this correlation mean?

What does this decision mean for our equal pay question:

5. How do you interpret these results in light of our question about equal pay for equal work?

5/20/2018 BUS 308 Weeks 1

34/43

for your significance level in making your decisions.

alculations you performed.

tion's mean salary for each gender.

2 one sample t-test outcomes (Question 1)?

High

square root of the sample size.>

salary difference between the genders in the population.

High

e than using 2 one-sample techniques when comparing two samples?

ed evenly across the grades and genders.

orm this test, ignore this limitation for this exercise.)

Do manual calculations per cell here (if desired)

A B C D E F

M Grad

Fem Grad

Male Und

Female Und

5/20/2018 BUS 308 Weeks 1

35/43

Sum =

For this exercise - ignore the requirement for a correction

for expected values less than 5.

tributed across grades in a similar pattern

Do manual calculations per cell here (if desired)

A B C D E F

M

F

Sum =

5/20/2018 BUS 308 Weeks 1

36/43

Week 5 Correlation and Regression

1. Create a correlation table for the variables in our data set. (Use analysis ToolPak or StatPl

a. Reviewing the data levels from week 1, what variables can be used in a Pearson's C

b. Place table here (C8 in Output range box):

c. Using r = approximately .28 as the signicant r value (at p = 0.05) for a correlation bsignificantly related to Salary?

To compa?

d. Looking at the above correlations - both significant or not - are there any surprises -

mean any relationships you expected to be meaningful and are not and vice-versa?

e. Does this help us answer our equal pay for equal work question?

2 Below is a regression analysis for salary being predicted/explained by the other variage, performance rating, service, gender, and degree variables. (Note: since salary

expressing an employees salary, we do not want to have both used in the same reg

Plase interpret the findings.

Ho: The regression equation is not significant.

Ha: The regression equation is significant.

Ho: The regression coefficient for each variable is not significant Note: techn

Ha: The regression coefficient for each variable is significant Listing it t

SalSUMMARY OUTPUT

Regression Statistics

Multiple R 0.99155907

R Square 0.9831894

Adjusted R Square 0.98084373

Standard Error 2.65759257

5/20/2018 BUS 308 Weeks 1

37/43

Observations 50

ANOVA

df SS MS F Significance F

Regression 6 17762.3 2960.38 419.1516 1.812E-36

Residual 43 303.7003 7.0628

Total 49 18066

Coefficients

Standard

Error t Stat P-value Lower 95% Upper 95%

Intercept -1.7496212 3.618368 -0.48354 0.631166 -9.046755 5.5475126

Midpoint 1.21670105 0.031902 38.1383 8.66E-35 1.1523638 1.2810383

Age -0.004628 0.065197 -0.07098 0.943739 -0.136111 0.1268547

Performace Rating -0.0565964 0.034495 -1.64071 0.108153 -0.126162 0.0129695

Service -0.0425004 0.084337 -0.50394 0.616879 -0.212582 0.1275814

Gender 2.42033721 0.860844 2.81159 0.007397 0.6842792 4.1563952

Degree 0.27553341 0.799802 0.3445 0.732148 -1.337422 1.8884885

Note: since Gender and Degree are expressed as 0 and 1, they are considered dumm

Interpretation:For t e Regress on as a w o e:

What is the value of the F statistic:


Is the p-value

5/20/2018 BUS 308 Weeks 1

38/43

Ha:

Coefficient hypotheses (one to stand for all the separate variables)

Ho:

Ha:

Put C94 in output range box

Interpretation:

For the Regression as a whole:

What is the value of the F statistic:


Is the p-value < 0.05?


What does this decision mean for our equal pay question:

For each of the coefficients: Intercept Midpoint Age

What is the coefficient's p-value for each of the variables:

Is the p-value < 0.05?

Do you reject or not reject each null hypothesis:

What are the coefficients for the significant variables?

Using only the significant variables, what is the equation? Compa =

5/20/2018 BUS 308 Weeks 1

39/43

Is gender a significant factor in compa:

If so, who gets paid more with all other things being equal?

How do we know?

4 Based on all of your results to date, do we have an answer to the question of are mal

If so, which gender gets paid more?How do we know?

Which is the best variable to use in analyzing pay practices - salary or compa? Wh

What is most interesting or surprising about the results we got doing the analysis du

5 Why did the single factor tests and analysis (such as t and single factor ANOVA tes

What outcomes in your life or work might benefit from a multiple regression exami

5/20/2018 BUS 308 Weeks 1

40/43

us:mac LE function Correlation.)

orrelation table (which is what Excel produces)?

tween 50 values, what variables are

y that I

ables in our sample (Midpoint, and compa are different ways of

ession.)

ically we have one for each input variable.

is way to save space.

5/20/2018 BUS 308 Weeks 1

41/43

Lower 95.0% Upper 95.0%

-9.046755043 5.547512618

1.152363828 1.281038273

-0.136110719 0.126854699

-0.126162375 0.012969494

-0.212582091 0.127581377

0.684279192 4.156395232

-1.337421655 1.888488483

y variables and can be used in a multiple regression equation.

Perf. Rat. Service Gender Degree

dependent

ering the same questions.

5/20/2018 BUS 308 Weeks 1

42/43

Perf. Rat. Service Gender Degree

5/20/2018 BUS 308 Weeks 1

43/43

es and females paid equally for equal work?

?

ring the last 5 weeks?

s on salary equality) not provide a complete answer to our salary equality question?

ation rather than a simpler one variable test?

Documents

BUS 308 Weeks 1