The document discusses an analysis of pay equality between male and female employees, focusing on salary data, performance ratings, and job grades. It includes methods for statistical testing like t-tests and ANOVA to assess equality of pay, summarizing key variables and experimental designs for exploring pay discrepancies. The overall aim is to draw conclusions on whether males and females are compensated equally for equal work.

1. DataIDSalaryCompaMidpoint AgePerformance
RatingServiceGenderRaiseDegreeGender1GrStudents: Copy the
Student Data file data values into this sheet to assist in doing
your weekly assignments.157.71.012573485805.70METhe
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)? 227.80.897315280703.90MBNote: to simplfy
the analysis, we will assume that jobs within each grade
comprise equal
work.3341.096313075513.61FB459.21.03857421001605.51MET
he column labels in the table
mean:549.51.0314836901605.71MDID – Employee sample
number Salary – Salary in thousands
675.71.1306736701204.51MFAge – Age in yearsPerformance
Rating - Appraisal rating (employee evaluation
score)741.71.0434032100815.71FCService – Years of service
(rounded)Gender – 0 = male, 1 = female
823.41.018233290915.81FAMidpoint – salary grade midpoint
Raise – percent of last raise980.81.206674910010041MFGrade
– job/pay gradeDegree (0= BSBA 1 =
MS)1023.61.027233080714.71FAGender1 (Male or
Female)Compa - salary divided by
midpoint1123.61.02423411001914.81FA1266.91.174575295220
4.50ME1341.61.0414030100214.70FC1421.50.93623329012161
FA1524.41.059233280814.91FA16390.975404490405.70MC176
8.81.2075727553131FE1834.91.1263131801115.60FB1923.21.0
08233285104.61MA20361.1603144701614.80FB2175.31.12467
43951306.31MF2256.71.182484865613.81FD2322.60.98423366
5613.30FA2451.51.072483075913.80FD2525.51.109234170404
0MA2622.90.994232295216.20FA2743.51.088403580703.91MC
2874.41.111674495914.40FF2973.51.097675295505.40MF3045.
70.9524845901804.30MD3123.71.031232960413.91FA3226.90.
867312595405.60MB3355.10.967573590905.51ME34280.90431
2680204.91MB3521.90.953232390415.30FA3623.71.032232775

2. 314.30FA3723.21.010232295216.20FA3857.61.0105745951104.
50ME3934.31.108312790615.50FB4024.41.062232490206.30M
A4140.51.012402580504.30MC4223.31.0122332100815.71FA4
377.21.1526742952015.50FF4456.90.9995745901605.21ME455
7.71.202483695815.21FD4665.41.1485739752003.91ME4756.8
0.997573795505.51ME4859.71.0485734901115.31FE4962.41.09
55741952106.60ME5056.50.9925738801204.60ME
Week 1Week 1.Measurement and Description - chapters 1 and
2The goal this week is to gain an understanding of our data set -
what kind of data we are looking at, some descriptive measurse,
and a look at how the data is distributed (shape).1Measurement
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, asthis 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.NominalOrdinalIntervalRatiob.For
each variable that you did not call ratio, why did you make that
decision?2The first step in analyzing data sets is to find some
summary descriptive statistics for key variables.For salary,
compa, age, performance rating, and service; find the mean,
standard deviation, and range for 3 groups: overall sample,
Females, and Males.You can use either the Data Analysis
Descriptive Statistics tool or the Fx =average and =stdev
functions. (the range must be found using the difference
between the =max and =min functions with Fx) functions.Note:
Place data to the right, if you use Descriptive statistics, place
that to the right as well.Some of the values are completed for
you - please finish the table.SalaryCompaAgePerf.
Rat.ServiceOverallMean35.785.99.0Standard
Deviation8.251311.41475.7177Note - data is a sample from the
larger company
populationRange304521FemaleMean32.584.27.9Standard
Deviation6.913.64.9Range26.045.018.0MaleMean38.987.610.0S
tandard Deviation8.48.76.4Range28.030.021.03What is the

3. probability for a:Probabilitya. Randomly selected person
being a male in grade E?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?4A key issue in comparing data sets is to see if they
are distributed/shaped the same. We can do this by looking at
some measures of wheresome selected values are within each
data set - that is how many values are above and below a
comparable value.For each group (overall, females, and males)
find:OverallFemaleMaleAThe value that cuts off the top 1/3
salary value in each group"=large" functioniThe z score for this
value within each group?Excel's standize functioniiThe normal
curve probability of exceeding this score:1-normsdist
functioniiiWhat is the empirical probability of being at or
exceeding this salary value?BThe value that cuts off the top 1/3
compa value in each group.iThe z score for this value within
each group?iiThe normal curve probability of exceeding this
score:iiiWhat is the empirical probability of being at or
exceeding this compa value?CHow do you interpret the
relationship between the data sets? What do they mean about
our equal pay for equal work question?5. What conclusions
can you make about the issue of male and female pay equality?
Are all of the results consistent? What is the difference between
the sal and compa measures of pay?Conclusions from looking at
salary results:Conclusions from looking at compa results:Do
both salary measures show the same results?Can we make any
conclusions about equal pay for equal work yet?
Week 2 Week 2Testing means - T-testsIn questions 2, 3, and 4
be sure to include the null and alternate hypotheses you will be
testing. In the first 4 questions use alpha = 0.05 in making your
decisions on rejecting or not rejecting the null
hypothesis.1Below are 2 one-sample t-tests comparing male and
female average salaries to the overall sample mean. (Note: a
one-sample t-test in Excel can be performed by selecting the 2-
sample unequal variance t-test and making the second variable =
Ho value - a constant.)Note: These values are not the same as

4. the data the assignment uses. The purpose is to analyze the
results of t-tests rather than directly answer our equal pay
question.Based on these results, how do you interpret the results
and what do these results suggest about the population means
for male and female average salaries?MalesFemalesHo: Mean
salary =45.00Ho: Mean salary =45.00Ha: Mean salary
=/=45.00Ha: Mean salary =/=45.00Note: While the results both
below are actually from Excel's t-Test: Two-Sample Assuming
Unequal Variances, having no variance in the Ho variable
makes the calculations default to the one-sample t-test outcome
- we are tricking Excel into doing a one sample test for
us.MaleHoFemaleHoMean5245Mean3845Variance3160Variance
334.66666666670Observations2525Observations2525Hypothesi
zed Mean Difference0Hypothesized Mean Difference0df24df24t
Stat1.9689038266t Stat-1.9132063573P(T<=t) one-
tail0.0303078503P(T<=t) one-tail0.0338621184t Critical one-
tail1.7108820799t Critical one-tail1.7108820799P(T<=t) two-
tail0.0606157006P(T<=t) two-tail0.0677242369t Critical two-
tail2.0638985616t Critical two-tail2.0638985616Conclusion: Do
not reject Ho; mean equals 45Conclusion: Do not reject Ho;
mean equals 45Note: the Female results are done for you, please
complete the male results.Is this a 1 or 2 tail test?Is this a 1 or 2
tail test?2 tail- why?- why?Ho contains =P-value is:P-value
is:0.0677242369Is P-value < 0.05 (one tail test) or 0.025 (two
tail test)?Is P-value < 0.05 (one tail test) or 0.025 (two tail
test)?NoWhy do we not reject the null hypothesis?Why do we
not reject the null hypothesis?P-value greater than (>) rejection
alphaInterpretation of test outcomes:2Based on our sample data
set, perform a 2-sample t-test to see if the population male and
female average salaries could be equal to each other.(Since we
have not yet covered testing for variance equality, assume the
data sets have statistically equal variances.)Ho: Male salary
mean = Female salary meanHa: Male salary mean =/= Female
salary meanTest to use:t-Test: Two-Sample Assuming Equal
VariancesP-value is:Is P-value < 0.05 (one tail test) or 0.025
(two tail test)?Reject or do not reject Ho:If the null hypothesis

5. was rejected, calculate the effect size value:If calculated, what
is the meaning of effect size measure:Interpretation:b.Is the one
or two sample t-test the proper/correct apporach to comparing
salary equality? Why?3Based on our sample data set, can the
male and female compas in the population be equal to each
other? (Another 2-sample t-test.)Again, please assume equal
variances for these groups.Ho:Ha:Statistical test to use:What is
the p-value:Is P-value < 0.05 (one tail test) or 0.025 (two tail
test)?Reject or do not reject Ho:If the null hypothesis was
rejected, calculate the effect size value:If calculated, what is the
meaning of effect size measure: Interpretation: 4Since
performance is often a factor in pay levels, is the average
Performance Rating the same for both genders?NOTE: do NOT
assume variances are equal in this situation.Ho:Ha:Test to use:t-
Test: Two-Sample Assuming Unequal VariancesWhat is the p-
value:Is P-value < 0.05 (one tail test) or 0.025 (two tail
test)?Do we REJ or Not reject the null?If the null hypothesis
was rejected, calculate the effect size value:If calculated, what
is the meaning of effect size measure:Interpretation:5If the
salary and compa mean tests in questions 2 and 3 provide
different results about male and female salary equality, which
would be more appropriate to use in answering the question
about salary equity? Why?What are your conclusions about
equal pay at this point?
Week 3Week 3Paired T-test and ANOVAFor this week's work,
again be sure to state the null and alternate hypotheses and use
alpha = 0.05 for our decisionvalue in the reject or do not reject
decision on the null hypothesis.1Many companies consider the
grade midpoint to be the "market rate" - the salary needed to
hire a new employee.SalaryMidpointDiffDoes the company, on
average, pay its existing employees at or above the market
rate?Use the data columns at the right to set up the paired data
set for the analysis.Null Hypothesis:Alt. Hypothesis:Statistical
test to use:What is the p-value:Is P-value < 0.05 (one tail test)
or 0.025 (two tail test)?What else needs to be checked on a 1-
tail test in order to reject the null?Do we REJ or Not reject the

6. null?If the null hypothesis was rejected, what is the effect size
value:If calculated, what is the meaning of effect size
measure:Interpretation of test results:Let's look at some other
factors that might influence pay - education(degree) and
performance ratings.2Last 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.)Here are the data values sorted by grade level.The
rating values sorted by grade have been placed in columns I - N
for you.ABCDEFNull Hypothesis:Ho: means equal for all
grades9080100908570Alt. Hypothesis:Ha: at least one mean is
unequal807510065100100Place B17 in Outcome range
box.1008090759595907080905595809580959095858095956590
90707595956090909575809590100Interpretation of test
results:What is the p-value:0.57If the ANVOA was done
correctly, this is the p-value shown.Is P-value < 0.05?Do we
REJ or Not reject the null?If the null hypothesis was rejected,
what is the effect size value (eta squared):Meaning of effect
size measure:What does that decision mean in terms of our
equal pay question:3While 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? Use the
input table to the right to list salaries under each grade level.
(Assume equal variance, and use the analysis toolpak function
ANOVA.) Null Hypothesis:If desired, place salaries per grade
in these columnsAlt. Hypothesis:ABCDEFPlace B51 in
Outcome range box.Note: Sometimes we see a p-value in the
format of 3.4E-5; this means move the decimal point left 5
places. In this example, the p-value is 0.000034What is the p-
value:Is P-value < 0.05?Do we REJ or Not reject the null?If the
null hypothesis was rejected, calculate the effect size value (eta
squared):If calculated, what is the meaning of effect size
measure:Interpretation:4The table and analysis below
demonstrate a 2-way ANOVA with replication. Please interpret

7. the results.Note: These values are not the same as the data the
assignment uses. The purpose of this question is to analyze the
result of a 2-way ANOVA test rather than directly answer our
equal pay question.BAMAHo: Average compas by gender are
equalMale1.0171.157Ha: Average compas by gender are not
equal0.8700.979Ho: Average compas are equal for each
degree1.0521.134Ha: Average compas are not equal for each
degree1.1751.149Ho: Interaction is not
significant1.0431.043Ha: Interaction is
significant1.0741.1341.0201.000Perform
analysis:0.9031.1220.9820.903Anova: Two-Factor With
Replication1.0861.0521.0751.140SUMMARYBAMATotal1.052
1.087MaleFemale1.0961.050Count1212241.0251.161Sum12.349
12.925.2491.0001.096Average1.02908333331.0751.0520416667
0.9561.000Variance0.0066864470.00651981820.00686604171.0
001.0411.0431.043Female1.0431.119Count1212241.2101.043Su
m12.79112.78725.5781.1871.000Average1.06591666671.06558
333331.065751.0430.956Variance0.0061024470.00421281060.0
049334131.0431.1291.1451.149TotalCount2424Sum25.1425.68
7Average1.04751.0702916667Variance0.00647034780.0051561
286ANOVASource of VariationSSdfMSFP-valueF
critSample0.002255020810.00225502080.38348211710.5389389
5074.0617064601 (This is the row variable or
gender.)Columns0.006233520810.00623352081.06005396090.3
0882956334.0617064601 (This is the column variable or
Degree.)Interaction0.006417187510.00641718751.09128776640
.30189150624.0617064601Within0.25873675440.0058803807To
tal0.273642479247Interpretation:For Ho: Average compas by
gender are equalHa: Average compas by gender are not
equalWhat is the p-value:Is P-value < 0.05?Do you reject or not
reject the null hypothesis:If the null hypothesis was rejected,
what 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 gradesWhat is the p-
value:Is P-value < 0.05?Do you reject or not reject the null
hypothesis:If the null hypothesis was rejected, what is the

8. effect size value (eta squared):Meaning of effect size
measure:For: Ho: Interaction is not significantHa: Interaction is
significantWhat is the p-value:Is P-value < 0.05?Do you reject
or not reject the null hypothesis:If the null hypothesis was
rejected, what is the effect size value (eta squared):Meaning of
effect size measure:What do these three decisions mean in terms
of our equal pay question:Place data values in these columns5.
Using the results up thru this week, what are your conclusions
about gender equal pay for equal work at this point?Dif
Week 4Week 4Confidence 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 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.1Using our sample data, construct a
95% confidence interval for the population's mean salary for
each gender. Interpret the results. MeanSt error t valueLow to
HighMalesFemales<Reminder: standard error is the sample
standard deviation divided by the square root of the sample
size.>Interpretation:2Using our sample data, construct a 95%
confidence interval for the mean salary difference between the
genders in the population. How does this compare to the
findings in week 2, question 2?DifferenceSt Err.T valueLow to
HighYes/NoCan the means be equal?Why?How does this
compare to the week 2, question 2 result (2 sampe t-
test)?Results are the same - means are not equal.a.Why is using
a two sample tool (t-test, confidence interval) a better choice
than using 2 one-sample techniques when comparing two
samples?3We found last week that the degree values within the
population do not impact compa rates. This does not mean that
degrees are distributed evenly across the grades and genders.Do
males and females have athe same distribution of degrees by
grade?(Note: while technically the sample size might not be
large enough to perform this test, ignore this limitation for this
exercise.)Ignore any cell size limitations.What are the
hypothesis statements:Ho: Ha:Note: You can either use the

9. Excel Chi-related functions or do the calculations
manually.Data InTablesThe Observed Table is completed for
you.OBSERVEDA BCDEFTotalIf desired, you can do manual
calculations per cell here.M Grad11115312A BCDEFFem
Grad53111213M GradMale Und22215113Fem GradFemale
Und71121012Male Und1575512650Female UndSum
=EXPECTEDM GradFor this exercise - ignore the requirement
for a correctionFem Gradfor expected values less than 5.Male
UndFemale UndInterpretation:What is the value of the chi
square statistic: What is the p-value associated with this value:
Is the p-value <0.05?Do you reject or not reject the null
hypothesis: If you rejected the null, what is the Cramer's V
correlation:What does this correlation mean?What does this
decision mean for our equal pay question: 4Based on our sample
data, can we conclude that males and females are distributed
across grades in a similar patternwithin the population?Again,
ignore any cell size limitations.What are the hypothesis
statements:Ho: Ha:Do manual calculations per cell here (if
desired)A BCDEFA BCDEFOBS COUNT - mMOBS COUNT -
fFSum = EXPECTEDWhat is the value of the chi square
statistic: What is the p-value associated with this value: Is the
p-value <0.05?Do you reject or not reject the null hypothesis: If
you rejected the null, what is the Phi correlation:If calculated,
what is the meaning of effect size measure: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?
Week 5Week 5 Correlation and Regression1. Create a
correlation table for the variables in our data set. (Use analysis
ToolPak or StatPlus:mac LE function Correlation.)a. Reviewing
the data levels from week 1, what variables can be used in a
Pearson's Correlation table (which is what Excel produces)?b.
Place table here (C8):c.Using r = approximately .28 as the
signicant r value (at p = 0.05) for a correlation between 50
values, what variables aresignificantly related to Salary?To
compa?d.Looking at the above correlations - both significant or

10. not - are there any surprises -by that I 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?2Below is a regression analysis for salary being
predicted/explained by the other variables in our sample
(Midpoint, age, performance rating, service, gender, and degree
variables. (Note: since salary and compa are different ways of
expressing an employee’s salary, we do not want to have both
used in the same regression.)Plase interpret the findings.Note:
These values are not the same as the data the assignment uses.
The purpose is to analyze the result of a regression test rather
than directly answer our equal pay question.Ho: The regression
equation is not significant.Ha: The regression equation is
significant.Ho: The regression coefficient for each variable is
not significant Note: technically we have one for each input
variable.Ha: The regression coefficient for each variable is
significant Listing it this way to save space.SalSUMMARY
OUTPUTRegression StatisticsMultiple R0.9915590747R
Square0.9831893985Adjusted R Square0.9808437332Standard
Error2.6575925726Observations50ANOVAdfSSMSFSignificanc
e
FRegression617762.29967387432960.383278979419.151611129
41.8121523852609E-
36Residual43303.70032612577.062798282Total4918066Coeffic
ientsStandard Errort StatP-valueLower 95%Upper 95%Lower
95.0%Upper 95.0%Intercept-1.74962121233.6183676583-
0.48353881570.6311664899-9.04675504275.547512618-
9.04675504275.547512618Midpoint1.21670105050.0319023509
38.13828811638.66416336978111E-
351.15236382831.28103827271.15236382831.2810382727Note:
These values are not the same as in the data the assignment
uses. The purpose is to analyze the result of a 2-way ANOVA
test rather than directly answer our equal pay question.Age-
0.00462801020.065197212-0.07098478760.9437389875-
0.13611071910.1268546987-
0.13611071910.1268546987Performace Rating-

11. 0.05659644050.0344950678-1.64071109710.1081531819-
0.12616237470.0129694936-
0.12616237470.0129694936Service-
0.04250035730.0843369821-0.50393500330.6168793519-
0.21258209120.1275813765-
0.21258209120.1275813765Gender2.4203372120.86084431762.
81158528040.00739661880.6842791924.1563952320.68427919
24.156395232Degree0.27553341430.79980230480.34450190090
.732148119-1.33742165471.8884884833-
1.33742165471.8884884833Note: since Gender and Degree are
expressed as 0 and 1, they are considered dummy variables and
can be used in a multiple regression equation.Interpretation:For
the Regression as a whole:What is the value of the F statistic:
What is the p-value associated with this value: Is the p-value
<0.05?Do you reject or not reject the null hypothesis: What
does this decision mean for our equal pay question: For each of
the coefficients:InterceptMidpointAgePerf.
Rat.ServiceGenderDegreeWhat is the coefficient's p-value for
each of the variables: NAIs the p-value < 0.05?NADo you reject
or not reject each null hypothesis: NAWhat are the coefficients
for the significant variables?Using the intercept coefficient and
only the significant variables, what is the equation?Salary =Is
gender a significant factor in salary:If so, who gets paid more
with all other things being equal?How do we know? 3Perform a
regression analysis using compa as the dependent variable and
the same independentvariables as used in question 2. Show the
result, and interpret your findings by answering the same
questions.Note: be sure to include the appropriate hypothesis
statements.Regression hypothesesHo:Ha:Coefficient
hyhpotheses (one to stand for all the separate
variables)Ho:Ha:Place c94 in output box.Interpretation:For the
Regression as a whole:What is the value of the F statistic: What
is the p-value associated with this value: Is the p-value <
0.05?Do you reject or not reject the null hypothesis: What does
this decision mean for our equal pay question: For each of the
coefficients: InterceptMidpointAgePerf.

12. Rat.ServiceGenderDegreeWhat is the coefficient's p-value for
each of the variables: NAIs the p-value < 0.05?NADo you reject
or not reject each null hypothesis: NAWhat are the coefficients
for the significant variables?Using the intercept coefficient and
only the significant variables, what is the equation?Compa = Is
gender a significant factor in compa:Regardless of statistical
significance, who gets paid more with all other things being
equal?How do we know? 4Based on all of your results to date,
Do we have an answer to the question of are males and females
paid equally for equal work?Does the company pay employees
equally for for equal work? How do we know?Which is the best
variable to use in analyzing pay practices - salary or compa?
Why?What is most interesting or surprising about the results we
got doing the analysis during the last 5 weeks?5Why did the
single factor tests and analysis (such as t and single factor
ANOVA tests on salary equality) not provide a complete answer
to our salary equality question?What outcomes in your life or
work might benefit from a multiple regression examination
rather than a simpler one variable test?