Statistical Calculations 5Statistical Calculations.docx

Statistical Calculations 5
Statistical Calculations
Jeffree Doerflinger
Instructor: Margarita Rovira
August 22, 2014
1. For assistance with these calculations, see the Recommended
Resources for Week One. Data, even numerically code
variables, can be one of 4 levels – nominal, ordinal, interval, or
ratio. It is important to identify which level a variable is, as
this impacts 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
ID
Gender
Gender 1
Ordinal
Degree
Grade
Midpoint
Interval
Salary
Age
Performance Rating
Service

Ratio
Compa
Raise
1. The 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 and standard
deviation 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. Note: Place data to
the right, if you use Descriptive statistics, place that to the right
as well:
Salary
Overall = 45
Male = 52
Female = 38
Compa
Overall = 1.062
Male = 1.056
Female = 1.069
Age
Overall = 35.72
Male = 38.92
Female = 32.52
Performance rating
Overall = 85.9
Male = 87.6
Female = 84.2
Service
Overall = 8.96
Male = 10
Female = 7.92

Standard Deviations
Salary
Overall = 19.20140301
Male = 17.77638883
Female = 18.29389698
Compa
Overall = 0.07682507
Male = 0.083789061
Female = 0.070344699
Age
Overall = 8.251258407
Male = 8.38609961
Female = 8.251258407
Performance rating
Overall = 11.41472375
Male = 8.674675786
Female = 13.59227722
Service
Overall = 5.717713258
Male = 6.357410374
Female = 4.906798005
2. What is the probability for a:
a. Randomly selected person being a male in grade E?
= 25/49*12/49
= 0.1249
b. Randomly selected male being in grade E?
= 10/25

= 0.4
c. Why are the results different?
When we look at the first instance it would show that a person
would be randomly chosen from the total population, and I look
at the second the individual or person is chosen randomly from
a group of only males.
4. For each group (overall, females, and males) find::
a. The value that cuts off the top 1/3 salary in each group.
Overall = 58
Male = 62
Female = 41
b. The z score for each value.
z = (X - μ) / σ
Overall = (58-45)/19.20 = 0.67708
Male = (62-52)/17.77 = 0.5627
Female = (41-38)/18.29 = 0.1640
c. The normal curve probability of exceeding this score.
Overall = 0.2332
Male = 0.2147
Female = 0.1332
d. What is the empirical probability of being at or exceeding
this salary value?
Overall = 0.2525
Male = 0.2214
Female = 0.1564
e. The score that cuts off the top 1/3 compa in each group.
Overall = 1.096
Male = 1.086
Female = 1.096
f. The z score for each value.
z = (X - μ) / σ
Overall = (1.096-1.062)/0.07683 = 0.4425
Male = (1.086-1.056)/0.08386 = 0.3577

Female = (1.096-1.069)/0.07034 = 0.3838
g. The normal curve probability of exceeding this score.
Overall = 0.5675
Male = 0.6523
Female = 0.6277
h. What is the empirical probability of being at or exceeding
this salary value?
Overall = 0.5573
Male = 0.6372
Female = 0.5986
i. How do you interpret the relationship between the data sets?
What do they mean about our equal pay for equal work
question?
The data indicates a higher pay ratio for the male employees
than the females. The overall comp scores relationship to the
individual is drawn that individuals pay that is not proportional
to the work rates. It is evident that the salaries vary for the
different work performance rate. Equal pay for equal work
relationship does not exist. Equal Pay Conclusions
j. What conclusions can you make about the issue of male and
female pay equality? Are all of the results consistent?
The results show non-equality on male and female pays for
equal work. The results from the analysis on pay because of
performance are not consistent.
k. What is the difference between the salary and compa
measures of pay?
The compa measures depend completely on the grade. The
higher your pay, the higher the resulting compa value will be in
the similar pay grades.
l. Conclusions from looking at salary results
There is no equality and consistency in the pay associated with
performance rate, it would show that equal pay for equal work
does not again exist. There is no clear trend on salaries from the
data
m. Conclusions from looking at compa results
Compa results are dependent on the job grade and the salaries of

the individuals.
n. Do both salary measures show the same results?
The salary results do not show the same trend or results
o. Can we make any conclusions about equal pay for equal work
yet?
From the data there is no trend for equal pay for equal work, so
yes.
How to Analyze a Film
Borrowed heavily from Russell Johnson, Department of Theatre,
Wright State University.
1. Assume that your reader is intelligent and has seen the film
you are writing about.
2. Write in present tense. The film is a living work of art. Do
not discuss the film, the plot, the characters, etc., in the past
tense.
3. Avoid the slice-of-life approach. This presumes that the film
is not a work of art, but is real life, and then discusses the
characters as if they really existed. Often, this approach leads to
one of the most common errors for people starting to write
about film: because you presume the film is “real life,” you
start criticizing components of the film as not being realistic.
These kinds of comments are not relevant, generally, because
films are works of art which don’t always function realistically.
4. Never merely summarize the plot. This is often the worst
thing you can do. Beware of going on for several paragraphs or
pages summarizing the plot, occasionally disguising the
summary by throwing in a comment like “thus revealing an
insight.” Remember that analysis is very different from plot
synopsis, and if all you are doing is retelling the story, you are
accomplishing virtually nothing.

5. Never ignore the images. Remember, don’t write your paper
as if you were working from a plot summary or the novel on
which the film may be based. The best kind of film analysis
strikes a good balance between the literary components of the
film and the visual components of the film -- showing how all
the elements, in a unified way, function.
6. Avoid writing your own personal response or prejudice. In
other words, don’t give a personal “movie review” or your
opinion of the quality of the film. Remember to analyze the
themes and images. When you analyze something, you are
trying to explain how it works, what it means, and how and why
it’s constructed the way it is. Do not use a newspaper or
magazine review as your model for writing. The evaluative
approach is not acceptable for an analytical paper. As such, you
should be very wary of using words like “great,” “thrilling,”
“interesting,” “boring,” etc.
7. Avoid the “Introduction/Conclusion” problem. This is when
you take almost one whole page to tell me what your are going
to do, write two pages, and then take one more page of
conclusion to tell me what you did. In general, avoid these
statements of purpose. For the most part, in a short analytical
paper, all you need to do is do it. Get into and out of the
argument and analysis as simply and directly as possible. You
should, of course, use examples to support your ideas.
8. Avoid putting all the ideas you didn’t know what do with into
one long, complicated paragraph.
9. Avoid the corollary to Rule #8: putting one idea in each
paragraph, with each paragraph being only one or two sentences
long and no real development of the idea.
10. Avoid sweeping generalizations, such as “A good movie
must always …” There are always exceptions.
11. Avoid the “Everything but the Kitchen Sink” approach. This

is when you mention every possible theme and image you can
think of, but you develop none of them thoroughly. Remember
to develop your argument and fine tune it. Always back up your
ideas and contentions with specific examples for support.
Ways to Approach the Film Analysis
1. You can try to “unlock” the film, by providing its “key” –
what is the film really about? How is the film organized
visually? What are its themes? What was the director trying to
say?
2. You can find a cultural theme or themes in the film and
compare/contrast these cultural concepts to the concepts you are
familiar with in the United States. Show how these themes are
developed throughout the film.
3. You can take one specific subject and show the relevance of
that subject to the film and the director’s sensibility (i.e., the
use of color, camera movement, relationship to contemporary
politics, treatment of women, and so forth).
GIVE ONLY A BRIEF (1 PARAGRAPH) SUMMARY OF THE
READINGS AND FILMS.Then, analyze and react. Tell me how
the readings and films are affecting your thinking. What ideas
do these readings spark? How do these readings and films fit
into the overall theme of the course? What comparisons can you
make between the readings/films and your own experiences?
What comparisons can you make between the readings and the
films we view? What are some of the cultural values addressed
in the readings and films?
DataSee comments at the right of the data
set.IDSalaryCompaMidpointAgePerformance
RatingServiceGenderRaiseDegreeGender1Grade8231.000233290

915.80FAThe 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)?
10220.956233080714.70FANote: to simplfy the analysis, we
will assume that jobs within each grade comprise equal
work.11231.00023411001914.80FA14241.04323329012160FAT
he column labels in the table
mean:15241.043233280814.90FAID – Employee sample number
Salary – Salary in thousands 23231.000233665613.31FAAge
– Age in yearsPerformance Rating – Appraisal rating
(Employee evaluation score)26241.043232295216.21FAService
– Years of service (rounded)Gender: 0 = male, 1 = female
31241.043232960413.90FAMidpoint – salary grade midpoint
Raise – percent of last raise35241.043232390415.31FAGrade –
job/pay gradeDegree (0= BSBA 1 =
MS)36231.000232775314.31FAGender1 (Male or
Female)Compa - salary divided by
midpoint37220.956232295216.21FA42241.0432332100815.70F
A3341.096313075513.60FB18361.1613131801115.61FB20341.0
963144701614.81FB39351.129312790615.51FB7411.025403210
0815.70FC13421.0504030100214.71FC22571.187484865613.80
FD24501.041483075913.81FD45551.145483695815.20FD17691
.2105727553130FE48651.1405734901115.31FE28751.11967449
5914.41FF43771.1496742952015.51FF19241.043233285104.61
MA25241.0432341704040MA40251.086232490206.30MA2270.
870315280703.90MB32280.903312595405.60MB34280.903312
680204.91MB16471.175404490405.70MC27401.000403580703.
91MC41431.075402580504.30MC5470.9794836901605.71MD3
0491.0204845901804.30MD1581.017573485805.70ME4661.157
57421001605.51ME12601.0525752952204.50ME33641.1225735
90905.51ME38560.9825745951104.50ME44601.0525745901605
.21ME46651.1405739752003.91ME47621.087573795505.51ME
49601.0525741952106.60ME50661.1575738801204.60ME6761.
1346736701204.51MF9771.149674910010041MF21761.134674
3951306.31MF29721.074675295505.40MF
Week 1Week 1.Measurement and Description - chapters 1 and

21Measurement 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.SalaryCompaAgePerf.
Rat.ServiceOverallMeanStandard
DeviationRangeFemaleMeanStandard
DeviationRangeMaleMeanStandard DeviationRange3What is the
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?4For each group (overall, females, and males)
find:OverallFemaleMalea.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 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 2Week 2Testing meansQ3In questions 2 and 3, be sure to
include the null and alternate hypotheses you will be testing.
HoFemaleMaleIn the first 3 questions use alpha = 0.05 in
making your decisions on rejecting or not rejecting the null
hypothesis.45341.01745410.8701Below are 2 one-sample t-tests
comparing male and female average salaries to the overall
sample mean. 45231.157(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 -- see column
S)45220.979Based on our sample, how do you interpret the
results and what do these results suggest about the population
means for male and female average
salaries?45231.134MalesFemales45421.149Ho: Mean salary =
45Ho: Mean salary = 4545241.052Ha: Mean salary =/= 45Ha:
Mean salary =/= 4545241.17545691.043Note: While the results
both below are actually from Excel's t-Test: Two-Sample
Assuming Unequal Variances, 45361.134having 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.45341.043MaleHoFemaleHo45571.000Mean5245Mean38454
5231.074Variance3160Variance334.6666666667045501.020Obs
ervations2525Observations252545240.903Hypothesized Mean
Difference0Hypothesized Mean
Difference045751.122df24df2445240.903t Stat1.9689038266t
Stat-1.913206357345240.982P(T<=t) one-
tail0.0303078503P(T<=t) one-tail0.033862118445231.086t
Critical one-tail1.7108820799t Critical one-
tail1.710882079945221.075P(T<=t) two-

tail0.0606157006P(T<=t) two-tail0.067724236945351.052t
Critical two-tail2.0638985616t Critical two-
tail2.063898561645241.140Conclusion: Do not reject Ho; mean
equals 45Conclusion: Do not reject Ho; mean equals
4545771.087Is this a 1 or 2 tail test?Is this a 1 or 2 tail test?-
why?- why?P-value is:P-value is:45551.052Is P-value > 0.05?Is
P-value > 0.05?45651.157Why do we not reject Ho?Why do we
not reject Ho?Interpretation:I would not dismiss H0, for an
alpha of 0.05, there is no distinction function between mean pay
and 45.2Based 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.)t = (X1-X2)/(Sx1+x2) (52-38) / sqrt(316/25 +
334.667/25)t=2.744Ho mean1-mean2 =0Ha: mean1 - mean 2 =/=
0P-value is:2.744Is P-value < 0.05?NoReject or do not reject
Ho:RejectIf the null hypothesis was rejected, what is the effect
size value:Meaning of effect size measure:Effect size = True
value - Hypothesized value0Interpretation:I can dismiss my null
hypothesis because the results are significant at .05.b.Since the
one and two tail t-test results provided different outcomes,
which is the proper/correct apporach to comparing salary
equality? Why?The two tail t-test would be fitting if the fact
that Two-sample hypothesis testing is factual investigation
intended to test if there is a distinction between two methods
from two separate populations.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.)t = (X1-X2)/(Sx1-
x2)(1.05624-1.0687)/ sqrt(.0070207641/25+.0049477156/25)-
0.01246/sqrt (.000280830564+.000197908624)-
0.01246/.021880t=-.56947the critical 2 tail number at .05
significance is 2.064What is the p-value:0.56947Is P-value <
0.05?YesReject or do not reject Ho:AcceptedIf the null
hypothesis was rejected, what is the effect size value:-Meaning
of effect size measure:- Interpretation: I can accept the null
hypothesis that male and female compas can be equal to each

other.4Since performance is often a factor in pay levels, is the
average Performance Rating the same for both genders?Ho
mean1-mean2 =0Ha: mean1 - mean 2 =/= 0Test to use:T-
Test1.0521.145What is the p-value:1.6245Is P-value <
0.05?NODo we REJ or Not reject the null?RejectIf the null
hypothesis was rejected, what is the effect size value:-Meaning
of effect size measure:-Interpretation:For average Performance
Rating is the same for both genders. This makes me want to
know if the rate of variation is growing larger or smaller over
time. This would let me know if the gap is improving or not.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?I would believe that the compensation
mean test is referring to 2 it would seem that this would also be
the better decision given the two tests. I feel that the compa
estimation takes the pay review out of the mathematical
statement by isolating the compensation by the midpoint.My
conclusion is that there is not enough data to focus on the data
equity.
Week 3Week 3At 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.1Last 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.)ABCDEFNull
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?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:2While 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? (Assume
equal variance, and use the analysis toolpak function ANOVA.)
Use the input table to the right to list salaries under each grade
level.Null Hypothesis:Alt. Hypothesis:ABCDEFPlace 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, what is the effect size value (eta
squared):Meaning of effect size measure:Interpretation:3The
table and analysis below demonstrate a 2-way ANOVA with
replication. Please interpret the results.BAMAHo: Average
compas by gender are equalMale1.0171.157Ha: Average compas
by gender are not equal0.8700.979Ho: Average compas are
equal for each degree1.0521.134Ho: 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,
size measure:For Ho: Average salaries are equal for all grades
Ha: Average salaries 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
effect size value (eta squared):Meaning of effect size
measure:For: Ho: Interaction is not significantHa: Interaction is
significantWhat is the p-value:Do you reject or not reject the
null hypothesis:If the null hypothesis was rejected, what is the
measure:What do these decisions mean in terms of our equal
pay question:4Many companies consider the grade midpoint to
be the "market rate" - what is needed to hire a new
employee.MidpointSalaryDoes 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 correl.What is the p-value: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: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.Meaning of effect size
measure:NAInterpretation:5. Using the results up thru this
week, what are your conclusions about gender equal pay for
equal work at this point?
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. How do they compare with
the findings in the week 2 one sample t-test outcomes (Question
1)?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)?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 degrees compa 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.)What
are the hypothesis statements:Ho: Ha:Note: You can either use
the Excel Chi-related functions or do the calculations
manually.Data input tables - graduate degrees by gender and
grade levelOBSERVEDA BCDEFTotalDo manual calculations
per cell here (if desired)M GradA BCDEFFem GradM GradMale
UndFem GradFemale UndMale UndFemale 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?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
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 in Output range box):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 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.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-
351.15236382831.28103827271.15236382831.2810382727Age-
0.00462801020.065197212-0.07098478760.9437389875-
0.13611071910.1268546987-
0.13611071910.1268546987Performace Rating-
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: 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?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 hypotheses
(one to stand for all the separate variables)Ho:Ha:Put C94 in
output range boxInterpretation: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: 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 = Is gender a
significant factor in compa:If so, 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?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?
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?

work.11231.00023411001914.80FA14241.04323329012160FAT
midpoint37220.956232295216.21FA42241.0432332100815.70F
A19241.043233285104.61MA25241.0432341704040MA40251.0
86232490206.30MA3341.096313075513.60FB18361.161313180
1115.61FB20341.0963144701614.81FB39351.129312790615.51
FB2270.870315280703.90MB32280.903312595405.60MB34280
.903312680204.91MB7411.0254032100815.70FC13421.050403
0100214.71FC16471.175404490405.70MC27401.000403580703
.91MC41431.075402580504.30MC22571.187484865613.80FD2
4501.041483075913.81FD45551.145483695815.20FD5470.9794
836901605.71MD30491.0204845901804.30MD17691.21057275
53130FE48651.1405734901115.31FE1581.017573485805.70ME
4661.15757421001605.51ME12601.0525752952204.50ME33641
.122573590905.51ME38560.9825745951104.50ME44601.05257
45901605.21ME46651.1405739752003.91ME47621.0875737955
05.51ME49601.0525741952106.60ME50661.1575738801204.60
ME28751.119674495914.41FF43771.1496742952015.51FF6761.
1346736701204.51MF9771.149674910010041MF21761.134674
3951306.31MF29721.074675295505.40MF

for equal work yet?
Week 2 Week 2Testing meansQ3In questions 2 and 3, be sure to
HoFemaleMaleFemaleIn the first 3 questions use alpha = 0.05 in
hypothesis.45341.0171.09645410.8701.0251Below are 2 one-
sample t-tests comparing male and female average salaries to
the overall sample mean. 45231.1571.000(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 -- see column S)45220.9790.956Based on our sample, how
do you interpret the results and what do these results suggest
about the population means for male and female average
salaries?45231.1341.000MalesFemales45421.1491.050Ho: Mean
salary = 45Ho: Mean salary = 4545241.0521.043Ha: Mean
salary =/= 45Ha: Mean salary =/=
4545241.1751.04345691.0431.210Note: While the results both
below are actually from Excel's t-Test: Two-Sample Assuming
Unequal Variances, 45361.1341.161having 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.45341.0431.096MaleHoFemaleHo45571.0001.187Mean5245
Mean384545231.0741.000Variance3160Variance334.666666666
7045501.0201.041Observations2525Observations252545240.90
31.043Hypothesized Mean Difference0Hypothesized Mean
Difference045751.1221.119df24df2445240.9031.043t
Stat1.9689038266t Stat-1.913206357345240.9821.043P(T<=t)
one-tail0.0303078503P(T<=t) one-
tail0.033862118445231.0861.000t Critical one-
tail1.7108820799t Critical one-

tail1.710882079945221.0750.956P(T<=t) two-
tail0.0606157006P(T<=t) two-
tail0.067724236945351.0521.129t Critical two-
tail2.0638985616t Critical two-
tail2.063898561645241.1401.043Conclusion: Do not reject Ho;
mean equals 45Conclusion: Do not reject Ho; mean equals
4545771.0871.149Is this a 1 or 2 tail test?Is this a 1 or 2 tail
test?- why?- why?P-value is:P-value is:45551.0521.145Is P-
value > 0.05?Is P-value > 0.05?45651.1571.140Why do we not
reject Ho?Why do we not reject Ho?Interpretation: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: Ha: Test to use:Place B43 in Outcome range
box.P-value is:Is P-value < 0.05?Reject or do not reject Ho:If
the null hypothesis was rejected, what is the effect size
value:Meaning of effect size measure:Interpretation:b.Since the
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.)Ho:Ha:Statistical test to use:Place
B75 in Outcome range box.What is the p-value:Is P-value <
0.05?Reject or do not reject Ho:If the null hypothesis was
rejected, what is the effect size value: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?Ho:Ha:Test to use:Place B106 in Outcome range
box.What is the p-value: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: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?
are equal across the grades for this
ANOVA.)ABCDEF9075100655595Null Hypothesis:performance
rating average is the same for all grades8080100759095Alt.
Hypothesis:perfomance rating is not the same for all
grades1007090958570Place B17 in Outcome range
box.90908090100100Anova: Single
Factor80808090959565959095SUMMARY958095GroupsCountS
umAverageVariance6090Column
115126584.3333333333153.09523809529075Column
2757081.428571428672.6190476197595Column
35450901009595Column 4541583157.510080Column
512104587.0833333333152.083333333385Column
6655091.6666666667116.66666666677090ANOVASource of
VariationSSdfMSFP-valueF critBetween
Groups519.20238095245103.84047619050.77898535580.57021
547742.4270401198Within
Groups5865.297619047644133.3022186147Total6384.549Interp
retation:What is the p-value:0.5702154774Is P-value <
0.05?noDo we REJ or Not reject the null?acceptIf the null
squared):0.0813223245Meaning of effect size measure:The
effect is moderateWhat does that decision mean in terms of our
equal pay question:It would seem that despite the pay, the

employees are putting in equal efforts despite the pay and even
the grades2While 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? (Assume equal variance, and
use the analysis toolpak function ANOVA.) Use the input table
to the right to list salaries under each grade level.Null
Hypothesis:Average salaries are the same for all gradesAlt.
Hypothesis:Average salaries are not the same for all
gradesABCDEF233441576975223642506577Place B55 in
Outcome range box.233447555876Anova: Single
Factor243540476677242743496076SUMMARY23286472Groups
CountSumAverageVariance242856Column
11535323.53333333330.69523809522460Column
2722231.714285714314.90476190482465Column
3521342.67.32362Column 4525851.617.82260Column
51275162.583333333314.81060606062466Column
6645375.53.5242425ANOVASource of VariationSSdfMSFP-
valueF critBetween
Groups17686.021428571453537.2042857143409.59411996921.
03856156092.4270401198Within
Groups379.9785714286448.6358766234Total1806649What is
the p-value:1.0385615609Is P-value < 0.05?yesDo you reject or
not reject the null hypothesis:RejectIf the null hypothesis was
rejected, what is the effect size value (eta
squared):0.0210328004Meaning of effect size
measure:SignificantInterpretation:The salaries are not the same
for all grades, our null hypothesis is true3The table and analysis
below demonstrate a 2-way ANOVA with replication. Please
interpret the results.BAMAHo: Average compas by gender are
equalMale1.0171.157Ha: Average compas by gender are not
equal0.8700.979Ho: Average compas are equal for each
degree1.0521.134Ho: Average compas are not equal for each
degree1.1751.149Ho: Interaction is not

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
critSample0.002255020810.00225502080.38348211710.5389389
gender.)Columns0.006233520810.00623352081.06005396090.3
.30189150624.0617064601Within0.25873675440.0058803807To
equalWhat is the p-value:0.5389389507Is P-value < 0.05?YesDo
you reject or not reject the null hypothesis:AcceptIf the null
measure:SignificantFor Ho: Average salaries are equal for all
grades Ha: Average salaries are not equal for all gradesWhat is
the p-value:0.3088295633Is P-value < 0.05?YesDo you reject or
not reject the null hypothesis:AcceptIf the null hypothesis was
rejected, what is the effect size value (eta
measure:WeakFor: Ho: Interaction is not significantHa:
Interaction is significantWhat is the p-value:0.3018915062Do
you reject or not reject the null hypothesis:AcceptIf the null
squared):0.0234509917Meaning of effect size measure:What do
these decisions mean in terms of our equal pay
question:Weak4Many companies consider the grade midpoint to

existing employees at or above the market
rate?232323222323Null Hypothesis:The company pays above
the market rate2324Alt. Hypothesis:The company does not pay
above market rate23242323Statistical test to
use:Correlation23242324Place the cursor in B160 for
correl.2324Column 1Column 22323Column 112322Column
20.98897178271232423242324232531343136313431353127312
831284041404240474040What is the p-value:Not Known4043Is
P-value < 0.05?Not Known4857Do we REJ or Not reject the
null?Not Known4850If 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.4855Meaning of effect size measure:Not
Known48474849Interpretation:The variables are postively
correlated at 0.98 factor5769576557585. Using the results up
thru this week, what are your conclusions about gender equal
pay for equal work at this point?5766The company does not pay
equally as per gender or as per the grades despite the fact that
all the perfomance ratings are averagely
equal576057645756576057655762576057666775677767766777
67766772

for equal work?
e
FRegression617762.29967387432960.383278979419.151611129
41.8121523852609E-
95.0%Upper 95.0%Intercept-1.74962121233.6183676583-
0.48353881570.6311664899-9.04675504275.547512618-

9.04675504275.547512618Midpoint1.21670105050.0319023509
38.13828811638.66416336978111E-
351.15236382831.28103827271.15236382831.2810382727Age-
0.00462801020.065197212-0.07098478760.9437389875-
0.13611071910.1268546987-
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-

work.11231.00023411001914.80FA14241.04323329012160FAT

midpoint37220.956232295216.21FA42241.0432332100815.70F
A3341.096313075513.60FB18361.1613131801115.61FB20341.0
963144701614.81FB39351.129312790615.51FB7411.025403210
0815.70FC13421.0504030100214.71FC22571.187484865613.80
FD24501.041483075913.81FD45551.145483695815.20FD17691
.2105727553130FE48651.1405734901115.31FE28751.11967449
5914.41FF43771.1496742952015.51FF19241.043233285104.61
MA25241.0432341704040MA40251.086232490206.30MA2270.
870315280703.90MB32280.903312595405.60MB34280.903312
680204.91MB16471.175404490405.70MC27401.000403580703.
91MC41431.075402580504.30MC5470.9794836901605.71MD3
0491.0204845901804.30MD1581.017573485805.70ME4661.157
57421001605.51ME12601.0525752952204.50ME33641.1225735
90905.51ME38560.9825745951104.50ME44601.0525745901605
.21ME46651.1405739752003.91ME47621.087573795505.51ME
49601.0525741952106.60ME50661.1575738801204.60ME6761.
1346736701204.51MF9771.149674910010041MF21761.134674
3951306.31MF29721.074675295505.40MF
1)?MeanSt error t valueLow to

HighMales523.55527776692.063898547344.6659.34Females383
.65877939572.063898547330.4545.55<Reminder: standard error
is the sample standard deviation divided by the square root of
the sample size.>Interpretation:If repeated observations are
taken, the mean salary of male employees is expected to lie
within 44.66 to 59.34 thousands about 95% of the time. If
repeated observations are taken, the mean salary of female
employees is expected to lie within 30.45 to 45.55 thousands
about 95% of the time. As per our previous findings in week 2
one sample t-test outcomes, the mean salary of the male
employees is 52 thousands and there is no evidence to suggest
that the mean salary of the male employees is significantly
different from the mean salary of the population, which is 45
thousand. The mean salary of the female employees is 38
thousands and there is no evidence to suggest that the mean
salary of the female employees is significantly different from
the mean salary of the popululation.The 95% confidence
intervals for the salaries of the male and the female employees
both contain the population mean salary of 45 thousand. This is
in accordance with our previous findings that the mean salary of
the male and female employees are not significantly different
from the mean salary of the popululation.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
High145.10163372532.01063472193.742478093524.257521906
5Yes/NoCan the means be equal?NoWhy?The confidence
interval for the difference of means does not contain 0. How
does this compare to the week 2, question 2 result (2 sampe t-
test)?As the confidence interval for the population's mean salary
difference for male and female employees does not include 0,
we can conclude that there is a significant difference between
the means at 95% level of confidence. This is in accordance
with our previous findings of week 2 two sample t-test outcome
that the mean salary of the male employees is significantly

different from the mean salary of the female employees, at 95%
level of confidence.a.Why is using a two sample tool (t-test,
techniques when comparing two samples?It reduces the number
of errors due to approximations. Females3We found last week
that the degrees compa values within the population.Count of
DegreeColumn Labels do not impact compa rates. This does not
mean that degrees are distributed evenly across the grades and
genders.Row LabelsABCDEFGrand TotalDo males and females
have athe same distribution of degrees by
grade?07112112(Note: while technically the sample size might
not be large enough to perform this test, ignore this limitation
for this exercise.)153111213Grand Total124232225What are the
hypothesis statements:Ho: Males and females have the same
distribution of degrees by grade.Ha:Males and females do not
have the same distribution of degrees by grade.Count of
DegreeColumn LabelsNote: You can either use the Excel Chi-
related functions or do the calculations manually.Row
LabelsABCDEFGrand TotalData input tables - graduate degrees
by gender and grade level022215113OBSERVEDA
BCDEFTotalDo manual calculations per cell here (if
desired)111115312M Grad11115312A BCDEFGrand
Total333210425Fem Grad53111213M
Grad1.87780.27520.03330.03331.56061.6900Male
Und22215113Fem
Grad0.31030.76510.06920.06921.44050.1241Female
Und71121012Male
Und0.92560.01780.37690.06921.13280.2010Total1575512650Fe
male Und3.21110.27520.03330.53331.22721.4400Sum
=17.6923076923EXPECTEDM Grad3.61.681.21.22.881.44For
this exercise - ignore the requirement for a correctionFem
Grad3.91.821.31.33.121.56for expected values less than 5.Male
Und3.91.821.31.33.121.56Female
Und3.61.681.21.22.881.44Interpretation:What is the value of
the chi square statistic: 17.6923076923What is the p-value
associated with this value: 0.2791871758Is the p-value

<0.05?NoDo you reject or not reject the null hypothesis: We do
not reject the null hypothesis.If you rejected the null, what is
the Cramer's V correlation:Not ApplicableWhat does this
correlation mean?Not ApplicableWhat does this decision mean
for our equal pay question: There is no evidence to suggest that
male and female employees have different distribution of
degrees by grade, at significance level of 0.05.4Based on our
sample data, can we conclude that males and females are
distributed across grades in a similar patternwithin the
population?What are the hypothesis statements:Count of
Gender1Column LabelsHo: Males and females have same
distribution across grades. Row LabelsABCDEFGrand
TotalHa:Males and females have different distribution across
grades. F124232225M333210425Do manual calculations per
cell here (if desired)Grand Total1575512650A BCDEFTotalA
BCDEOBS COUNT -
m333210425M2.70000.07140.10000.10002.6667OBS COUNT -
f124232225F2.70000.07140.10000.10002.6667Total1575512650
Sum = 11.2762EXPECTED7.53.52.52.5637.53.52.52.563What is
the value of the chi square statistic: 11.2762What is the p-value
associated with this value: 0.0461707397Is the p-value
<0.05?YesDo you reject or not reject the null hypothesis: We
reject the null hypothesis.If you rejected the null, what is the
Phi correlation:0.96937224What does this correlation mean?The
extent of relationship between gender and grades is strong.What
does this decision mean for our equal pay question: Males and
females have different distribution across grades, and this might
be accountable for the difference in the mean salaries of males
and females.5. How do you interpret these results in light of
our question about equal pay for equal work?The mean salaries
of males are significantly higher that the mean salaries of
females, at significance level of 0.05. The distribution of males
and females across grades are also significantly different, at
significance level of 0.05. This difference might be the
underlying factor for the difference in the mean salaries of
males and females.

work.11231.00023411001914.80FA14241.04323329012160FAT
midpoint37220.956232295216.21FA42241.0432332100815.70F
A3341.096313075513.60FB18361.1613131801115.61FB20341.0
963144701614.81FB39351.129312790615.51FB7411.025403210
0815.70FC13421.0504030100214.71FC22571.187484865613.80
FD24501.041483075913.81FD45551.145483695815.20FD17691
.2105727553130FE48651.1405734901115.31FE28751.11967449
5914.41FF43771.1496742952015.51FF19241.043233285104.61
MA25241.0432341704040MA40251.086232490206.30MA2270.
870315280703.90MB32280.903312595405.60MB34280.903312
680204.91MB16471.175404490405.70MC27401.000403580703.
91MC41431.075402580504.30MC5470.9794836901605.71MD3
0491.0204845901804.30MD1581.017573485805.70ME4661.157
57421001605.51ME12601.0525752952204.50ME33641.1225735
90905.51ME38560.9825745951104.50ME44601.0525745901605
.21ME46651.1405739752003.91ME47621.087573795505.51ME

49601.0525741952106.60ME50661.1575738801204.60ME6761.
1346736701204.51MF9771.149674910010041MF21761.134674
3951306.31MF29721.074675295505.40MF

for equal work yet?
Week 2 Week 2Testing meansQ3In questions 2 and 3, be sure to
HoFemaleMaleFemaleIn the first 3 questions use alpha = 0.05 in
hypothesis.45341.0171.09645410.8701.0251Below are 2 one-
sample t-tests comparing male and female average salaries to
the overall sample mean. 45231.1571.000(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 -- see column S)45220.9790.956Based on our sample, how
do you interpret the results and what do these results suggest
about the population means for male and female average
salaries?45231.1341.000MalesFemales45421.1491.050Ho: Mean
salary = 45Ho: Mean salary = 4545241.0521.043Ha: Mean
salary =/= 45Ha: Mean salary =/=
4545241.1751.04345691.0431.210Note: While the results both
below are actually from Excel's t-Test: Two-Sample Assuming
Unequal Variances, 45361.1341.161having 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.45341.0431.096MaleHoFemaleHo45571.0001.187Mean5245
Mean384545231.0741.000Variance3160Variance334.666666666
7045501.0201.041Observations2525Observations252545240.90
31.043Hypothesized Mean Difference0Hypothesized Mean

Difference045751.1221.119df24df2445240.9031.043t
Stat1.9689038266t Stat-1.913206357345240.9821.043P(T<=t)
one-tail0.0303078503P(T<=t) one-
tail0.033862118445231.0861.000t Critical one-
tail1.7108820799t Critical one-
tail1.710882079945221.0750.956P(T<=t) two-
tail0.0606157006P(T<=t) two-
tail0.067724236945351.0521.129t Critical two-
tail2.0638985616t Critical two-
tail2.063898561645241.1401.043Conclusion: Do not reject Ho;
mean equals 45Conclusion: Do not reject Ho; mean equals
4545771.0871.149Is this a 1 or 2 tail test?Is this a 1 or 2 tail
test?- why?- why?P-value is:P-value is:45551.0521.145Is P-
value > 0.05?Is P-value > 0.05?45651.1571.140Why do we not
reject Ho?Why do we not reject Ho?Interpretation: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: Ha: Test to use:Place B43 in Outcome range
box.P-value is:Is P-value < 0.05?Reject or do not reject Ho:If
the null hypothesis was rejected, what is the effect size
value:Meaning of effect size measure:Interpretation:b.Since the
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.)Ho:Ha:Statistical test to use:Place
B75 in Outcome range box.What is the p-value:Is P-value <
0.05?Reject or do not reject Ho:If the null hypothesis was
rejected, what is the effect size value: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?Ho:Ha:Test to use:Place B106 in Outcome range
box.What is the p-value: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: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?
are equal across the grades for this ANOVA.)ABCDEFNull
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?If the null hypothesis was rejected,
size measure:What does that decision mean in terms of our
equal pay question:2While 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? (Assume
equal variance, and use the analysis toolpak function ANOVA.)
Use the input table to the right to list salaries under each grade
level.Null Hypothesis:Alt. Hypothesis:ABCDEFPlace 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
squared):Meaning of effect size measure:Interpretation:3The
table and analysis below demonstrate a 2-way ANOVA with
replication. Please interpret the results.BAMAHo: Average

compas by gender are equalMale1.0171.157Ha: Average compas
by gender are not equal0.8700.979Ho: Average compas are
equal for each degree1.0521.134Ho: Average compas are not
equal for each degree1.1751.149Ho: Interaction is not
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
critSample0.002255020810.00225502080.38348211710.5389389
gender.)Columns0.006233520810.00623352081.06005396090.3
.30189150624.0617064601Within0.25873675440.0058803807To
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,
size measure:For Ho: Average salaries are equal for all grades
Ha: Average salaries 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
measure:For: Ho: Interaction is not significantHa: Interaction is
significantWhat is the p-value:Do you reject or not reject the
null hypothesis:If the null hypothesis was rejected, what is the

measure:What do these decisions mean in terms of our equal
pay question:4Many companies consider the grade midpoint to
existing employees at or above the market rate?Null
Hypothesis:Alt. Hypothesis:Statistical test to use:Place the
cursor in B160 for correl.What is the p-value: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: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.Meaning of effect size
measure:NAInterpretation:5. Using the results up thru this
week, what are your conclusions about gender equal pay for
equal work at this point?

for equal work?

e
FRegression617762.29967387432960.383278979419.151611129
41.8121523852609E-
95.0%Upper 95.0%Intercept-1.74962121233.6183676583-
0.48353881570.6311664899-9.04675504275.547512618-
9.04675504275.547512618Midpoint1.21670105050.0319023509
38.13828811638.66416336978111E-
351.15236382831.28103827271.15236382831.2810382727Age-
0.00462801020.065197212-0.07098478760.9437389875-
0.13611071910.1268546987-
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-

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