bus 308 weeks 1
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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
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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
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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
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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
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: 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
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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
Standard Deviation 18.29 0.07 6.88 13.59 4.91
Range 55 0.254 26 45 18
Male Mean 52.0 1.0562 38.9 87.6 10.0
Standard Deviation 17.78 0.08 8.39 8.67 6.36
Range 53 0.305 28 30 21
3 What is the probability for a:
a. Randomly selected person being a male in grade E?
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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
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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
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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
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st case male is the population and we are choosing those males who got grade E
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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
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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:
Place B75 in Outcome range box.
If the null hypothesis was rejected,
what is the effect size value:
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What is the p-value:
Is P-value < 0.05?
Reject or do not reject Ho:
Meaning of effect size measure:
Interpretation:
4 Since performance is often a factor in pay levels, is the average Performance Rating th
Ho:
Ha:
Test to use:
Place B106 in Outcome range box.
If the null hypothesis was rejected,
what is the effect size value:
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What is the p-value:
Is P-value < 0.05?
Do we REJ or Not reject the null?
Meaning of effect size measure:
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
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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
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r/correct apporach to comparing salary equality? Why?
al to each other? (Another 2-sample t-test.)
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same for both genders?
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ale and female salary equality,
Why?
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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
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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:
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?
Meaning of effect size measure:
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):
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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:
Place B55 in Outcome range box.
What is the p-value:
Is P-value < 0.05?
Do you reject or not reject the null hypothesis:
Meaning of effect size measure:
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):
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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
What is the p-value:
Is P-value < 0.05?
For Ho: Average compas by gender are equal
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Do you reject or not reject the null hypothesis:
Meaning of effect size measure:
Ha: Average salaries are not equal
What is the p-value:Is P-value < 0.05?
Do you reject or not reject the null hypothesis:
Meaning of effect size measure:
For: Ho: Interaction is not significan Ha: Interaction is significant
What is the p-value:
Do you reject or not reject the null hypothesis:
Meaning of effect size measure:
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.
If the null hypothesis was rejected, what is the effect size
value (eta squared):
If the null hypothesis was rejected, what is the effect size
value (eta squared):
For Ho: Average salaries are equal for all grades
If the null hypothesis was rejected, what is the effect sizevalue (eta squared):
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What is the p-value:
Is P-value < 0.05?
Do we REJ or Not reject the null?
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.
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bit more spread out.
d females in the population.
the same for all grades?
A B C D E F
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ption.
and use the analysis toolpak function ANOVA.)
A B C D E F
interpret the results.
equal
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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
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or all grades
to hire a new employee. Midpoint Salary
?
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y for equal work at this point?
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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
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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
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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?
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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
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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 =
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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
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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:
What is the p-value associated with this value:
Is the p-value
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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:
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: 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 =
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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
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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.
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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.
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Perf. Rat. Service Gender Degree
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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?
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