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Copy of Student_Assignment_File.11.01.2016.xlsx

Data

ID Salary Compa-ratio Midpoint Age Performance Rating Service Gender Raise Degree Gender1 Grade Copy Employee Data set to this page.
The ongoing question that the weekly assignments will focus on is: Are males and females paid the same for equal work (under the Equal Pay Act)?
Note: to simplfy the analysis, we will assume that jobs within each grade comprise equal work.
The column labels in the table mean:
ID – Employee sample number Salary – Salary in thousands
Age – Age in years Performance Rating – Appraisal rating (Employee evaluation score)
SERvice – Years of service Gender: 0 = male, 1 = female
Midpoint – salary grade midpoint Raise – percent of last raise
Grade – job/pay grade Degree (0= BS\BA 1 = MS)
Gender1 (Male or Female) Compa-ratio - salary divided by midpoint

Week 2

This assignment covers the material presented in weeks 1 and 2. Six Questions
Before starting this assignment, make sure the the assignment data from the Employee Salary Data Set file is copied over to this Assignment file.
You can do this either by a copy and paste of all the columns or by opening the data file, right clicking on the Data tab, selecting Move or Copy, and copying the entire sheet to this file
(Weekly Assignment Sheet or whatever you are calling your master assignment file).
It is highly recommended that you copy the data columns (with labels) and paste them to the right so that whatever you do will not disrupt the original data values and relationships.
To Ensure full credit for each question, you need to show how you got your results. For example, Question 1 asks for several data values. If you obtain them using descriptive statistics,
then the cells should have an "=XX" formula in them, where XX is the column and row number showing the value in the descriptive statistics table. If you choose to generate each
value using fxfunctions, then each function should be located in the cell and the location of the data values should be shown.
So, Cell D31 - as an example - shoud contain something like "=T6" or "=average(T2:T26)". Having only a numerical value will not earn full credit.
The reason for this is to allow instructors to provide feedback on Excel tools if the answers are not correct - we need to see how the results were obtained.
In starting the analysis on a research question, we focus on overall descriptive statistics and seeing if differences exist. Probing into reasons and mitigating factors is a follow-up activity.
1 The first step in analyzing data sets is to find some summary descriptive statistics for key variables. Since the assignment problems will
focus mostly on the compa-ratios, we need to find the mean, standard deviations, and range for our groups: Males, Females, and Overall.
Sorting the compa-ratios into male and females will require you copy and paste the Compa-ratio and Gender1 columns, and then sort on Gender1.
The values for age, performance rating, and service are provided for you for future use, and - if desired - to test your approach to the compa-ratio answers
(see if you can replicate the values).
You can use either the Data Analysis Descriptive Statistics tool or the Fx =average and =stdev functions.
The range can be found using the difference between the =max and =min functions with Fx functions or from Descriptive Statistics.
Suggestion: Copy and paste the compa-ratio data to the right (Column T) and gender data in column U.
If you use Descriptive statistics, Place the output table in row 1 of a column to the right.
If you did not use Descriptive Statistics, make sure your cells show the location of the data (Example: =average(T2:T51)
Compa-ratio Age Perf. Rat. Service
Overall Mean 35.7 85.9 9.0
Standard Deviation 8.2513 11.4147 5.7177 Note - remember the data is a sample from the larger company population
Range 30 45 21
Female Mean 32.5 84.2 7.9
Standard Deviation 6.9 13.6 4.9
Range 26.0 45.0 18.0
Male Mean 38.9 87.6 10.0
Standard Deviation 8.4 8.7 6.4
Range 28.0 30.0 21.0
A key issue in comparing data sets is to see if they are distributed/shaped the same. At this point we can do this
by looking at the probabilities that males and females are distributed in the same way for a grade levels.
2 Empirical Probability: What is the probability for a: Probability
a.       Randomly selected person being in grade E or above?
b.      Randomly selected person being a male in grade E or above?
c.      Randomly selected male being in grade E or above?
d. Why are the results different?
3 Normal Curve based probability: For each group (overall, females, males), what are the values for each question below?:
Make sure your answer cells show the Excel function and cell location of the data used.
A The probability of being in the top 1/3 of the compa-ratio distribution.
Note, we can find the cutoff value for the top 1/3 using the fx Large function: =large(range, value).
Value is the number that identifies the x-largest value. For the top 1/3 value would be the value that starts the top 1/3 of the range,
For the overall group, this would be the 50/3 or 17th (rounded), for the gender groups, it would be the 25/3 = 8th (rounded) value.
Overall Female Male All of the functions below are in the fx statistical list.
i. How nany salaries are in the top 1/3 (rounded to nearest whole number) for each group? Use the "=ROUND" function (found in Math or All list)
ii What Compa-ratio value starts the top 1/3 of the range for each group? Use the "=LARGE" function
iii What is the z-score for this value? Use Excel's STANDARDIZE function
iv. What is the normal curve probability of exceeding this score? Use "=1-NORM.S.DIST" function
B How do you interpret the relationship between the data sets? What does this suggest about our equal pay for equal work question?
4 Based on our sample data set, can the male and female compa-ratios in the population be equal to each other?
A First, we need to determine if these two groups have equal variances, in order to decide which t-test to use.
What is the data input ranged used for this question:
Step 1: Ho:
Ha:
Step 2: Decision Rule:
Step 3: Statistical test:
Why?
Step 4: Conduct the test - place cell B77 in the output location box.
Step 5: Conclusion and Interpretation
What is the p-value:
Is the P-value < 0.05 (for a one tail test) or 0.025 (for a two tail test)?
What is your decision: REJ or NOT reject the null?
What does this result say about our question of variance equality?
B Are male and female average compa-ratios equal?
(Regardless of the outcome of the above F-test, assume equal variances for this test.)
What is the data input ranged used for this question:
Step 1: Ho:
Ha:
Step 2: Decision Rule:
Step 3: Statistical test:
Why?
Step 4: Conduct the test - place cell B109 in the output location box.
Step 5: Conclusion and Interpretation
What is the p-value:
Is the P-value < 0.05 (for a one tail test) or 0.025 (for a two tail test)?
What is your decision: REJ or NOT reject the null?
What does your decision on rejecting the null hypothesis mean?
If the null hypothesis was rejected, calculate the effect size value:
If the effect size was calculated, what doe the result mean in terms of why the null hypothesis was rejected?
What does the result of this test tell us about our question on salary equality?
5 Is the Female average compa-ratio equal to or less than the midpoint value of 1.00?
This question is the same as: Does the company, pay its females - on average - at or below the grade midpoint (which is considered the market rate)?
Suggestion: Use the data column T to the right for your null hypothesis value.
What is the data input ranged used for this question:
Step 1: Ho:
Ha:
Step 2: Decision Rule:
Step 3: Statistical test:
Why?
Step 4: Conduct the test - place cell B162 in the output location box.
Step 5: Conclusion and Interpretation
What is the p-value:
Is the P-value < 0.05 (for a one tail test) or 0.025 (for a two tail test)?
What, besides the p-value, needs to be considered with a one tail test?
Decision: Reject or do not reject Ho?
What does your decision on rejecting the null hypothesis mean?
If the null hypothesis was rejected, calculate the effect size value:
If the effect size was calculated, what doe the result mean in terms of why the null hypothesis was rejected?
What does the result of this test tell us about our question on salary equality?
6 Considering both the salary information in the lectures and your compa-ratio information, what conclusions can you reach about equal pay for equal work?
Why - what statistical results support this conclusion?

Week 3

Week 3 ANOVA Three Questions
Remember to show how you got your results in the appropriate cells. For questions using functions, show the input range when asked.
Group name: G1 G2 G3 G4 G5 G6
1 One interesting question is are the average compa-ratios equal across salary ranges of 10K each. Salary Intervals: 22-29 30-39 40-49 50-59 60-69 70-79
While compa-ratios remove the impact of grade on salaries, are they different for different pay levels, Compa-ratio values:
that is are people at different levels paid differently relative to the midpoint? (Put data values at right.)
What is the data input ranged used for this question:
Step 1: Ho:
Ha:
Step 2: Decision Rule:
Step 3: Statistical test:
Why?
Step 4: Conduct the test - place cell b16 in the output location box.
Step 5: Conclusions and Interpretation
What is the p-value?
Is P-value < 0.05?
What is your decision: REJ or NOT reject the null?
If the null hypothesis was rejected, what is the effect size value (eta squared)?
If calculated, what does the effect size value tell us about why the null hypothesis was rejected?
What does that decision mean in terms of our equal pay question?
2 If the null hypothesis in question 1 was rejected, which pairs of means differ? Why?
Groups Compared Diff T +/- Term Low to High Difference Significant? Why?
G1 G2
G1 G3
G1 G4
G1 G5
G1 G6
G2 G3
G2 G4
G2 G5
G2 G6
G3 G4
G3 G5
G3 G6
G4 G5
G4 G6
G5 G6
3 Since compa is already a measure of pay for equal work, do these results impact
your conclusion on equal pay for equal work? Why or why not?

Week 4

Regression and Corellation Five Questions Compa-ratio Midpoint Age Performance Rating Service Raise Degree Gender
Remember to show how you got your results in the appropriate cells. For questions using functions, show the input range when asked.
1 Create a correlation table using Compa-ratio and the other interval level variables, except for Salary.
Suggestion, place data in columns T - Y.
What range was placed in the Correlation input range box:
Place C9 in output box.
b What are the statistically significant correlations related to Compa-ratio? T = Significant r =
c Are there any surprises - correlations you though would be significant and are not, or non significant correlations you thought would be?
d Why does or does not this information help answer our equal pay question?
2 Perform a regression analysis using compa as the dependent variable and the variables used in Q1 along with
including the dummy variables. Show the result, and interpret your findings by answering the following questions.
Suggestion: Place the dummy variables values to the right of column Y.
What range was placed in the Regression input range box:
Note: be sure to include the appropriate hypothesis statements.
Regression hypotheses
Ho:
Ha:
Coefficient hyhpotheses (one to stand for all the separate variables)
Ho:
Ha:
Place B36 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?
What is your decision: REJ or NOT reject the null?
What does this decision mean?
For each of the coefficients: Midpoint Age Perf. Rat. Service Gender Degree
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 the intercept coefficient and only the significant variables, what is the equation? Compa-ratio =
Is gender a significant factor in compa-ratio?
Regardless of statistical significance, who gets paid more with all other things being equal?
How do we know?
3 What does regression analysis show us about analyzing complex measures?
4 Between the lecture results and your results, what else would you like to know
before answering our question on equal pay? Why?
5 Between the lecture results and your results, what is your answer to the question
of equal pay for equal work for males and females? Why?

Randomized BUS308 Data - 2017.09.01-1.xlsm

Data

ID Salary Compa Midpoint Age Performance Rating Service Gender Raise Degree Gender1 Gr
1 61.6 1.081 57 34 85 8 0 5.7 0 M E The ongoing question that the weekly assignments will focus on is: Are males and females paid the same for equal work (under the Equal Pay Act)?
2 27.7 0.895 31 52 80 7 0 3.9 0 M B Note: to simplfy the analysis, we will assume that jobs within each grade comprise equal work.
3 35.1 1.132 31 30 75 5 1 3.6 1 F B
4 58 1.018 57 42 100 16 0 5.5 1 M E The column labels in the table mean:
5 48.2 1.004 48 36 90 16 0 5.7 1 M D ID – Employee sample number Salary – Salary in thousands
6 78.1 1.165 67 36 70 12 0 4.5 1 M F Age – Age in years Performance Rating - Appraisal rating (employee evaluation score)
7 41.3 1.032 40 32 100 8 1 5.7 1 F C Service – Years of service (rounded) Gender – 0 = male, 1 = female
8 22.1 0.962 23 32 90 9 1 5.8 1 F A Midpoint – salary grade midpoint Raise – percent of last raise
9 73.9 1.103 67 49 100 10 0 4 1 M F Grade – job/pay grade Degree (0= BS\BA 1 = MS)
10 23.1 1.003 23 30 80 7 1 4.7 1 F A Gender1 (Male or Female) Compa - salary divided by midpoint
11 23.3 1.012 23 41 100 19 1 4.8 1 F A
12 64.7 1.135 57 52 95 22 0 4.5 0 M E
13 41.1 1.027 40 30 100 2 1 4.7 0 F C
14 24 1.045 23 32 90 12 1 6 1 F A
15 22.6 0.984 23 32 80 8 1 4.9 1 F A
16 42.2 1.054 40 44 90 4 0 5.7 0 M C
17 63.7 1.118 57 27 55 3 1 3 1 F E
18 34.5 1.113 31 31 80 11 1 5.6 0 F B
19 24.3 1.055 23 32 85 1 0 4.6 1 M A
20 34.1 1.101 31 44 70 16 1 4.8 0 F B
21 77.2 1.152 67 43 95 13 0 6.3 1 M F
22 60.3 1.257 48 48 65 6 1 3.8 1 F D
23 23.1 1.004 23 36 65 6 1 3.3 0 F A
24 56.3 1.173 48 30 75 9 1 3.8 0 F D
25 25 1.087 23 41 70 4 0 4 0 M A 1.06848 0.0788733795 43.42 19.2012152393
26 23.5 1.020 23 22 95 2 1 6.2 0 F A 1.06132 0.0841312071 46.8 19.6160436038
27 46.9 1.172 40 35 80 7 0 3.9 1 M C .
28 78.3 1.169 67 44 95 9 1 4.4 0 F F
29 76.3 1.139 67 52 95 5 0 5.4 0 M F
30 49.3 1.027 48 45 90 18 0 4.3 0 M D
31 23.6 1.028 23 29 60 4 1 3.9 1 F A
32 26.5 0.855 31 25 95 4 0 5.6 0 M B Compa A B C D E F
33 57.5 1.008 57 35 90 9 0 5.5 1 M E F mean 1.0141666667 1.1205 1.0375 1.1243333333 1.175 1.134
34 28.6 0.923 31 26 80 2 0 4.9 1 M B m 1.0573333333 0.892 1.0833333333 0.9995 1.0818 1.12275
35 22.6 0.984 23 23 90 4 1 5.3 0 F A
36 23.6 1.026 23 27 75 3 1 4.3 0 F A F Stdev 0.0337876614 0.0311608729 0.0176776695 0.0751620472 0.0494974747 0.0212132034
37 23 0.999 23 22 95 2 1 6.2 0 F A m 0.0248260616 0.0190525589 0.0877971146 0.028991378 0.0607029196 0.0332603367
38 58.8 1.032 57 45 95 11 0 4.5 0 M E
39 33.9 1.094 31 27 90 6 1 5.5 0 F B
40 23.8 1.034 23 24 90 2 0 6.3 0 M A
41 45.8 1.144 40 25 80 5 0 4.3 0 M C
42 24.2 1.051 23 32 100 8 1 5.7 1 F A
43 75.6 1.128 67 42 95 20 1 5.5 0 F F
44 61.8 1.085 57 45 90 16 0 5.2 1 M E
45 56.9 1.185 48 36 95 8 1 5.2 1 F D
46 60.2 1.057 57 39 75 20 0 3.9 1 M E
47 57.2 1.003 57 37 95 5 0 5.5 1 M E
48 69.5 1.219 57 34 90 11 1 5.3 1 F E
49 63 1.105 57 41 95 21 0 6.6 0 M E
50 59.6 1.046 57 38 80 12 0 4.6 0 M E

Sheet1

Sal Compa G Mid Age EES SR G Raise Deg SUMMARY OUTPUT SUMMARY OUTPUT
24 1.045 1 23 32 90 9 1 5.8 1
24.2 1.053 1 23 30 80 7 1 4.7 1 Regression Statistics Regression Statistics
23.4 1.018 1 23 41 100 19 1 4.8 1 Multiple R 0.7050179484 Multiple R 0.9931286935
23.4 1.017 1 23 32 90 12 1 6 1 R Square 0.4970503076 R Square 0.9863046018
22.6 0.983 1 23 32 80 8 1 4.9 1 Adjusted R Square 0.4132253589 Adjusted R Square 0.9840220355
22.9 0.995 1 23 36 65 6 1 3.3 0 Standard Error 0.0561252686 Standard Error 2.4352822665
23.1 1.003 1 23 22 95 2 1 6.2 0 Observations 50 Observations 50
23.3 1.011 1 23 29 60 4 1 3.9 1
22.7 0.985 1 23 23 90 4 1 5.3 0 ANOVA ANOVA
23.5 1.023 1 23 27 75 3 1 4.3 0 df SS MS F Significance F df SS MS F Significance F
23 1.002 1 23 22 95 2 1 6.2 0 Regression 7 0.1307500775 0.0186785825 5.9296225662 0.0000782906 Regression 7 17938.424611863 2562.632087409 432.1033638177 5.29906273684337E-37
24 1.042 1 23 32 100 8 1 5.7 1 Residual 42 0.1323019225 0.0031500458 Residual 42 249.085188137 5.9305997175
35.5 1.145 1 31 30 75 5 1 3.6 1 Total 49 0.263052 Total 49 18187.5098
34.7 1.119 1 31 31 80 11 1 5.6 0
35.5 1.146 1 31 44 70 16 1 4.8 0 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%
35.2 1.136 1 31 27 90 6 1 5.5 0 Intercept 0.9486238772 0.0817167716 11.6086803119 0 0.7837127557 1.1135349987 0.7837127557 1.1135349987 Intercept -4.8714544587 3.54570071 -1.3739045839 0.1767599037 -12.0269681853 2.2840592678 -12.0269681853 2.2840592678
40.4 1.01 1 40 32 100 8 1 5.7 1 Mid 0.0034995027 0.0006492568 5.3900133356 0.0000029767 0.0021892495 0.0048097559 0.0021892495 0.0048097559 Mid 1.2284155048 0.0281713308 43.6051641629 1.32019333894083E-36 1.1715634576 1.2852675521 1.1715634576 1.2852675521
42.7 1.068 1 40 30 100 2 1 4.7 0 Age 0.0005527738 0.0014459446 0.3822925256 0.7041721007 -0.0023652605 0.0034708081 -0.0023652605 0.0034708081 Age 0.0368279425 0.0627397124 0.5869957178 0.5603489282 -0.0897859231 0.1634418081 -0.0897859231 0.1634418081
53.4 1.112 1 48 48 65 6 1 3.8 1 EES -0.0018462553 0.0010252155 -1.8008461371 0.0789105539 -0.0039152239 0.0002227133 -0.0039152239 0.0002227133 EES -0.0821579785 0.0444842245 -1.8469014451 0.0718147225 -0.171930778 0.007614821 -0.171930778 0.007614821
51.5 1.072 1 48 30 75 9 1 3.8 0 SR -0.0004182288 0.0018278101 -0.2288141345 0.820123898 -0.004106899 0.0032704414 -0.004106899 0.0032704414 SR -0.0778484529 0.079308905 -0.9815852701 0.3319249969 -0.2379003029 0.0822033971 -0.2379003029 0.0822033971
49.8 1.037 1 48 36 95 8 1 5.2 1 G 0.0646649961 0.0183396697 3.5259629624 0.001034866 0.0276540443 0.101675948 0.0276540443 0.101675948 G 2.9145083112 0.7957605113 3.6625445343 0.000693549 1.3085985836 4.5204180389 1.3085985836 4.5204180389
68.3 1.198 1 57 27 55 3 1 3 1 Raise 0.0146549564 0.0139088976 1.0536389608 0.2980722322 -0.0134143354 0.0427242483 -0.0134143354 0.0427242483 Raise 0.6763294824 0.6035087689 1.1206622295 0.2687988764 -0.5416005215 1.8942594864 -0.5416005215 1.8942594864
65.4 1.148 1 57 34 90 11 1 5.3 1 Deg 0.0014675988 0.0161098249 0.0910996125 0.9278465471 -0.0310433441 0.0339785418 -0.0310433441 0.0339785418 Deg 0.0345044482 0.6990072742 0.0493620731 0.9608647532 -1.3761493419 1.4451582383 -1.3761493419 1.4451582383
78.4 1.17 1 67 44 95 9 1 4.4 0
75.9 1.133 1 67 42 95 20 1 5.5 0
24 1.044 0 23 32 85 1 0 4.6 1
23.3 1.012 0 23 41 70 4 0 4 0
24.1 1.049 0 23 24 90 2 0 6.3 0
27.5 0.887 0 31 52 80 7 0 3.9 0 t-Test: Two-Sample Assuming Equal Variances
27.1 0.875 0 31 25 95 4 0 5.6 0
27.7 0.895 0 31 26 80 2 0 4.9 1 Variable 1 Variable 2
40.8 1.019 0 40 44 90 4 0 5.7 0 Mean 1.06684 1.04836
43.9 1.097 0 40 35 80 7 0 3.9 1 Variance 0.00430164 0.00648099
41 1.025 0 40 25 80 5 0 4.3 0 Observations 25 25
48.7 1.014 0 48 36 90 16 0 5.7 1 Pooled Variance 0.005391315
49.4 1.029 0 48 45 90 18 0 4.3 0 Hypothesized Mean Difference 0
64.4 1.13 0 57 34 85 8 0 5.7 0 df 48
64.5 1.132 0 57 42 100 16 0 5.5 1 t Stat 0.8898352784
58.9 1.033 0 57 52 95 22 0 4.5 0 P(T<=t) one-tail 0.188996287
57.9 1.016 0 57 35 90 9 0 5.5 1 t Critical one-tail 1.6772241961
59 1.035 0 57 45 95 11 0 4.5 0 P(T<=t) two-tail 0.3779925741
63.3 1.111 0 57 45 90 16 0 5.2 1 t Critical two-tail 2.0106347576
56.8 0.996 0 57 39 75 20 0 3.9 1
58 1.017 0 57 37 95 5 0 5.5 1
62.4 1.094 0 57 41 95 21 0 6.6 0
63.8 1.12 0 57 38 80 12 0 4.6 0
79 1.179 0 67 36 70 12 0 4.5 1
77 1.149 0 67 49 100 10 0 4 1
74.8 1.116 0 67 43 95 13 0 6.3 1
76 1.135 0 67 52 95 5 0 5.4 0