BUS308 statistics week 3

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equal_pay___week_3.xlsx
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Data

ID Sal Compa Mid Age EES SER G Raise Deg Gen1 Gr
1 58 1.017 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 0.870 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 34 1.096 31 30 75 5 1 3.6 1 F B
4 66 1.157 57 42 100 16 0 5.5 1 M E The column labels in the table mean:
5 47 0.979 48 36 90 16 0 5.7 1 M D ID – Employee sample number Sal – Salary in thousands
6 76 1.134 67 36 70 12 0 4.5 1 M F Age – Age in years EES – Appraisal rating (Employee evaluation score)
7 41 1.025 40 32 100 8 1 5.7 1 F C SER – Years of service G – Gender (0 = male, 1 = female)
8 23 1.000 23 32 90 9 1 5.8 1 F A Mid – salary grade midpoint Raise – percent of last raise
9 77 1.149 67 49 100 10 0 4 1 M F Grade – job/pay grade Deg (0= BS\BA 1 = MS)
10 22 0.956 23 30 80 7 1 4.7 1 F A Gen1 (Male or Female) Compa - salary divided by midpoint, a measure of salary that removes the impact of grade
11 23 1.000 23 41 100 19 1 4.8 1 F A
12 60 1.052 57 52 95 22 0 4.5 0 M E This data should be treated as a sample of employees taken from a company that has about 1,000
13 42 1.050 40 30 100 2 1 4.7 0 F C employees using a random sampling approach.
14 24 1.043 23 32 90 12 1 6 1 F A
15 24 1.043 23 32 80 8 1 4.9 1 F A
16 47 1.175 40 44 90 4 0 5.7 0 M C Mac Users: The homework in this course assumes students have Windows Excel, and
17 69 1.210 57 27 55 3 1 3 1 F E can load the Analysis ToolPak into their version of Excel.
18 36 1.161 31 31 80 11 1 5.6 0 F B The analysis tool pak has been removed from Excel for Windows, but a free third-party
19 24 1.043 23 32 85 1 0 4.6 1 M A tool that can be used (found on an answers Microsoft site) is:
20 34 1.096 31 44 70 16 1 4.8 0 F B http://www.analystsoft.com/en/products/statplusmacle
21 76 1.134 67 43 95 13 0 6.3 1 M F Like the Microsoft site, I make cannot guarantee the program, but do know that
22 57 1.187 48 48 65 6 1 3.8 1 F D Statplus is a respected statistical package. You may use other approaches or tools
23 23 1.000 23 36 65 6 1 3.3 0 F A as desired to complete the assignments.
24 50 1.041 48 30 75 9 1 3.8 0 F D
25 24 1.043 23 41 70 4 0 4 0 M A
26 24 1.043 23 22 95 2 1 6.2 0 F A
27 40 1.000 40 35 80 7 0 3.9 1 M C
28 75 1.119 67 44 95 9 1 4.4 0 F F
29 72 1.074 67 52 95 5 0 5.4 0 M F
30 49 1.020 48 45 90 18 0 4.3 0 M D
31 24 1.043 23 29 60 4 1 3.9 1 F A
32 28 0.903 31 25 95 4 0 5.6 0 M B
33 64 1.122 57 35 90 9 0 5.5 1 M E
34 28 0.903 31 26 80 2 0 4.9 1 M B
35 24 1.043 23 23 90 4 1 5.3 0 F A
36 23 1.000 23 27 75 3 1 4.3 0 F A
37 22 0.956 23 22 95 2 1 6.2 0 F A
38 56 0.982 57 45 95 11 0 4.5 0 M E
39 35 1.129 31 27 90 6 1 5.5 0 F B
40 25 1.086 23 24 90 2 0 6.3 0 M A
41 43 1.075 40 25 80 5 0 4.3 0 M C
42 24 1.043 23 32 100 8 1 5.7 1 F A
43 77 1.149 67 42 95 20 1 5.5 0 F F
44 60 1.052 57 45 90 16 0 5.2 1 M E
45 55 1.145 48 36 95 8 1 5.2 1 F D
46 65 1.140 57 39 75 20 0 3.9 1 M E
47 62 1.087 57 37 95 5 0 5.5 1 M E
48 65 1.140 57 34 90 11 1 5.3 1 F E
49 60 1.052 57 41 95 21 0 6.6 0 M E
50 66 1.157 57 38 80 12 0 4.6 0 M E
http://www.analystsoft.com/en/products/statplusmacle

Week 1

Week 1. Describing the data.
<Use right click on the row numbers at the left to insert rows below each question for your results and comments.>
1 Using the Excel Analysis ToolPak function descriptive statistics, generate and show the descriptive statistics for each appropriate variable in the sample data set.
a. For which variables in the data set does this function not work correctly for? Why?
2 Sort the data by Gen or Gen 1 (into males and females) and find the mean and standard deviation for each gender for the following variables:
sal, compa, age, sr and raise. Use either the descriptive stats function or the Fx functions (average and stdev).
3 What is the probability for a:
a.       Randomly selected person being a male in grade E?
b.      Randomly selected male being in grade E?
c. Why are the results different?
4 Find:
a. The z score for each male salary, based on only the male salaries.
b. The z score for each female salary, based on only the female salaries.
c. The z score for each female compa, based on only the female compa values.
d. The z score for each male compa, based on only the male compa values.
e. What do the distributions and spread suggest about male and female salaries?
Why might we want to use compa to measure salaries between males and females?
5 Based on this sample, what conclusions can you make about the issue of male and female pay equality?
Are all of the results consistent with your conclusion? If not, why not?

Week 2

Week 2 Testing means with the t-test <Note: use right click on row numbers to insert rows to perform analysis below any question>
For questions 2 and 3 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.
1 Below are 2 one-sample t-tests comparing male and female average salaries to the overall sample mean.
Based on our sample, how do you interpret the results and what do these results suggest about the population means for male and female salaries?
Males Females
Ho: Mean salary = 45 Ho: Mean salary = 45
Ha: Mean salary =/= 45 Ha: Mean salary =/= 45
Note when performing a one sample test with ANOVA, the second variable (Ho) is listed as the same value for every corresponding value in the data set.
t-Test: Two-Sample Assuming Unequal Variances t-Test: Two-Sample Assuming Unequal Variances
Since the Ho variable has Var = 0, variances are unequal; this test defaults to 1 sample t in this situation
Male Ho Female Ho
Mean 52 45 Mean 38 45
Variance 316 0 Variance 334.6666666667 0
Observations 25 25 Observations 25 25
Hypothesized Mean Difference 0 Hypothesized Mean Difference 0
df 24 df 24
t Stat 1.9689038266 t Stat -1.9132063573
P(T<=t) one-tail 0.0303078503 P(T<=t) one-tail 0.0338621184
t Critical one-tail 1.7108820799 t Critical one-tail 1.7108820799
P(T<=t) two-tail 0.0606157006 P(T<=t) two-tail 0.0677242369
t Critical two-tail 2.0638985616 t Critical two-tail 2.0638985616
Conclusion: Do not reject Ho; mean equals 45 Conclusion: Do not reject Ho; mean equals 45
Interpretation:
2 Based on our sample results, perform a 2-sample t-test to see if the population male and female salaries could be equal to each other.
3 Based on our sample results, can the male and female compas in the population be equal to each other? (Another 2-sample t-test.)
4 What other information would you like to know to answer the question about salary equity between the genders? Why?
5 If the salary and compa mean tests in questions 3 and 4 provide different results about male and female salary equality,
which would be more appropriate to use in answering the question about salary equity? Why?
What are your conclusions about equal pay at this point?

Week 3

Week 3 Testing multiple means with ANOVA <Note: use right click on row numbers to insert rows to perform analysis below any question>
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.
1.      Based on the sample data, can the average(mean) salary in the population be the same for each of the grade levels? (Assume equal variance, and use the analysis toolpak function ANOVA.)
Set up the input table/range to use as follows: Put all of the salary values for each grade under the appropriate grade label.
Be sure to incllude the null and alternate hypothesis along with the statistical test and result.
A B C D E F Note: Assume equal variances for all grades.
2.      The table and analysis below demonstrate a 2-way ANOVA with replication. Please interpret the results.
Grade
Gender A B C D E F
M 24 27 40 47 56 76 The salary values were randomly picked for each cell.
25 28 47 49 66 77
F 22 34 41 50 65 75
24 36 42 57 69 77
Ho: Average salaries are equal for all grades
Ha: Average salaries are not equal for all grades
Ho: Average salaries by gender are equal
Ha: Average salaries by gender are not equal
Ho: Interaction is not significant
Ha: Interaction is significant
Perform analysis:
Anova: Two-Factor With Replication
SUMMARY A B C D E F Total
M
Count 2 2 2 2 2 2 12
Sum 49 55 87 96 122 153 562
Average 24.5 27.5 43.5 48 61 76.5 46.8333333333
Variance 0.5 0.5 24.5 2 50 0.5 364.5151515152
F
Count 2 2 2 2 2 2 12
Sum 46 70 83 107 134 152 592
Average 23 35 41.5 53.5 67 76 49.3333333333
Variance 2 2 0.5 24.5 8 2 367.3333333333
Total
Count 4 4 4 4 4 4
Sum 95 125 170 203 256 305
Average 23.75 31.25 42.5 50.75 64 76.25
Variance 1.5833333333 19.5833333333 9.6666666667 18.9166666667 31.3333333333 0.9166666667
ANOVA
Source of Variation SS df MS F P-value F crit
Sample 37.5 1 37.5 3.8461538462 0.0734833371 4.7472253467
Columns 7841.8333333333 5 1568.3666666667 160.8581196581 0.0000000001 3.1058752391 Note: a number with an E after it (E9 or E-6, for example)
Interaction 91.5 5 18.3 1.8769230769 0.1723082608 3.1058752391 means we move the decimal point that number of places.
Within 117 12 9.75 For example, 1.2E4 becomes 12000; while 4.56E-5 becomes 0.0000456
Total 8087.8333333333 23
Do we reject or not reject each of the null hypotheses? What do your conclusions mean about the population values being tested?
Interpretation:
3.    Using our sample results, can we say that the compa values in the population are equal by grade and/or gender, and are independent of each factor?
Grade Be sure to include the null and alternate hypothesis along with the statistical test and result.
Gender A B C D E F <Randomly pick compas to fill each cell - for exampe, a compa
M for the intersection of M and A might be 1.043.>
<If desired, you can use the compa values that relate to the
F salary values used in question 2 for a more direct comparison of the two
outcomes.>
Conduct and show the results of a 2-way ANOVA with replication using the completed table above. The results should look something like those in question 2.
Interpret the results. Are the average compas for each gender (listed as sample) equal? For each grade? Do grade and gender interaction impact compa values?
4.   Pick any other variable you are interested in and do a simple 2-way ANOVA without replication. Why did you pick this variable and what do the results show?
Variable name: Be sure to include the null and alternate hypothesis along with the statistical test and result.
Gender A B C D E F
M Hint: use mean values in the boxes.
F
5.   Using the results for this week, What are your conclusions about gender equal pay for equal work at this point?

Week 4

Week 4 Confidence Intervals and Chi Square (Chs 11 - 12) Let's look at some other factors that might influence pay. Q1 Q2 <Note: use right click on row numbers to insert rows to perform analysis below any question>
For question 3 below, be sure to list the null and alternate hypothesis statements. Use .05 for your significance level in making your decisions. Gr Deg Gen1 Sal
For full credit, you need to also show the statistical outcomes - either the Excel test result or the calculations you performed. A 0 F 34
1 One question we might have is if the distribution of graduate and undergraduate degrees independent of the grade the employee? A 0 F 41
(Note: this is the same as asking if the degrees are distributed the same way.)
Based on the analysis of our sample data (shown below), what is your answer?
Ho: The populaton correlation between grade and degree is 0. C 0 F 77
Ha: The population correlation between grade and degree is > 0
Perform analysis:
OBSERVED A B C D E F Total
COUNT - M or 0 7 5 3 2 5 3 25
COUNT - F or 1 8 2 2 3 7 3 25
total 15 7 5 5 12 6 50
EXPECTED
7.5 3.5 2.5 2.5 6 3 25 <Highlighting each cell with show how the value
7.5 3.5 2.5 2.5 6 3 25 is found: row total times column total divided by
15 7 5 5 12 6 50 grand total.>
By using either the Excel Chi Square functions or calculating the results directly as the text shows, do we
reject or not reject the null hypothesis? What does your conclusion mean?
Interpretation:
2 Using our sample data, we can 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)?
Males Mean St error Low to High
52 3.6587793957 44.4482793272 59.5517206728 Results are mean +/-2.064*standard error
Females 38 3.6227541769 30.5226353789 45.4773646211 2.064 is t value for 95% interval
<Reminder: standard error is the sample standard deviation divided by the square root of the sample size.>
Interpretation:
C 0 F 55
D 1 M 77
3 Based on our sample data, can we conclude that males and females are distributed across grades in a similar pattern within the population? D 1 M 60
4 Using our sample data, construct a 95% confidence interval for the population's mean service difference for each gender.
Do they intersect or overlap? How do these results compare to the findings in week 2, question 2?
5 How do you interpret these results in light of our question about equal pay for equal work?

Week 5

Week 5 Correlation and Regression
For each question involving a statistical test below, 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.
1 Create a correlation table for the variables in our data set. (Use analysis ToolPak function Correlation.)
a. Interpret the results. What variables seem to be important in seeing if we pay males and females equally for equal work?
2 Below is a regression analysis for salary being predicted/explained by the other variables in our sample (Mid,
age, ees, sr, raise, and deg 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.)
Ho: The regression equation is not significant.
Ha: The regression equation is significant.
Ho: The regression coefficient for each variable is not significant
Ha: The regression coefficient for each variable is significant
Sal The analysis used Sal as the y (dependent variable) and
SUMMARY OUTPUT mid, age, ees, sr, g, raise, and deg as the dependent
variables (entered as a range).
Regression Statistics
Multiple R 0.9921549762
R Square 0.9843714969
Adjusted R Square 0.9817667464
Standard Error 2.5927763074
Observations 50
ANOVA
df SS MS F Significance F
Regression 7 17783.6554628284 2540.5222089755 377.9139268848 8.44042689148567E-36
Residual 42 282.3445371716 6.7224889803
Total 49 18066
Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%
Intercept -4.009 3.775 -1.062 0.294 -11.627 3.609 -11.627 3.609
Mid 1.220 0.030 40.674 0.000 1.159 1.280 1.159 1.280
Age 0.029 0.067 0.439 0.663 -0.105 0.164 -0.105 0.164
EES -0.096 0.047 -2.020 0.050 -0.191 -0.000 -0.191 -0.000
SR -0.074 0.084 -0.876 0.386 -0.244 0.096 -0.244 0.096
G 2.552 0.847 3.012 0.004 0.842 4.261 0.842 4.261
Raise 0.834 0.643 1.299 0.201 -0.462 2.131 -0.462 2.131
Deg 1.002 0.744 1.347 0.185 -0.500 2.504 -0.500 2.504
Interpretation: Do you reject or not reject the regression null hypothesis?
Do you reject or not reject the null hypothesis for each variable?
What is the regression equation, using only significant variables if any exist?
What does result tell us about equal pay for equal work for males and females?
3 Perform a regression analysis using compa as the dependent variable and the same independent
variables 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.
4 Based on all of your results to date, is gender a factor in the pay practices of this company? Why or why not?
Which is the best variable to use in analyzing pay practices - salary or compa? Why?
5 Why 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?