BUS 308 Weeks 1

See comments at the right of the data set. ID Salary Compa Midpoint 8 10 11 14 15 23 26 31 35 36 37 42 3 18 20 39 7 13 22 24 45 17 48 28 43 19 25 40 2 32 34 16 27 41 5 30 1 4 12

23 22 23 24 24 23 24 24 24 23 22 24 34 36 34 35 41 42 57 50 55 69 65 75 77 24 24 25 27 28 28 47 40 43 47 49 58 66 60

1.000 0.956 1.000 1.043 1.043 1.000 1.043 1.043 1.043 1.000 0.956 1.043 1.096 1.161 1.096 1.129 1.025 1.050 1.187 1.041 1.145 1.210 1.140 1.119 1.149 1.043 1.043 1.086 0.870 0.903 0.903 1.175 1.000 1.075 0.979 1.020 1.017 1.157 1.052

23 23 23 23 23 23 23 23 23 23 23 23 31 31 31 31 40 40 48 48 48 57 57 67 67 23 23 23 31 31 31 40 40 40 48 48 57 57 57

Age 32 30 41 32 32 36 22 29 23 27 22 32 30 31 44 27 32 30 48 30 36 27 34 44 42 32 41 24 52 25 26 44 35 25 36 45 34 42 52

Performanc Service Gender Raise e Rating 90 9 1 5.8 80 7 1 4.7 100 19 1 4.8 90 12 1 6 80 8 1 4.9 65 6 1 3.3 95 2 1 6.2 60 4 1 3.9 90 4 1 5.3 75 3 1 4.3 95 2 1 6.2 100 8 1 5.7 75 5 1 3.6 80 11 1 5.6 70 16 1 4.8 90 6 1 5.5 100 8 1 5.7 100 2 1 4.7 65 6 1 3.8 75 9 1 3.8 95 8 1 5.2 55 3 1 3 90 11 1 5.3 95 9 1 4.4 95 20 1 5.5 85 1 0 4.6 70 4 0 4 90 2 0 6.3 80 7 0 3.9 95 4 0 5.6 80 2 0 4.9 90 4 0 5.7 80 7 0 3.9 80 5 0 4.3 90 16 0 5.7 90 18 0 4.3 85 8 0 5.7 100 16 0 5.5 95 22 0 4.5

33 38 44 46 47 49 50 6 9 21 29

64 56 60 65 62 60 66 76 77 76 72

1.122 0.982 1.052 1.140 1.087 1.052 1.157 1.134 1.149 1.134 1.074

57 57 57 57 57 57 57 67 67 67 67

35 45 45 39 37 41 38 36 49 43 52

90 95 90 75 95 95 80 70 100 95 95

9 11 16 20 5 21 12 12 10 13 5

0 0 0 0 0 0 0 0 0 0 0

5.5 4.5 5.2 3.9 5.5 6.6 4.6 4.5 4 6.3 5.4

Degree Gender1 Grade 0 0 0 0 0 1 1 0 1 1 1 0 0 1 1 1 0 1 0 1 0 0 1 1 1 1 0 0 0 0 1 0 1 0 1 0 0 1 0

F F F F F F F F F F F F F F F F F F F F F F F F F M M M M M M M M M M M M M M

A A A A A A A A A A A A B B B B C C D D D E E F F A A A B B B C C C D D E E E

The ongoing question that the weekly assignments will focus on is: Are males and fem

Note: to simplfy the analysis, we will assume that jobs within each grade comprise equ

The column labels in the table mean: ID – Employee sample number Age – Age in years Service – Years of service (rounded) Midpoint – salary grade midpoint Grade – job/pay grade Gender1 (Male or Female)

Salary – Salary in thousands Performance Rating – Appraisal rating Gender: 0 = male, 1 = female Raise – percent of last raise Degree (0= BS\BA 1 = MS) Compa - salary divided by midpoint

1 0 1 1 1 0 0 1 1 1 0

M M M M M M M M M M M

E E E E E E E F F F F 10

ill focus on is: Are males and females paid the same for equal work (under the Equal Pay Act)?

s within each grade comprise equal work.

Salary in thousands nce Rating – Appraisal rating (Employee evaluation score) 0 = male, 1 = female percent of last raise 0= BS\BA 1 = MS) salary divided by midpoint

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 about the order, th

No one variable is ratio because no variable values tells about the order among them so they are ratio varia

2

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, standard deviation, and range for 3 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. 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?

b. c. 4 a. b. c. d. e. f. g. h. i.

5.

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? Why are the results different?

For each group (overall, females, and males) find: The value that cuts off the top 1/3 salary in each group. The z score for each value: The normal curve probability of exceeding this score: What is the empirical probability of being at or exceeding this salary value? The value that cuts off the top 1/3 compa in each group. The z score for each value: The normal curve probability of exceeding this score: What is the empirical probability of being at or exceeding this compa value? How do you interpret the relationship between the data sets? What do they mean about our equal pay for 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 variable in the

What conclusions can you make about the issue of male and female pay equality? Are all of the results co 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 compa are no

y tell us about the order, they tell us the exact value between units

em so they are ratio variables.

for key variables. eviation, and range for 3 groups: overall sample, Females, and Males. e and =stdev functions. ons with Fx) functions.

Probability 0.4

0.83

The results are different because population and samples are different for both the cases. In the first case male is the 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 about our equal pay for equal work question?

emaining variable in the data set is high, actually thy are dependent to each other. Are all of the results consistent?

salary and compa are not equal therefore we canot say that equal pay for equal work

es. In the first case male is the population and we are choosing those males who got grade E

Week 2

1

Testing means In questions 2 and 3, be sure to include the null and alternate hypotheses you will be testing. In the first 3 questions use alpha = 0.05 in making your decisions on rejecting or not rejecting the nul

Below are 2 one-sample t-tests comparing male and female average salaries to the overall sample me (Note: a one-sample t-test in Excel can be performed by selecting the 2-sample unequal variance t-tes Based on our sample, how do you interpret the results and what do these results suggest about the pop 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 Assuming Unequal having no variance in the Ho variable makes the calculations default to the one-sample t-test outcome Male

Ho

Mean 52 45 Variance 316 0 Observations 25 25 Hypothesized Mean Difference 0 df 24 t Stat 1.96890383 P(T