Statistics Assignment

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Data

ID Salary Compa Midpoint Age Performance Rating Service Gender Raise Degree Gender1 Gr Students: Copy the Student Data file data values into this sheet to assist in doing your weekly assignments.
1 60 1.053 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 26.8 0.866 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 34.7 1.120 31 30 75 5 1 3.6 1 F B
4 57.9 1.016 57 42 100 16 0 5.5 1 M E The column labels in the table mean:
5 48.5 1.010 48 36 90 16 0 5.7 1 M D ID – Employee sample number Salary – Salary in thousands
6 74.3 1.109 67 36 70 12 0 4.5 1 M F Age – Age in years Performance Rating - Appraisal rating (employee evaluation score)
7 42 1.050 40 32 100 8 1 5.7 1 F C Service – Years of service (rounded) Gender – 0 = male, 1 = female
8 23.6 1.025 23 32 90 9 1 5.8 1 F A Midpoint – salary grade midpoint Raise – percent of last raise
9 74.2 1.107 67 49 100 10 0 4 1 M F Grade – job/pay grade Degree (0= BS\BA 1 = MS)
10 22.6 0.984 23 30 80 7 1 4.7 1 F A Gender1 (Male or Female) Compa - salary divided by midpoint
11 23.4 1.018 23 41 100 19 1 4.8 1 F A
12 61.7 1.082 57 52 95 22 0 4.5 0 M E
13 41.3 1.033 40 30 100 2 1 4.7 0 F C
14 22.9 0.997 23 32 90 12 1 6 1 F A
15 24.9 1.084 23 32 80 8 1 4.9 1 F A
16 46.6 1.166 40 44 90 4 0 5.7 0 M C
17 66.5 1.166 57 27 55 3 1 3 1 F E
18 36.3 1.170 31 31 80 11 1 5.6 0 F B
19 24.5 1.064 23 32 85 1 0 4.6 1 M A
20 34.3 1.107 31 44 70 16 1 4.8 0 F B
21 76.7 1.145 67 43 95 13 0 6.3 1 M F
22 57.3 1.193 48 48 65 6 1 3.8 1 F D
23 22.5 0.979 23 36 65 6 1 3.3 0 F A
24 54.7 1.140 48 30 75 9 1 3.8 0 F D
25 24.5 1.067 23 41 70 4 0 4 0 M A
26 23 0.998 23 22 95 2 1 6.2 0 F A
27 39.4 0.985 40 35 80 7 0 3.9 1 M C
28 75.4 1.125 67 44 95 9 1 4.4 0 F F
29 72 1.075 67 52 95 5 0 5.4 0 M F
30 46 0.958 48 45 90 18 0 4.3 0 M D
31 24 1.045 23 29 60 4 1 3.9 1 F A
32 26.9 0.867 31 25 95 4 0 5.6 0 M B
33 59.8 1.049 57 35 90 9 0 5.5 1 M E
34 26.5 0.856 31 26 80 2 0 4.9 1 M B
35 22.6 0.982 23 23 90 4 1 5.3 0 F A
36 23.4 1.017 23 27 75 3 1 4.3 0 F A
37 23.3 1.014 23 22 95 2 1 6.2 0 F A
38 65.4 1.147 57 45 95 11 0 4.5 0 M E
39 36.1 1.164 31 27 90 6 1 5.5 0 F B
40 24.2 1.053 23 24 90 2 0 6.3 0 M A
41 45.2 1.130 40 25 80 5 0 4.3 0 M C
42 22.7 0.989 23 32 100 8 1 5.7 1 F A
43 77.2 1.152 67 42 95 20 1 5.5 0 F F
44 63.2 1.108 57 45 90 16 0 5.2 1 M E
45 51 1.062 48 36 95 8 1 5.2 1 F D
46 63.7 1.117 57 39 75 20 0 3.9 1 M E
47 62.9 1.104 57 37 95 5 0 5.5 1 M E
48 69.6 1.221 57 34 90 11 1 5.3 1 F E
49 63.5 1.114 57 41 95 21 0 6.6 0 M E
50 61.4 1.078 57 38 80 12 0 4.6 0 M E

Week 1

Week 1. Measurement and Description - chapters 1 and 2
The goal this week is to gain an understanding of our data set - what kind of data we are looking at, some descriptive measurse, and a
look at how the data is distributed (shape).
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
b. For each variable that you did not call ratio, why did you make that decision?
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 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.
Some of the values are completed for you - please finish the table.
Salary Compa Age Perf. Rat. Service
Overall Mean 35.7 85.9 9.0
Standard Deviation 8.2513 11.4147 5.7177 Note - 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
3 What is the probability for a: Probability
a.       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?
4 A key issue in comparing data sets is to see if they are distributed/shaped the same. We can do this by looking at some measures of where
some selected values are within each data set - that is how many values are above and below a comparable value.
For each group (overall, females, and males) find: Overall Female Male
A The value that cuts off the top 1/3 salary value in each group "=large" function
i The z score for this value within each group? Excel's standize function
ii The normal curve probability of exceeding this score: 1-normsdist function
iii What is the empirical probability of being at or exceeding this salary value?
B The value that cuts off the top 1/3 compa value in each group.
i The z score for this value within each group?
ii The normal curve probability of exceeding this score:
iii What is the empirical probability of being at or exceeding this compa value?
C 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?