Descriptive Statistics including Probability Week 1 of the assignment would need to be completed by Monday, the assignment has show proof of work, and each

Descriptive Statistics including Probability Week 1 of the assignment would need to be completed by Monday, the assignment has show proof of work, and each week a new section of the assignment has to be turned in. Inside the Excel spreadsheet it contains the data in the first section that will be used in the following 4 weeks. ID
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
Salary Compa- Midpoint
ratio
62.3
27.8
35.6
59.2
47.3
73.7
40.9
23.7
76
23.9
22.7
60.1
42.2
23.3
21.5
45.2
70.7
33.8
23.8
32.9
78.2
53.4
23.2
60
24.3
22.7
41.1
76.6
75.4
47.2
23.5
26.8
59.7
27.9
23
23.2
24.6
60.2
35.1
25.6
1.093
0.896
1.149
1.038
0.986
1.100
1.023
1.030
1.134
1.038
0.988
1.055
1.055
1.012
0.935
1.129
1.241
1.089
1.036
1.061
1.167
1.113
1.009
1.249
1.058
0.989
1.027
1.143
1.125
0.984
1.020
0.866
1.047
0.900
1.000
1.007
1.069
1.057
1.132
1.112
57
31
31
57
48
67
40
23
67
23
23
57
40
23
23
40
57
31
23
31
67
48
23
48
23
23
40
67
67
48
23
31
57
31
23
23
23
57
31
23
Age
34
52
30
42
36
36
32
32
49
30
41
52
30
32
32
44
27
31
32
44
43
48
36
30
41
22
35
44
52
45
29
25
35
26
23
27
22
45
27
24
Performance Service Gender
Rating
85
80
75
100
90
70
100
90
100
80
100
95
100
90
80
90
55
80
85
70
95
65
65
75
70
95
80
95
95
90
60
95
90
80
90
75
95
95
90
90
8
7
5
16
16
12
8
9
10
7
19
22
2
12
8
4
3
11
1
16
13
6
6
9
4
2
7
9
5
18
4
4
9
2
4
3
2
11
6
2
0
0
1
0
0
0
1
1
0
1
1
0
1
1
1
0
1
1
0
1
0
1
1
1
0
1
0
1
0
0
1
0
0
0
1
1
1
0
1
0
Raise Degree Gender1
5.7
3.9
3.6
5.5
5.7
4.5
5.7
5.8
4
4.7
4.8
4.5
4.7
6
4.9
5.7
3
5.6
4.6
4.8
6.3
3.8
3.3
3.8
4
6.2
3.9
4.4
5.4
4.3
3.9
5.6
5.5
4.9
5.3
4.3
6.2
4.5
5.5
6.3
0
0
1
1
1
1
1
1
1
1
1
0
0
1
1
0
1
0
1
0
1
1
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
M
M
F
M
M
M
F
F
M
F
F
M
F
F
F
M
F
F
M
F
M
F
F
F
M
F
M
F
M
M
F
M
M
M
F
F
F
M
F
M
41
42
43
44
45
46
47
48
49
50
44.6
24.3
74.6
65.3
51.8
60.2
62.1
62.6
63.7
56.8
1.115
1.055
1.114
1.145
1.080
1.057
1.090
1.099
1.117
0.997
40
23
67
57
48
57
57
57
57
57
25
32
42
45
36
39
37
34
41
38
80
100
95
90
95
75
95
90
95
80
5
8
20
16
8
20
5
11
21
12
0
1
1
0
1
0
0
1
0
0
4.3
5.7
5.5
5.2
5.2
3.9
5.5
5.3
6.6
4.6
0
1
0
1
1
1
1
1
0
0
M
F
F
M
F
M
M
F
M
M
Grade
E
B
B
E
D
F
C
A
F
A
A
E
C
A
A
C
E
B
A
B
F
D
A
D
A
A
C
F
F
D
A
B
E
B
A
A
A
E
B
A
Do not manipuilate Data set on this page, copy
to another page to make changes
The ongoing question that the weekly assignments will focus on is: Are males and females paid the same
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 scor
Service – Years of service (rounded)
Gender – 0 = male, 1 = female
Midpoint – salary grade midpointRaise – percent of last raise
Grade – job/pay grade
Degree (0= BSBA 1 = MS)
Gender1 (Male or Female)
Compa-ratio – salary divided by midpoint
C
A
F
E
D
E
E
E
E
E
Week 1: Descriptive Statistics, including Probability
While the lectures will examine our equal pay question from the compa-ratio viewpoint, our weekly assignments will
examining the issue using the salary measure.
The purpose of this assignmnent is two fold:
1. Demonstrate mastery with Excel tools.
2. Develop descriptive statistics to help examine the question.
3. Interpret descriptive outcomes
The first issue in examining salary data to determine if we – as a company – are paying males and females equally for
descriptive statistics to give us something to make a preliminary decision on whether we have an issue or not.
1
Descriptive Statistics: Develop basic descriptive statistics for Salary
The first step in analyzing data sets is to find some summary descriptive statistics for key variables.
Suggestion: Copy the gender1 and salary columns from the Data tab to columns T and U at the right.
Then use Data Sort (by gender1) to get all the male and female salary values grouped together.
a.
Use the Descriptive Statistics function in the Data Analysis tab
to develop the descriptive statistics summary for the overall
group’s overall salary. (Place K19 in output range.)
Highlight the mean, sample standard deviation, and range.
Using Fx (or formula) functions find the following (be sure to show the formula
and not just the value in each cell) asked for salary statistics for each gender:
Male
Female
Mean:
Sample Standard Deviation:
Range:
b.
2
Develop a 5-number summary for the overall, male, and female SALARY variable.
For full credit, show the excel formulas in each cell rather than simply the numerical answer.
Overall Males
Females
Max
3rd Q
Midpoint
1st Q
Min
3
Location Measures: comparing Male and Female midpoints to the overall Salary data range.
For full credit, show the excel formulas in each cell rather than simply the numerical answer.
Male
Using the entire Salary range and the M and F midpoints found in Q2
a. What would each midpoint’s percentile rank be in the overall range?
b. What is the normal curve z value for each midpoint within overall range?
4
Probability Measures: comparing Male and Female midpoints to the overall Salary data range
For full credit, show the excel formulas in each cell rather than simply the numerical answer.
Male
Using the entire Salary range and the M and F midpoints found in Q2, find
a. The Empirical Probability of equaling or exceeding (=>) that value for
b. The Normal curve Prob of => that value for each group
5
Conclusions: What do you make of these results? Be sure to include findings from this week’s lectures as
In comparing the overall, male, and female outcomes, what relationship(s) see, to exist between the data se
What does this suggest about our equal pay for equal work question?
t, our weekly assignments will focus on
males and females equally for doing equal work is to develop some
e have an issue or not.
stics for key variables.
mns T and U at the right.
Place Excel outcome in Cell K19
alary data range.
umerical answer.
Female
Use Excel’s =PERCENTRANK.EXC function
Use Excel’s =STANDARDIZE function
l Salary data range
umerical answer.
Female
Show the calculation formula = value/50 or =countif(range,”>=”&cell)/50
Use “=1-NORM.S.DIST” function
s from this week’s lectures as well.
e, to exist between the data sets?
Week 2: Identifying Significant Differences – part 1
To Ensure full credit for each question, you need to show how you got your results. This involves either showing wh
or showing the excel formula in each cell.
Be sure to copy the appropriate data columns from the data tab to
As with our examination of compa-ratio in the lecture, the first question we have about salary between the genders in
What we do, depends upon our findings.
1
As with the compa-ratio lecture example, we want to examine salary variation within the groups – are they
a
What is the data input ranged used for this question:
b
c.
Which is needed for this question: a one- or two-tail hypothesis statement and test ?
Answer:
Why:
Step 1:
Step 2:
Step 3:
Step 4:
Step 5:
Ho:
Ha:
Significance (Alpha):
Test Statistic and test:
Why this test?
Decision rule:
Conduct the test – place test function in cell k10
Step 6: Conclusion and Interpretation
What is the p-value:
What is your decision: REJ or NOT reject the null?
Why?
What is your conclusion about the variance in the
population for male and female salaries?
2
Once we know about variance quality, we can move on to means: Are male and female average salaries eq
(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:
b
Does this question need a one or two-tail hypothesis statement and test?
Why:
Ho:
Ha:
Significance (Alpha):
Test Statistic and test:
Why this test?
Decision rule:
Conduct the test – place test function in cell K35
c.
a
Step 1:
Step 2:
Step 3:
Step 4:
Step 5:
Step 6: Conclusion and Interpretation
What is the p-value:
What is your decision: REJ or NOT reject the null?
Why?
What is your conclusion about the means in the population for
male and female salaries?
3
Education is often a factor in pay differences.
Do employees with an advanced degree (degree = 1) have higher average salaries?
Note: assume equal variance for the salaries in each degree for this question.
a
What is the data input ranged used for this question:
b
c.
Step 1:
Step 2:
Step 3:
Step 4:
Step 5:
Does this question need a one or two-tail hypothesis statement and test?
Why:
Ho:
Ha:
Significance (Alpha):
Test Statistic and test:
Why this test?
Decision rule:
Conduct the test – place test function in cell K60
Step 6: Conclusion and Interpretation
What is the p-value:
Is the t value in the t-distribution tail indicated by the
arrow in the Ha claim?
What is your decision: REJ or NOT reject the null?
Why?
What is your conclusion about the impact of education on
average salaries?
4
Considering both the compa-ratio information from the lectures and your salary information, what conclusi
Why – what statistical results support this conclusion?
olves either showing where the data you used is located
mns from the data tab to the right for your use this week.
y between the genders involves equality – are they the same or different?
Use Cell K10 for the Excel test outcome location.
Use Cell K35 for the Excel test outcome location.
Use Cell K60 for the Excel test outcome location.
ormation, what conclusions can you reach about equal pay for equal work?
Week 3: Identifying Significant Differences – part 2
To Ensure full credit for each question, you need to show how you got your results. This involves either showing wh
or showing the excel formula in each cell.
Be sure to copy the appropriate data columns from
1
A good pay program will have different average salaries by grade. Is this the case for our company?
a
What is the data input ranged used for this question:
Note: assume equal variances for each grade, even though this may not be accurate, for purposes of this question.
b.
Step 1:
Step 2:
Step 3:
Step 4:
Step 5:
Ho:
Ha:
Significance (Alpha):
Test Statistic and test:
Why this test?
Decision rule:
Conduct the test – place test function in cell K08
Step 6: Conclusion and Interpretation
What is the p-value:
What is your decision: REJ or NOT reject the null?
Why?
What is your conclusion about the means in the
population for grade salaries?
2
If the null hypothesis in question 1 was rejected, which pairs of means differ?
(Use the values from the ANOVA table to complete the follow table.)
Groups
Compared
Mean Diff.
T value used +/- Term
Low
A-B
A-C
A-D
A-E
A-F
B-C
B-D
B-E
B-E
C-D
C-E
C-F
D-E
D-F
E-F
3
One issue in salary is the grade an employee is in – higher grades have higher salaries.
This suggests that one question to ask is if males and females are distributed in a similar pattern across the
a
What is the data input ranged used for this question:
b.
Step 1:
Step 2:
Step 3:
Step 4:
Step 5:
Ho:
Ha:
Significance (Alpha):
Test Statistic and test:
Why this test?
Decision rule:
Conduct the test – place test function in cell K54
Step 6: Conclusion and Interpretation
What is the p-value:
What is your decision: REJ or NOT reject the null?
Why?
What is your conclusion about the means in the
population for male and female salaries?
4
What implications do this week’s analysis have for our equal pay question?
Why – what statistical results support this conclusion?
This involves either showing where the data you used is located
he appropriate data columns from the data tab to the right for your use this week.
he case for our company?
Use Cell K08 for the Excel test outcome location.
ate, for purposes of this question.
to
High
Difference
Significant? Why?
Use Cell K54 for the Excel test outcome location.
Place the actual distribution in the table below.
A
B
C
D
Male
Female
E
Place the expected distribution in the table below.
A
B
C
D
E
Male
Female
Data Input Table:
Group name:
List salaries within each grade
A
B
Salary Range Groups
C
D
F
F
nge Groups
E
F
Week 4: Identifying relationships – correlations and regression
To Ensure full credit for each question, you need to show how you got your results. This involves either showing wh
or showing the excel formula in each cell.
Be sure to copy the appropriate data columns from the data ta
1
What is the correlation between and among the interval/ratio level variables with salary? (Do not include c
a. Create the correlation table.
i.
What is the data input ranged used for this question:
ii. Create a correlation table in cell K08.
b. Technically, we should perform a hypothesis testing on each correlation to determine
if it is significant or not. However, we can be faithful to the process and save some
time by finding the minimum correlation that would result in a two tail rejection of the null.
We can then compare each correlation to this value, and those exceeding it (in either a
positive or negative direction) can be considered statistically significant.
i. What is the t-value we would use to cut off the two tails?
T=
ii. What is the associated correlation value related to this t-value? r =
c. What variable(s) is(are) significantly correlated to salary?
d. Are there any surprises – correlations you though would be significant and are not, or non significant cor
e. Why does or does not this information help answer our equal pay question?
2
Perform a regression analysis using salary as the dependent variable and the variables used in Q1 along wit
our two dummy variables – gender and education. Show the result, and interpret your findings by answerin
Suggestion: Add the dummy variables values to the right of the last data columns used for Q1.
What is the multiple regression equation predicting/explaining salary using all of our possible variables exc
a.
What is the data input ranged used for this question:
b.
Step 1: State the appropriate hypothesis statements:
Ho:
Ha:
Step 2: Significance (Alpha):
Step 3: Test Statistic and test:
Why this test?
Step 4: Decision rule:
Step 5: Conduct the test – place test function in cell M34
Step 6: Conclusion and Interpretation
What is the p-value:
What is your decision: REJ or NOT reject the null?
Why?
What is your conclusion about the factors influencing
the population salary values?
c.
If we rejected the null hypothesis, we need to test the significance of each of the variable coeff
Step 1: State the appropriate coefficient hypothesis statements:
(Write a single pair, we w
Ho:
Ha:
Step 2: Significance (Alpha):
Step 3: Test Statistic and test:
Why this test?
Step 4: Decision rule:
Step 5: Conduct the test
Note, in this case the test has been performed and is part of the Regression output ab
Step 6: Conclusion and Interpretation
Place the t and p-values in the following table
Identify your decision on rejecting the null for each variable. If you reject the null, p
Midpoint
Age
Perf. Rat. Seniority
Raise
Gender
t-value:
P-value:
Rejection Decision:
If Null is rejected, what is the
variable’s coefficient value?
Using the intercept coefficient and only the significant variables, what is the equation?
Salary =
d.
Is gender a significant factor in salary?
e.
Regardless of statistical significance, who gets paid more with all other things being equal?
f.
How do we know?
3
After considering the compa-ratio based results in the lectures and your salary based results, what else wou
before answering our question on equal pay? Why?
4
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?
5
What does regression analysis show us about analyzing complex measures?
olves either showing where the data you used is located
olumns from the data tab to the right for your use this week.
alary? (Do not include compa-ratio in this question.)
Use Cell K08 for the Excel test outcome location.
ot, or non significant correlations you thought would be?
les used in Q1 along with
our findings by answering the following questions.
ur possible variables except compa-ratio?
Use Cell M34 for the Excel test outcome location.
ach of the variable coefficients.
Write a single pair, we will use it for each variable separately.)
he Regression output above.
. If you reject the null, place the coefficient in the table.
Degree
is the equation?
r things being equal?
d results, what else would you like to know

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