Part 1 : Descriptive Statistics, including Probability
While the lectures will examine our equal pay question from the compa-ratio viewpoint, our weekly assignments will focus on 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 doing equal work is to develop some 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 Place Excel outcome in Cell K19 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.
b. 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
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Male |
Female |
| Mean: |
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| Sample Standard Deviation: |
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| Range: |
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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.
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Overall |
Males |
Females |
| Max |
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| 3rd Q |
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| Midpoint |
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| 1st Q |
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| Min |
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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.
Using the entire Salary range and the M and F midpoints found in Q2 Male Female
a. What would each midpoint's percentile rank be in the overall range? Use Excel's =PERCENTRANK.EXC function
b. What is the normal curve z value for each midpoint within overall range? Use Excel's =STANDARDIZE function
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. Using the entire Salary range and the M and F midpoints found in Q2, find Male Female
a. The Empirical Probability of equaling or exceeding (=>) that value for Show the calculation formula = value/50 or =countif(range,">="&cell)/50
b. The Normal curve Prob of => that value for each group Use "=1-NORM.S.DIST" function
5 Conclusions: What do you make of these results? Be sure to include findings from this week's lectures as well. In comparing the overall, male, and female outcomes, what relationship(s) see, to exist between the data sets?
What does this suggest about our equal pay for equal work question?
Part 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 where the data you used is located or showing the excel formula in each cell. Be sure to copy the appropriate data columns from the data tab to the right for your use this week.
As with our examination of compa-ratio in the lecture, the first question we have about salary between the genders involves equality - are they the same or different?
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 equal? Use Cell K10 for the Excel test outcome location.
a What is the data input ranged used for this question:
b Which is needed for this question: a one- or two-tail hypothesis statement and test ?
Answer:
Why:
c. Step 1: 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 k10
What is the p-value:
What is your decision: REJ or NOT reject the null?
Why?
Step 6: Conclusion and Interpretation
What is your conclusion about the variance in the population for male and femlae salaries?
2 Once we know about variance quality, we can move on to means: Are male and female average salaries equal? Use Cell K35 for the Excel test outcome location.
(Regardless of the outcome of the above F-test, assume equal variances for this test.)
a 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:
c. Step 1: 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 K35
What is the p-value:
What is your decision: REJ or NOT reject the null?
Why?
Step 6: Conclusion and Interpretation
What is your conclusion about the means in the population for male and femlae salaries?
3 Education is often a factor in pay differences.
Do employees with an advanced degree (degree = 1) have higher average salaries? Use Cell K60 for the Excel test outcome location.
a 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:
c. Step 1: 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 K60
What is the p-value:
What else must be considered in a one tail test before reaching a conclusion?
What is your decision: REJ or NOT reject the null?
Why?
Step 6: Conclusion and Interpretation
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 conclusions can you reach about equal pay for equal work?
Why - what statistical results support this conclusion?
Attachment:- Student Worksheet.rar