In starting the analysis on a research question, we focus on overall descriptive statistics and seeing if differences exist. Probing into reasons and mitigating factors is a follow-up activity.
The first step in analyzing data sets is to find some summary descriptive statistics for key variables. Since the assignment problems will focus mostly on the comparatios, we need to find the mean, standard deviations, and range for our groups: Males, Females, and Overall.
Sorting the comparatios into male and females will require you copy and paste the Comparatio and Gender1 columns, and then sort on Gender1.
The values for age, performance rating, and service are provided for you for future use, and - if desired - to test your approach to the comparatio answers (see if you can replicate the values).
You can use either the Data Analysis Descriptive Statistics tool or the Fx =average and =stdev functions.
The range can be found using the difference between the =max and =min functions with Fx functions or from Descriptive Statistics.
Suggestion: Copy and paste the compa-ratio data to the right (Column T) and gender data in column U.
If you use Descriptive statistics, Place the output table in row 1 of a column to the right.
If you did not use Descriptive Statistics, make sure your cells show the location of the data (Example: =average(T2:T51)
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Compa-ratio
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Age
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Perf. Rat.
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Service
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Overall
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Mean
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35.7
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85.9
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9.0
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Standard Deviation
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8.2513
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11.4147
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5.7177
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Range
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30
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45
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21
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Female
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Mean
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32.5
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84.2
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7.9
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Standard Deviation
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6.9
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13.6
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4.9
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Range
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26.0
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45.0
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18.0
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Male
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Mean
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38.9
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87.6
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10.0
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Standard Deviation
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8.4
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8.7
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6.4
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Range
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28.0
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30.0
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21.0
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Note - remember the data is a sample from the larger company population
A key issue in comparing data sets is to see if they are distributed/shaped the same. At this point we can do this by looking at the probabilities that males and females are distributed in the same way for a grade levels.
2. Empirical Probability: What is the probability for a:
a. Randomly selected person being in grade E or above?
b. Randomly selected person being a male in grade E or above?
c. Randomly selected male being in grade E or above?
d. Why are the results different?
3. Normal Curve based probability: For each group (overall, females, males), what are the values for each question below?:
Make sure your answer cells show the Excel function and cell location of the data used.
A. The probability of being in the top 1/3 of the compa-ratio distribution.
Note, we can find the cutoff value for the top 1/3 using the fx Large function: =large(range, value).
Value is the number that identifies the x-largest value. For the top 1/3 value would be the value that starts the top 1/3 of the range,
For the overall group, this would be the 50/3 or 17th (rounded), for the gender groups, it would be the 25/3 = 8th (rounded) value.
i. How many salaries are in the top 1/3 (rounded to nearest whole number) for each group?
ii. What Comparatio value starts the top 1/3 of the range for each group?
iii. What is the z-score for this value?
iv. What is the normal curve probability of exceeding this score?
B. How do you interpret the relationship between the data sets? What does this suggest about our equal pay for equal work question?
4. Based on our sample data set, can the male and female compa-ratios in the population be equal to each other?
A. First, we need to determine if these two groups have equal variances, in order to decide which t-test to use.
What is the data input ranged used for this question.
B. Are male and female average comparatios equal? (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.
5. Is the Female average compa-ratio equal to or less than the midpoint value of 1.00?
This question is the same as: Does the company, pay its females - on average - at or below the grade midpoint (which is considered the market rate)?
Suggestion: Use the data column T to the right for your null hypothesis value.
What is the data input ranged used for this question.
What does your decision on rejecting the null hypothesis mean?
If the effect size was calculated, what does the result mean in terms of why the null hypothesis was rejected?
What does the result of this test tell us about our question on salary equality?
6. Considering both the salary information in the lectures and your comparatio information, what conclusions can you reach about equal pay for equal work?
Why - what statistical results support this conclusion?
Only Do Week 2.
Attachment:- Assignment.rar