Part -1:
It is highly recommended that you copy the data columns (with labels) and paste them to the right so that whatever you do will not disrupt the original data values and relationships.
To Ensure full credit for each question, you need to show how you got your results. For example, Question 1 asks for several data values. If you obtain them using descriptive statistics, then the cells should have an "=XX" formula in them, where XX is the column and row number showing the value in the descriptive statistics table. If you choose to generate each value using fxfunctions, then each function should be located in the cell and the location of the data values should be shown.
So, Cell D31 - as an example - shoud contain something like "=T6" or "=average(T2:T26)". Having only a numerical value will not earn full credit.
The reason for this is to allow instructors to provide feedback on Excel tools if the answers are not correct - we need to see how the results were obtained.
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.
1 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 compa-ratios, we need to find the mean, standard deviations, and range for our groups: Males, Females, and Overall.
Sorting the compa-ratios into male and females will require you copy and paste the Compa-ratio 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 compa-ratio 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)
|
|
Compa-ratio |
Age |
Perf. Rat. |
Service |
| Overall |
Mean |
|
35.7 |
85.9 |
9.0 |
|
Standard Deviation |
|
8.2513 |
11.4147 |
5.7177 |
|
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 |
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 nany salaries are in the top 1/3 (rounded to nearest whole number) for each group?
ii What Compa-ratio 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:
Step 1: Ho:
Ha:
Step 2: Decision Rule:
Step 3: Statistical test:
Why?
Step 4: Conduct the test - place cell B77 in the output location box.
Step 5: Conclusion and Interpretation
What is the p-value:
Is the P-value < 0.05 (for a one tail test) or 0.025 (for a two tail test)?
What is your decision: REJ or NOT reject the null?
What does this result say about our question of variance equality?
B Are male and female average compa-ratios 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:
Step 1: Ho:
Ha:
Step 2: Decision Rule:
Step 3: Statistical test:
Why?
Step 4: Conduct the test - place cell B109 in the output location box.
Step 5: Conclusion and Interpretation
What is the p-value:
Is the P-value < 0.05 (for a one tail test) or 0.025 (for a two tail test)?
What is your decision: REJ or NOT reject the null?
What does your decision on rejecting the null hypothesis mean?
If the null hypothesis was rejected, calculate the effect size value:
If the effect size was calculated, what doe 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?
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:
Step 1: Ho:
Ha:
Step 2: Decision Rule:
Step 3: Statistical test:
Why?
Step 4: Conduct the test - place cell B162 in the output location box.
Step 5: Conclusion and Interpretation
What is the p-value:
Is the P-value < 0.05 (for a one tail test) or 0.025 (for a two tail test)?
What, besides the p-value, needs to be considered with a one tail test?
Decision: Reject or do not reject Ho?
What does your decision on rejecting the null hypothesis mean?
If the null hypothesis was rejected, calculate the effect size value:
If the effect size was calculated, what doe 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 compa-ratio information, what conclusions can you reach about equal pay for equal work?
Why - what statistical results support this conclusion?
Part -2: ANOVA Questions
Remember to show how you got your results in the appropriate cells. For questions using functions, show the input range when asked.
1 One interesting question is are the average compa-ratios equal across salary ranges of 10K each. While compa-ratios remove the impact of grade on salaries, are they different for different pay levels, that is are people at different levels paid differently relative to the midpoint? (Put data values at right.)
What is the data input ranged used for this question:
Step 1: Ho:
Ha:
Step 2: Decision Rule:
Step 3: Statistical test:
Why?
Step 4: Conduct the test - place cell b16 in the output location box.
Step 5: Conclusions and Interpretation
What is the p-value?
Is P-value < 0.05?
What is your decision: REJ or NOT reject the null?
If the null hypothesis was rejected, what is the effect size value (eta squared)?
If calculated, what does the effect size value tell us about why the null hypothesis was rejected?
What does that decision mean in terms of our equal pay question?
2 If the null hypothesis in question 1 was rejected, which pairs of means differ?
Groups Compared Diff T +/- Term Low to High
G1 G2
G1 G3
G1 G4
G1 G5
G1 G6
G2 G3
G2 G4
G2 G5
G2 G6
G3 G4
G3 G5
G3 G6
G4 G5
G4 G6
G5 G6
3 Since compa is already a measure of pay for equal work, do these results impact your conclusion on equal pay for equal work? Why or why not?
Part -3
Remember to show how you got your results in the appropriate cells. For questions using functions, show the input range when asked.
1 Create a correlation table using Compa-ratio and the other interval level variables, except for Salary.
Suggestion, place data in columns T - Y.
Place C9 in output box.
b What are the statistically significant correlations related to Compa-ratio?
c Are there any surprises - correlations you though would be significant and are not, or non significant correlations you thought would be?
d Why does or does not this information help answer our equal pay question?
2 Perform a regression analysis using compa as the dependent variable and the variables used in Q1 along with including the dummy variables. Show the result, and interpret your findings by answering the following questions.
Suggestion: Place the dummy variables values to the right of column Y.
Note: be sure to include the appropriate hypothesis statements.
Regression hypotheses
Ho:
Ha:
Coefficient hyhpotheses (one to stand for all the separate variables)
Ho:
Ha:
Place B36 in output box.
Interpretation:
For the Regression as a whole:
What is the value of the F statistic:
What is the p-value associated with this value:
Is the p-value < 0.05?
What is your decision: REJ or NOT reject the null?
What does this decision mean?
For each of the coefficients:
What is the coefficient's p-value for each of the variables:
Is the p-value < 0.05?
Do you reject or not reject each null hypothesis:
What are the coefficients for the significant variables?
Using the intercept coefficient and only the significant variables, what is the equation?
Is gender a significant factor in compa-ratio?
Regardless of statistical significance, who gets paid more with all other things being equal?
How do we know?
3 What does regression analysis show us about analyzing complex measures?
4 Between the lecture results and your results, what else would you like to know before answering our question on equal pay? Why?
5 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?
Attachment:- Assignment worksheet.rar