Let's look at some other factors that might influence pay. Complete the problems included in the resources below and submit your work in an Excel document. Be sure to show all of your work and clearly label all calculations.
All statistical calculations will use the Employee Salary Data Set and the Weekly Assignment Sheet.
Part -1:
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.
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 |
| |
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:
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:
A The value that cuts off the top 1/3 salary 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 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?
Part -2:
1 Below are 2 one-sample t-tests comparing male and female average salaries to the overall sample mean.
(Note: a one-sample t-test in Excel can be performed by selecting the 2-sample unequal variance t-test and making the second variable = Ho value - a constant.)
Note: These values are not the same as the data the assignment uses. The purpose is to analyze the results of t-tests rather than directly answer our equal pay question.
Based on these results, how do you interpret the results and what do these results suggest about the population means for male and female average salaries?
| Males |
|
|
|
Females |
|
| Ho: Mean salary = |
45.00 |
|
|
Ho: Mean salary = |
45.00 |
| Ha: Mean salary =/= |
45.00 |
|
|
Ha: Mean salary =/= |
45.00 |
Note: While the results both below are actually from Excel's t-Test: Two-Sample Assuming Unequal Variances, having no variance in the Ho variable makes the calculations default to the one-sample t-test outcome - we are tricking Excel into doing a one sample test for us.
| |
Male |
Ho |
|
|
Female |
Ho |
|
| Mean |
52 |
45 |
|
Mean |
38 |
45 |
|
| Variance |
316 |
0 |
|
Variance |
334.667 |
0 |
|
| Observations |
25 |
25 |
|
Observations |
25 |
25 |
|
| Hypothesized Mean Difference |
0 |
|
|
Hypothesized Mean Difference |
0 |
|
|
| df |
24 |
|
|
df |
24 |
|
|
| t Stat |
1.968903827 |
|
|
t Stat |
-1.91321 |
|
|
| P(T<=t) one-tail |
0.03030785 |
|
|
P(T<=t) one-tail |
0.03386 |
|
|
| t Critical one-tail |
1.71088208 |
|
|
t Critical one-tail |
1.71088 |
|
|
| P(T<=t) two-tail |
0.060615701 |
|
|
P(T<=t) two-tail |
0.06772 |
|
|
| t Critical two-tail |
2.063898562 |
|
|
t Critical two-tail |
2.0639 |
|
|
| Conclusion: Do not reject Ho; mean equals 45 |
Conclusion: Do not reject Ho; mean equals 45 |
2 Based on our sample data set, perform a 2-sample t-test to see if the population male and female average salaries could be equal to each other.
(Since we have not yet covered testing for variance equality, assume the data sets have statistically equal variances.)
Ho: Male salary mean = Female salary mean
Ha: Male salary mean =/= Female salary mean
Test to use: t-Test: Two-Sample Assuming Equal Variances
P-value is:
Is P-value < 0.05 (one tail test) or 0.25 (two tail test)?
Reject or do not reject Ho:
If the null hypothesis was rejected, calculate the effect size value:
If calculated, what is the meaning of effect size measure:
Interpretation:
b. Is the one or two sample t-test the proper/correct apporach to comparing salary equality? Why?
3 Based on our sample data set, can the male and female compas in the population be equal to each other? (Another 2-sample t-test.)
Again, please assume equal variances for these groups.
Ho:
Ha:
Statistical test to use:
What is the p-value:
Is P-value < 0.05 (one tail test) or 0.25 (two tail test)?
Reject or do not reject Ho:
If the null hypothesis was rejected, calculate the effect size value:
If calculated, what is the meaning of effect size measure:
Interpretation:
4 Since performance is often a factor in pay levels, is the average Performance Rating the same for both genders?
NOTE: do NOT assume variances are equal in this situation.
What is the p-value:
Is P-value < 0.05 (one tail test) or 0.25 (two tail test)?
Do we REJ or Not reject the null?
If the null hypothesis was rejected, calculate the effect size value:
If calculated, what is the meaning of effect size measure:
Interpretation:
5 If the salary and compa mean tests in questions 2 and 3 provide different results about male and female salary equality,
which would be more appropriate to use in answering the question about salary equity? Why?
What are your conclusions about equal pay at this point?
Part -3:
1 Many companies consider the grade midpoint to be the "market rate" - the salary needed to hire a new employee.
Does the company, on average, pay its existing employees at or above the market rate?
Use the data columns at the right to set up the paired data set for the analysis.
What is the p-value:
Is P-value < 0.05 (one tail test) or 0.25 (two tail test)?
What else needs to be checked on a 1-tail test in order to reject the null?
Do we REJ or Not reject the null?
If the null hypothesis was rejected, what is the effect size value:
If calculated, what is the meaning of effect size measure:
Interpretation of test results:
Let's look at some other factors that might influence pay - education(degree) and performance ratings.
2 Last week, we found that average performance ratings do not differ between males and females in the population.
Now we need to see if they differ among the grades. Is the average performace rating the same for all grades?
(Assume variances are equal across the grades for this ANOVA.)
The rating values sorted by grade have been placed in columns I - N for you.
Null Hypothesis: Ho: means equal for all grades
Alt. Hypothesis: Ha: at least one mean is unequal
Place B17 in Outcome range box.
Interpretation of test results:
What is the p-value:
Is P-value < 0.05?
Do we REJ or Not reject the null?
If the null hypothesis was rejected, what is the effect size value (eta squared):
Meaning of effect size measure:
What does that decision mean in terms of our equal pay question:
3 While it appears that average salaries per each grade differ, we need to test this assumption.
Is the average salary the same for each of the grade levels?
Use the input table to the right to list salaries under each grade level.
(Assume equal variance, and use the analysis toolpak function ANOVA.)
Null Hypothesis:
Alt. Hypothesis:
4 The table and analysis below demonstrate a 2-way ANOVA with replication. Please interpret the results.
Note: These values are not the same as the data the assignment uses. The purpose of this question is to analyze the result of a 2-way ANOVA test rather than directly answer our equal pay question.
Ho: Average compas by gender are equal
Ha: Average compas by gender are not equal
Ho: Average compas are equal for each degree
Ha: Average compas are not equal for each degree
Ho: Interaction is not significant
Ha: Interaction is significant
Interpretation:
For Ho: Average compas by gender are equal Ha: Average compas by gender are not equal
What is the p-value:
Is P-value < 0.05?
Do you reject or not reject the null hypothesis:
If the null hypothesis was rejected, what is the effect size value (eta squared):
Meaning of effect size measure:
For Ho: Average compas are equal for all degrees Ha: Average compas are not equal for all grades
What is the p-value:
Is P-value < 0.05?
Do you reject or not reject the null hypothesis:
If the null hypothesis was rejected, what is the effect size value (eta squared):
Meaning of effect size measure:
For: Ho: Interaction is not significant Ha: Interaction is significant
What is the p-value:
Is P-value < 0.05?
Do you reject or not reject the null hypothesis:
If the null hypothesis was rejected, what is the effect size value (eta squared):
Meaning of effect size measure:
What do these three decisions mean in terms of our equal pay question:
5. Using the results up thru this week, what are your conclusions about gender equal pay for equal work at this point?
Part -4:
1 Using our sample data, construct a 95% confidence interval for the population's mean salary for each gender.
Interpret the results.
2 Using our sample data, construct a 95% confidence interval for the mean salary difference between the genders in the population.
How does this compare to the findings in week 2, question 2?
How does this compare to the week 2, question 2 result (2 sampe t-test)?
a. Why is using a two sample tool (t-test, confidence interval) a better choice than using 2 one-sample techniques when comparing two samples?
3 We found last week that the degree values within the population do not impact compa rates.
This does not mean that degrees are distributed evenly across the grades and genders.
Do males and females have athe same distribution of degrees by grade?
(Note: while technically the sample size might not be large enough to perform this test, ignore this limitation for this exercise.)
Ignore any cell size limitations.
What are the hypothesis statements:
Interpretation:
4 Based on our sample data, can we conclude that males and females are distributed across grades in a similar pattern within the population?
What is the value of the chi square statistic:
What is the p-value associated with this value:
Is the p-value <0.05?
Do you reject or not reject the null hypothesis:
If you rejected the null, what is the Phi correlation:
If calculated, what is the meaning of effect size measure:
What does this decision mean for our equal pay question:
5. How do you interpret these results in light of our question about equal pay for equal work?
Part -5:
1. Create a correlation table for the variables in our data set. (Use analysis ToolPak or StatPlus:mac LE function Correlation.)
a. Reviewing the data levels from week 1, what variables can be used in a Pearson's Correlation table (which is what Excel produces)?
b. Place table here (C8):
c. Using r = approximately .28 as the signicant r value (at p = 0.05) for a correlation between 50 values, what variables are significantly related to Salary?
To compa?
d. Looking at the above correlations - both significant or not - are there any surprises -by that I mean any relationships you expected to be meaningful and are not and vice-versa?
e. Does this help us answer our equal pay for equal work question?
2 Below is a regression analysis for salary being predicted/explained by the other variables in our sample (Midpoint, age, performance rating, service, gender, and degree variables. (Note: since salary and compa are different ways of expressing an employee's salary, we do not want to have both used in the same regression.)
Plase interpret the findings.
Note: These values are not the same as the data the assignment uses. The purpose is to analyze the result of a regression test rather than directly answer our equal pay question.
Ho: The regression equation is not significant.
Ha: The regression equation is significant.
Ho: The regression coefficient for each variable is not significant
Ha: The regression coefficient for each variable is significant
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?
Do you reject or not reject the null hypothesis:
What does this decision mean for our equal pay question:
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 salary:
If so, who gets paid more with all other things being equal?
How do we know?
3 Perform a regression analysis using compa as the dependent variable and the same independent variables as used in question 2. Show the result, and interpret your findings by answering the same questions.
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:
Attachment:- data sheet.rar