Statistics Assignment

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Data

ID Salary Compa Midpoint Age Performance Rating Service Gender Raise Degree Gender1 Gr Students: Copy the Student Data file data values into this sheet to assist in doing your weekly assignments.
1 60 1.053 57 34 85 8 0 5.7 0 M E The ongoing question that the weekly assignments will focus on is: Are males and females paid the same for equal work (under the Equal Pay Act)?
2 26.8 0.866 31 52 80 7 0 3.9 0 M B Note: to simplfy the analysis, we will assume that jobs within each grade comprise equal work.
3 34.7 1.120 31 30 75 5 1 3.6 1 F B
4 57.9 1.016 57 42 100 16 0 5.5 1 M E The column labels in the table mean:
5 48.5 1.010 48 36 90 16 0 5.7 1 M D ID – Employee sample number Salary – Salary in thousands
6 74.3 1.109 67 36 70 12 0 4.5 1 M F Age – Age in years Performance Rating - Appraisal rating (employee evaluation score)
7 42 1.050 40 32 100 8 1 5.7 1 F C Service – Years of service (rounded) Gender – 0 = male, 1 = female
8 23.6 1.025 23 32 90 9 1 5.8 1 F A Midpoint – salary grade midpoint Raise – percent of last raise
9 74.2 1.107 67 49 100 10 0 4 1 M F Grade – job/pay grade Degree (0= BS\BA 1 = MS)
10 22.6 0.984 23 30 80 7 1 4.7 1 F A Gender1 (Male or Female) Compa - salary divided by midpoint
11 23.4 1.018 23 41 100 19 1 4.8 1 F A
12 61.7 1.082 57 52 95 22 0 4.5 0 M E
13 41.3 1.033 40 30 100 2 1 4.7 0 F C
14 22.9 0.997 23 32 90 12 1 6 1 F A
15 24.9 1.084 23 32 80 8 1 4.9 1 F A
16 46.6 1.166 40 44 90 4 0 5.7 0 M C
17 66.5 1.166 57 27 55 3 1 3 1 F E
18 36.3 1.170 31 31 80 11 1 5.6 0 F B
19 24.5 1.064 23 32 85 1 0 4.6 1 M A
20 34.3 1.107 31 44 70 16 1 4.8 0 F B
21 76.7 1.145 67 43 95 13 0 6.3 1 M F
22 57.3 1.193 48 48 65 6 1 3.8 1 F D
23 22.5 0.979 23 36 65 6 1 3.3 0 F A
24 54.7 1.140 48 30 75 9 1 3.8 0 F D
25 24.5 1.067 23 41 70 4 0 4 0 M A
26 23 0.998 23 22 95 2 1 6.2 0 F A
27 39.4 0.985 40 35 80 7 0 3.9 1 M C
28 75.4 1.125 67 44 95 9 1 4.4 0 F F
29 72 1.075 67 52 95 5 0 5.4 0 M F
30 46 0.958 48 45 90 18 0 4.3 0 M D
31 24 1.045 23 29 60 4 1 3.9 1 F A
32 26.9 0.867 31 25 95 4 0 5.6 0 M B
33 59.8 1.049 57 35 90 9 0 5.5 1 M E
34 26.5 0.856 31 26 80 2 0 4.9 1 M B
35 22.6 0.982 23 23 90 4 1 5.3 0 F A
36 23.4 1.017 23 27 75 3 1 4.3 0 F A
37 23.3 1.014 23 22 95 2 1 6.2 0 F A
38 65.4 1.147 57 45 95 11 0 4.5 0 M E
39 36.1 1.164 31 27 90 6 1 5.5 0 F B
40 24.2 1.053 23 24 90 2 0 6.3 0 M A
41 45.2 1.130 40 25 80 5 0 4.3 0 M C
42 22.7 0.989 23 32 100 8 1 5.7 1 F A
43 77.2 1.152 67 42 95 20 1 5.5 0 F F
44 63.2 1.108 57 45 90 16 0 5.2 1 M E
45 51 1.062 48 36 95 8 1 5.2 1 F D
46 63.7 1.117 57 39 75 20 0 3.9 1 M E
47 62.9 1.104 57 37 95 5 0 5.5 1 M E
48 69.6 1.221 57 34 90 11 1 5.3 1 F E
49 63.5 1.114 57 41 95 21 0 6.6 0 M E
50 61.4 1.078 57 38 80 12 0 4.6 0 M E

Week 1

Week 1. Measurement and Description - chapters 1 and 2
The goal this week is to gain an understanding of our data set - what kind of data we are looking at, some descriptive measurse, and a
look at how the data is distributed (shape).
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.
Nominal Ordinal Interval Ratio
Gender ID
Degree Salary
Gender1 Compa
Grade Mid point
Performance
Servics
raise
b. For each variable that you did not call ratio, why did you make that decision?
ratio tells us about the order,exact value between units no one variable is ratio since no variable tells us about the order among them hence they are ratio variables
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. Note - data is a sample from the larger company population
Salary Compa Age Perf. Rat. Service
Mean 45.022 1.6030 35.7 85.9 9.0
Overall Standard Deviation 19.2080 0.0820 8.2513 11.4147 5.7177
Range 54.7 0.365 30 45 21
Mean 38.21 1.0730 32.5 84.2 7.9
Female Standard Deviation 18.5 0.0760 6.9 13.6 4.9
Range 54.7 0.242 26.0 45.0 18.0
Mean 51.83 1.0530 38.9 87.6 10.0
Male Standard Deviation 17.7 0.0870 8.4 8.7 6.4
Range 52.5 0.310 28.0 30.0 21.0
3
What is the probability for a: probability
a.       Randomly selected person being a male in grade E? 0.17
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? 0.83
c. Why are the results different? results are diffferent due to the samples and population for both cases are different.The first case the population is male and we are choosing males who have grade E
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: Overall Female Male
A The value that cuts off the top 1/3 salary value in each group 42 22.7 39.4 "=large" function
i The z score for this value within each group? 0.204 -0.837 0.064 Excel's standize function
ii The normal curve probability of exceeding this score: 0.419 0.799 0.474 1-normsdist function
iii What is the empirical probability of being at or exceeding this salary value? 0.419 0.950 0.632
B The value that cuts off the top 1/3 compa value in each group. 1.025 1.043 1.075
i The z score for this value within each group? -0.632 -0.115 -0.123
ii The normal curve probability of exceeding this score: 0.736 0.546 0.312
iii What is the empirical probability of being at or exceeding this compa value? 0.736 0.546 0.312
C How do you interpret the relationship between the data sets? What do they mean about our equal pay for equal work question?
by using correlation matrix to find relationship between the variables
Equal pay for equal works means that the correlation of the salaries with remaining variable in the data are dependent to each other and are set high
5 What conclusions can you make about the issue of male and female pay equality? Are all of the results consistent?
Yes the result is consistent
means of compa and salaries are not equal
What is the difference between the sal and compa measures of pay?
Females and males salary are not equal
Conclusions from looking at salary results:
Taking a look at the female and male salaries payment are not equal
Conclusions from looking at compa results:
Compa payment results are not equal
Do both salary measures show the same results?
Yes for both cases the payments results are not equal both for female and male
Can we make any conclusions about equal pay for equal work yet?
No since the payments for males and female according to compa and salary are not equal hence we cannot say equal pay for equal work

Week 2

Week 2 Testing means - T-tests Salary Compa Performance Rating
In questions 2, 3, and 4 be sure to include the null and alternate hypotheses you will be testing. Male Female Male Female Male Female
In the first 4 questions use alpha = 0.05 in making your decisions on rejecting or not rejecting the null hypothesis. 60 34.7 1.053 1.120 85 75
26.8 42 0.866 1.050 80 100
1 Below are 2 one-sample t-tests comparing male and female average salaries to the overall sample mean. 57.9 23.6 1.016 1.025 100 90
(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.) 48.5 22.6 1.010 0.984 90 80
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. 74.3 23.4 1.109 1.018 70 100
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? 74.2 41.3 1.107 1.033 100 100
61.7 22.9 1.082 0.997 95 90
Males Females 46.6 24.9 1.166 1.084 90 80
Ho: Mean salary = 45.00 Ho: Mean salary = 45.00 24.5 66.5 1.064 1.166 85 55
Ha: Mean salary =/= 45.00 Ha: Mean salary =/= 45.00 76.7 36.3 1.145 1.170 95 80
24.5 34.3 1.067 1.107 70 70
Note: While the results both below are actually from Excel's t-Test: Two-Sample Assuming Unequal Variances, 39.4 57.3 0.985 1.193 80 65
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. 72 22.5 1.075 0.979 95 65
Male Ho Female Ho 46 54.7 0.958 1.140 90 75
Mean 52 45 Mean 38 45 26.9 23 0.867 0.998 95 95
Variance 316 0 Variance 334.6666666667 0 59.8 75.4 1.049 1.125 90 95
Observations 25 25 Observations 25 25 26.5 24 0.856 1.045 80 60
Hypothesized Mean Difference 0 Hypothesized Mean Difference 0 65.4 22.6 1.147 0.982 95 90
df 24 df 24 24.2 23.4 1.053 1.017 90 75
t Stat 1.9689038266 t Stat -1.9132063573 45.2 23.3 1.130 1.014 80 95
P(T<=t) one-tail 0.0303078503 P(T<=t) one-tail 0.0338621184 63.2 36.1 1.108 1.164 90 90
t Critical one-tail 1.7108820799 t Critical one-tail 1.7108820799 63.7 22.7 1.117 0.989 75 100
P(T<=t) two-tail 0.0606157006 P(T<=t) two-tail 0.0677242369 62.9 77.2 1.104 1.152 95 95
t Critical two-tail 2.0638985616 t Critical two-tail 2.0638985616 63.5 51 1.114 1.062 95 95
Conclusion: Do not reject Ho; mean equals 45 Conclusion: Do not reject Ho; mean equals 45 61.4 69.6 1.078 1.221 80 90
Note: the Female results are done for you, please complete the male results.
Is this a 1 or 2 tail test? 2 tail test Is this a 1 or 2 tail test? 2 tail
- why? Ho contains = - why? Ho contains =
P-value is: 0.0606157006 P-value is: 0.0677242369
Is P-value < 0.05 (one tail test) or 0.025 (two tail test)? No Is P-value < 0.05 (one tail test) or 0.025 (two tail test)? No
Why do we not reject the null hypothesis? P-value greater than (>) rejection alpha Why do we not reject the null hypothesis? P-value greater than (>) rejection alpha
Interpretation of test outcomes: There is no evidence, at α = 0.05 significance, that the mean salary of the male employees is significantly different from the mean salary of the population.
There is no evidence, at α = 0.05 significance, that the mean salary of the female employees is significantly different from the mean salary of the population.
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
t-Test: Two-Sample Assuming Equal Variances
Male Female
Mean 51.832 38.212
Variance 313.2339333333 343.4369333333
Observations 25 25
Pooled Variance 328.3354333333
Hypothesized Mean Difference 0
df 48
t Stat 2.6574997806
P(T<=t) one-tail 0.0053297951
t Critical one-tail 1.6772241961
P(T<=t) two-tail 0.0106595903
t Critical two-tail 2.0106347576
P-value is: 0.0106595903
Is P-value < 0.05 (one tail test) or 0.025 (two tail test)? Yes
Reject or do not reject Ho: Reject Ho
If the null hypothesis was rejected, calculate the effect size value: 0.7516544463
If calculated, what is the meaning of effect size measure: The effect size is large. The large effect size indicates that there is considerable difference between the mean salaries of male and female employees.
Interpretation: There is sufficient evidence, at α = 0.05 significance, that the mean salary of the male employees is significantly different from the mean salary of the female employees.
b. Is the one or two sample t-test the proper/correct apporach to comparing salary equality? Why?
The two sample t-test is the proper/correct approach to comparing salary equality among male and female employees as we have two independent samples; one for males and another for female employees.
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: Male compa mean = Female compa mean
Ha: Male compa mean =/= Female compa mean
Statistical test to use: t-Test: Two-Sample Assuming Equal Variances
t-Test: Two-Sample Assuming Equal Variances
Male Female
Mean 1.05304 1.0734
Variance 0.0076257067 0.0057514167
Observations 25 25
Pooled Variance 0.0066885617
Hypothesized Mean Difference 0
df 48
t Stat -0.8801696972
P(T<=t) one-tail 0.1915765137
t Critical one-tail 1.6772241961
P(T<=t) two-tail 0.3831530275
t Critical two-tail 2.0106347576
What is the p-value: 0.3831530275
Is P-value < 0.05 (one tail test) or 0.025 (two tail test)? No
Reject or do not reject Ho: Do Not Reject Ho
If the null hypothesis was rejected, calculate the effect size value: Not Applicable
If calculated, what is the meaning of effect size measure: Not Applicable
Interpretation: There is no evidence, at α = 0.05 significance, that the mean compa of the male employees is significantly different from the mean compa of the female employees.
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.
Ho: Male performance rating mean = Female performance rating mean
Ha: Male performance rating mean =/= Female performance rating mean
Test to use: t-Test: Two-Sample Assuming Unequal Variances
t-Test: Two-Sample Assuming Equal Variances
Male Female
Mean 87.6 84.2
Variance 75.25 184.75
Observations 25 25
Pooled Variance 130
Hypothesized Mean Difference 0
df 48
t Stat 1.054295244
P(T<=t) one-tail 0.1485129687
t Critical one-tail 1.6772241961
P(T<=t) two-tail 0.2970259373
t Critical two-tail 2.0106347576
What is the p-value: 0.2970259373
Is P-value < 0.05 (one tail test) or 0.025 (two tail test)? No
Do we REJ or Not reject the null? Do Not Reject Ho
If the null hypothesis was rejected, calculate the effect size value: Not Applicable
If calculated, what is the meaning of effect size measure: Not Applicable
Interpretation: There is no evidence, at α = 0.05 significance, that the mean performance rating of the male employees is significantly different from the mean performance rating of the female employees.
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?
The compa mean test is more appropriate to use in answering the question about salary equity as compa is a measure of salary after removing the impact of grade and therefore it reduces the bias in salary due to grade.
What are your conclusions about equal pay at this point?
The overall conclusion about equal pay at this point is that male and female employees are paid equally for equal work.

Week 3

Week 3 Paired T-test and ANOVA
For this week's work, again be sure to state the null and alternate hypotheses and use alpha = 0.05 for our decision
value in the reject or do not reject decision on the null hypothesis.
1 Many companies consider the grade midpoint to be the "market rate" - the salary needed to hire a new employee. Salary Midpoint Diff
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.
Null Hypothesis:
Alt. Hypothesis:
Statistical test to use:
What is the p-value:
Is P-value < 0.05 (one tail test) or 0.025 (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.) Here are the data values sorted by grade level.
The rating values sorted by grade have been placed in columns I - N for you. A B C D E F
Null Hypothesis: Ho: means equal for all grades 90 80 100 90 85 70
Alt. Hypothesis: Ha: at least one mean is unequal 80 75 100 65 100 100
Place B17 in Outcome range box. 100 80 90 75 95 95
90 70 80 90 55 95
80 95 80 95 90 95
85 80 95 95
65 90 90
70 75
95 95
60 90
90 95
75 80
95
90
100
Interpretation of test results:
What is the p-value: 0.57 If the ANVOA was done correctly, this is the p-value shown.
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: If desired, place salaries per grade in these columns
Alt. Hypothesis: A B C D E F
Place B51 in Outcome range box.
Note: Sometimes we see a p-value in the format of 3.4E-5; this means move the decimal point left 5 places. In this example, the p-value is 0.000034
What is the p-value:
Is P-value < 0.05?
Do we REJ or Not reject the null?
If the null hypothesis was rejected, calculate the effect size value (eta squared):
If calculated, what is the meaning of effect size measure:
Interpretation:
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.
BA MA Ho: Average compas by gender are equal
Male 1.017 1.157 Ha: Average compas by gender are not equal
0.870 0.979 Ho: Average compas are equal for each degree
1.052 1.134 Ha: Average compas are not equal for each degree
1.175 1.149 Ho: Interaction is not significant
1.043 1.043 Ha: Interaction is significant
1.074 1.134
1.020 1.000 Perform analysis:
0.903 1.122
0.982 0.903 Anova: Two-Factor With Replication
1.086 1.052
1.075 1.140 SUMMARY BA MA Total
1.052 1.087 Male
Female 1.096 1.050 Count 12 12 24
1.025 1.161 Sum 12.349 12.9 25.249
1.000 1.096 Average 1.0290833333 1.075 1.0520416667
0.956 1.000 Variance 0.006686447 0.0065198182 0.0068660417
1.000 1.041
1.043 1.043 Female
1.043 1.119 Count 12 12 24
1.210 1.043 Sum 12.791 12.787 25.578
1.187 1.000 Average 1.0659166667 1.0655833333 1.06575
1.043 0.956 Variance 0.006102447 0.0042128106 0.004933413
1.043 1.129
1.145 1.149 Total
Count 24 24
Sum 25.14 25.687
Average 1.0475 1.0702916667
Variance 0.0064703478 0.0051561286
ANOVA
Source of Variation SS df MS F P-value F crit
Sample 0.0022550208 1 0.0022550208 0.3834821171 0.5389389507 4.0617064601 (This is the row variable or gender.)
Columns 0.0062335208 1 0.0062335208 1.0600539609 0.3088295633 4.0617064601 (This is the column variable or Degree.)
Interaction 0.0064171875 1 0.0064171875 1.0912877664 0.3018915062 4.0617064601
Within 0.25873675 44 0.0058803807
Total 0.2736424792 47
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:
Place data values in these columns
5.   Using the results up thru this week, what are your conclusions about gender equal pay for equal work at this point? Dif

Week 4

Week 4 Confidence Intervals and Chi Square (Chs 11 - 12)
For questions 3 and 4 below, be sure to list the null and alternate hypothesis statements. Use .05 for your significance level in making your decisions.
For full credit, you need to also show the statistical outcomes - either the Excel test result or the calculations you performed.
1 Using our sample data, construct a 95% confidence interval for the population's mean salary for each gender.
Interpret the results.
Mean St error t value Low to High
Males
Females
<Reminder: standard error is the sample standard deviation divided by the square root of the sample size.>
Interpretation:
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?
Difference St Err. T value Low to High
Yes/No
Can the means be equal? Why?
How does this compare to the week 2, question 2 result (2 sampe t-test)? Results are the same - means are not equal.
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:
Ho:
Ha:
Note: You can either use the Excel Chi-related functions or do the calculations manually.
Data InTables The Observed Table is completed for you.
OBSERVED A B C D E F Total If desired, you can do manual calculations per cell here.
M Grad 1 1 1 1 5 3 12 A B C D E F
Fem Grad 5 3 1 1 1 2 13 M Grad
Male Und 2 2 2 1 5 1 13 Fem Grad
Female Und 7 1 1 2 1 0 12 Male Und
15 7 5 5 12 6 50 Female Und
Sum =
EXPECTED
M Grad For this exercise - ignore the requirement for a correction
Fem Grad for expected values less than 5.
Male Und
Female Und
Interpretation:
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 Cramer's V correlation:
What does this correlation mean?
What does this decision mean for our equal pay question:
4 Based on our sample data, can we conclude that males and females are distributed across grades in a similar pattern
within the population? Again, ignore any cell size limitations.
What are the hypothesis statements:
Ho:
Ha:
Do manual calculations per cell here (if desired)
A B C D E F A B C D E F
OBS COUNT - m M
OBS COUNT - f F
Sum =
EXPECTED
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?

Week 5

Week 5 Correlation and Regression
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 Note: technically we have one for each input variable.
Ha: The regression coefficient for each variable is significant Listing it this way to save space.
Sal
SUMMARY OUTPUT
Regression Statistics
Multiple R 0.9915590747
R Square 0.9831893985
Adjusted R Square 0.9808437332
Standard Error 2.6575925726
Observations 50
ANOVA
df SS MS F Significance F
Regression 6 17762.2996738743 2960.383278979 419.1516111294 1.8121523852609E-36
Residual 43 303.7003261257 7.062798282
Total 49 18066
Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%
Intercept -1.7496212123 3.6183676583 -0.4835388157 0.6311664899 -9.0467550427 5.547512618 -9.0467550427 5.547512618
Midpoint 1.2167010505 0.0319023509 38.1382881163 8.66416336978111E-35 1.1523638283 1.2810382727 1.1523638283 1.2810382727 Note: These values are not the same as in the data the assignment uses. The purpose is to analyze the result of a 2-way ANOVA test rather than directly answer our equal pay question.
Age -0.0046280102 0.065197212 -0.0709847876 0.9437389875 -0.1361107191 0.1268546987 -0.1361107191 0.1268546987
Performace Rating -0.0565964405 0.0344950678 -1.6407110971 0.1081531819 -0.1261623747 0.0129694936 -0.1261623747 0.0129694936
Service -0.0425003573 0.0843369821 -0.5039350033 0.6168793519 -0.2125820912 0.1275813765 -0.2125820912 0.1275813765
Gender 2.420337212 0.8608443176 2.8115852804 0.0073966188 0.684279192 4.156395232 0.684279192 4.156395232
Degree 0.2755334143 0.7998023048 0.3445019009 0.732148119 -1.3374216547 1.8884884833 -1.3374216547 1.8884884833
Note: since Gender and Degree are expressed as 0 and 1, they are considered dummy variables and can be used in a multiple regression equation.
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: Intercept Midpoint Age Perf. Rat. Service Gender Degree
What is the coefficient's p-value for each of the variables: NA
Is the p-value < 0.05? NA
Do you reject or not reject each null hypothesis: NA
What are the coefficients for the significant variables?
Using the intercept coefficient and only the significant variables, what is the equation? Salary =
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:
Place c94 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?
Do you reject or not reject the null hypothesis:
What does this decision mean for our equal pay question:
For each of the coefficients: Intercept Midpoint Age Perf. Rat. Service Gender Degree
What is the coefficient's p-value for each of the variables: NA
Is the p-value < 0.05? NA
Do you reject or not reject each null hypothesis: NA
What are the coefficients for the significant variables?
Using the intercept coefficient and only the significant variables, what is the equation? Compa =
Is gender a significant factor in compa:
Regardless of statistical significance, who gets paid more with all other things being equal?
How do we know?
4 Based on all of your results to date,
Do we have an answer to the question of are males and females paid equally for equal work?
Does the company pay employees equally for for equal work?
How do we know?
Which is the best variable to use in analyzing pay practices - salary or compa? Why?
What is most interesting or surprising about the results we got doing the analysis during the last 5 weeks?
5 Why did the single factor tests and analysis (such as t and single factor ANOVA tests on salary equality) not provide a complete answer to our salary equality question?
What outcomes in your life or work might benefit from a multiple regression examination rather than a simpler one variable test?