Buisness BUS 308 week 4 homework due today.
dwp56bus308.online.2014.5.29.bh_.employee_salary_data_set.xls_5.xlsx
Data
See comments at the right of the data set. | ||||||||||||||||
ID | Salary | Compa | Midpoint | Age | Performance Rating | Service | Gender | Raise | Degree | Gender1 | Grade | |||||
8 | 23 | 1.000 | 23 | 32 | 90 | 9 | 1 | 5.8 | 0 | F | A | 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)? | ||||
10 | 22 | 0.956 | 23 | 30 | 80 | 7 | 1 | 4.7 | 0 | F | A | Note: to simplfy the analysis, we will assume that jobs within each grade comprise equal work. | ||||
11 | 23 | 1.000 | 23 | 41 | 100 | 19 | 1 | 4.8 | 0 | F | A | |||||
14 | 24 | 1.043 | 23 | 32 | 90 | 12 | 1 | 6 | 0 | F | A | The column labels in the table mean: | ||||
15 | 24 | 1.043 | 23 | 32 | 80 | 8 | 1 | 4.9 | 0 | F | A | ID – Employee sample number | Salary – Salary in thousands | |||
23 | 23 | 1.000 | 23 | 36 | 65 | 6 | 1 | 3.3 | 1 | F | A | Age – Age in years | Performance Rating – Appraisal rating (Employee evaluation score) | |||
26 | 24 | 1.043 | 23 | 22 | 95 | 2 | 1 | 6.2 | 1 | F | A | Service – Years of service (rounded) | Gender: 0 = male, 1 = female | |||
31 | 24 | 1.043 | 23 | 29 | 60 | 4 | 1 | 3.9 | 0 | F | A | Midpoint – salary grade midpoint | Raise – percent of last raise | |||
35 | 24 | 1.043 | 23 | 23 | 90 | 4 | 1 | 5.3 | 1 | F | A | Grade – job/pay grade | Degree (0= BS\BA 1 = MS) | |||
36 | 23 | 1.000 | 23 | 27 | 75 | 3 | 1 | 4.3 | 1 | F | A | Gender1 (Male or Female) | Compa - salary divided by midpoint | |||
37 | 22 | 0.956 | 23 | 22 | 95 | 2 | 1 | 6.2 | 1 | F | A | |||||
42 | 24 | 1.043 | 23 | 32 | 100 | 8 | 1 | 5.7 | 0 | F | A | |||||
3 | 34 | 1.096 | 31 | 30 | 75 | 5 | 1 | 3.6 | 0 | F | B | |||||
18 | 36 | 1.161 | 31 | 31 | 80 | 11 | 1 | 5.6 | 1 | F | B | |||||
20 | 34 | 1.096 | 31 | 44 | 70 | 16 | 1 | 4.8 | 1 | F | B | |||||
39 | 35 | 1.129 | 31 | 27 | 90 | 6 | 1 | 5.5 | 1 | F | B | |||||
7 | 41 | 1.025 | 40 | 32 | 100 | 8 | 1 | 5.7 | 0 | F | C | |||||
13 | 42 | 1.050 | 40 | 30 | 100 | 2 | 1 | 4.7 | 1 | F | C | |||||
22 | 57 | 1.187 | 48 | 48 | 65 | 6 | 1 | 3.8 | 0 | F | D | |||||
24 | 50 | 1.041 | 48 | 30 | 75 | 9 | 1 | 3.8 | 1 | F | D | |||||
45 | 55 | 1.145 | 48 | 36 | 95 | 8 | 1 | 5.2 | 0 | F | D | |||||
17 | 69 | 1.210 | 57 | 27 | 55 | 3 | 1 | 3 | 0 | F | E | |||||
48 | 65 | 1.140 | 57 | 34 | 90 | 11 | 1 | 5.3 | 1 | F | E | |||||
28 | 75 | 1.119 | 67 | 44 | 95 | 9 | 1 | 4.4 | 1 | F | F | |||||
43 | 77 | 1.149 | 67 | 42 | 95 | 20 | 1 | 5.5 | 1 | F | F | |||||
19 | 24 | 1.043 | 23 | 32 | 85 | 1 | 0 | 4.6 | 1 | M | A | |||||
25 | 24 | 1.043 | 23 | 41 | 70 | 4 | 0 | 4 | 0 | M | A | |||||
40 | 25 | 1.086 | 23 | 24 | 90 | 2 | 0 | 6.3 | 0 | M | A | |||||
2 | 27 | 0.870 | 31 | 52 | 80 | 7 | 0 | 3.9 | 0 | M | B | |||||
32 | 28 | 0.903 | 31 | 25 | 95 | 4 | 0 | 5.6 | 0 | M | B | |||||
34 | 28 | 0.903 | 31 | 26 | 80 | 2 | 0 | 4.9 | 1 | M | B | |||||
16 | 47 | 1.175 | 40 | 44 | 90 | 4 | 0 | 5.7 | 0 | M | C | |||||
27 | 40 | 1.000 | 40 | 35 | 80 | 7 | 0 | 3.9 | 1 | M | C | |||||
41 | 43 | 1.075 | 40 | 25 | 80 | 5 | 0 | 4.3 | 0 | M | C | |||||
5 | 47 | 0.979 | 48 | 36 | 90 | 16 | 0 | 5.7 | 1 | M | D | |||||
30 | 49 | 1.020 | 48 | 45 | 90 | 18 | 0 | 4.3 | 0 | M | D | |||||
1 | 58 | 1.017 | 57 | 34 | 85 | 8 | 0 | 5.7 | 0 | M | E | |||||
4 | 66 | 1.157 | 57 | 42 | 100 | 16 | 0 | 5.5 | 1 | M | E | |||||
12 | 60 | 1.052 | 57 | 52 | 95 | 22 | 0 | 4.5 | 0 | M | E | |||||
33 | 64 | 1.122 | 57 | 35 | 90 | 9 | 0 | 5.5 | 1 | M | E | |||||
38 | 56 | 0.982 | 57 | 45 | 95 | 11 | 0 | 4.5 | 0 | M | E | |||||
44 | 60 | 1.052 | 57 | 45 | 90 | 16 | 0 | 5.2 | 1 | M | E | |||||
46 | 65 | 1.140 | 57 | 39 | 75 | 20 | 0 | 3.9 | 1 | M | E | |||||
47 | 62 | 1.087 | 57 | 37 | 95 | 5 | 0 | 5.5 | 1 | M | E | |||||
49 | 60 | 1.052 | 57 | 41 | 95 | 21 | 0 | 6.6 | 0 | M | E | |||||
50 | 66 | 1.157 | 57 | 38 | 80 | 12 | 0 | 4.6 | 0 | M | E | |||||
6 | 76 | 1.134 | 67 | 36 | 70 | 12 | 0 | 4.5 | 1 | M | F | |||||
9 | 77 | 1.149 | 67 | 49 | 100 | 10 | 0 | 4 | 1 | M | F | |||||
21 | 76 | 1.134 | 67 | 43 | 95 | 13 | 0 | 6.3 | 1 | M | F | |||||
29 | 72 | 1.074 | 67 | 52 | 95 | 5 | 0 | 5.4 | 0 | M | F | |||||
Week 1
Week 1. | Measurement and Description - chapters 1 and 2 | ||||||||||
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 | ||||||||
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. | |||||||||||
Salary | Compa | Age | Perf. Rat. | Service | |||||||
Overall | Mean | ||||||||||
Standard Deviation | |||||||||||
Range | |||||||||||
Female | Mean | ||||||||||
Standard Deviation | |||||||||||
Range | |||||||||||
Male | Mean | ||||||||||
Standard Deviation | |||||||||||
Range | |||||||||||
3 | What is the probability for a: | Probability | |||||||||
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 | For each group (overall, females, and males) find: | Overall | Female | Male | |||||||
a. | The value that cuts off the top 1/3 salary in each group. | ||||||||||
b. | The z score for each value: | ||||||||||
c. | The normal curve probability of exceeding this score: | ||||||||||
d. | What is the empirical probability of being at or exceeding this salary value? | ||||||||||
e. | The value that cuts off the top 1/3 compa in each group. | ||||||||||
f. | The z score for each value: | ||||||||||
g. | The normal curve probability of exceeding this score: | ||||||||||
h. | What is the empirical probability of being at or exceeding this compa value? | ||||||||||
i. | 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? | |||||||||||
Week 2
Week 2 | Testing means | Q3 | ||||||||||||||||||||
In questions 2 and 3, be sure to include the null and alternate hypotheses you will be testing. | Ho | Female | male | Male | Female | |||||||||||||||||
In the first 3 questions use alpha = 0.05 in making your decisions on rejecting or not rejecting the null hypothesis. | 45 | 34 | 24 | 1.017 | 1.096 | |||||||||||||||||
45 | 41 | 24 | 0.870 | 1.025 | ||||||||||||||||||
1 | Below are 2 one-sample t-tests comparing male and female average salaries to the overall sample mean. | 45 | 23 | 25 | 1.157 | 1.000 | ||||||||||||||||
(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 -- see column S) | 45 | 22 | 27 | 0.979 | 0.956 | |||||||||||||||||
Based on our sample, how do you interpret the results and what do these results suggest about the population means for male and female average salaries? | 45 | 23 | 28 | 1.134 | 1.000 | |||||||||||||||||
Males | Females | 45 | 42 | 28 | 1.149 | 1.050 | ||||||||||||||||
Ho: Mean salary = 45 | Ho: Mean salary = 45 | 45 | 24 | 47 | 1.052 | 1.043 | ||||||||||||||||
Ha: Mean salary =/= 45 | Ha: Mean salary =/= 45 | 45 | 24 | 40 | 1.175 | 1.043 | ||||||||||||||||
, | 45 | 69 | 43 | 1.043 | 1.210 | |||||||||||||||||
Note: While the results both below are actually from Excel's t-Test: Two-Sample Assuming Unequal Variances, | 45 | 36 | 47 | 1.134 | 1.161 | |||||||||||||||||
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. | 45 | 34 | 49 | 1.043 | 1.096 | |||||||||||||||||
Male | Ho | Female | Ho | 45 | 57 | 58 | 1.000 | 1.187 | ||||||||||||||
Mean | 52 | 45 | Mean | 38 | 45 | 45 | 23 | 66 | 1.074 | 1.000 | ||||||||||||
Variance | 316 | 0 | Variance | 334.6666666667 | 0 | 45 | 50 | 60 | 1.020 | 1.041 | ||||||||||||
Observations | 25 | 25 | Observations | 25 | 25 | 45 | 24 | 64 | 0.903 | 1.043 | ||||||||||||
Hypothesized Mean Difference | 0 | Hypothesized Mean Difference | 0 | 45 | 75 | 56 | 1.122 | 1.119 | ||||||||||||||
df | 24 | df | 24 | 45 | 24 | 60 | 0.903 | 1.043 | ||||||||||||||
t Stat | 1.9689038266 | t Stat | -1.9132063573 | 45 | 24 | 65 | 0.982 | 1.043 | ||||||||||||||
P(T<=t) one-tail | 0.0303078503 | P(T<=t) one-tail | 0.0338621184 | 45 | 23 | 62 | 1.086 | 1.000 | ||||||||||||||
t Critical one-tail | 1.7108820799 | t Critical one-tail | 1.7108820799 | 45 | 22 | 60 | 1.075 | 0.956 | ||||||||||||||
P(T<=t) two-tail | 0.0606157006 | P(T<=t) two-tail | 0.0677242369 | 45 | 35 | 66 | 1.052 | 1.129 | ||||||||||||||
t Critical two-tail | 2.0638985616 | t Critical two-tail | 2.0638985616 | 45 | 24 | 76 | 1.140 | 1.043 | ||||||||||||||
Conclusion: Do not reject Ho; mean equals 45 | Conclusion: Do not reject Ho; mean equals 45 | 45 | 77 | 77 | 1.087 | 1.149 | ||||||||||||||||
Is this a 1 or 2 tail test? | 1 | Is this a 1 or 2 tail test? | 45 | 55 | 76 | 1.052 | 1.145 | |||||||||||||||
- why? | because the hypothis specifies only a difference,not a direction | because the hypothis specifies only a difference,not a direction | 45 | 65 | 72 | 1.157 | 1.140 | |||||||||||||||
P-value is: | 0.060615701 | P-value is: | 0.0677 | |||||||||||||||||||
Is P-value > 0.05? | yes | Is P-value > 0.05? | yes | |||||||||||||||||||
Why do we not reject Ho? | because the value is higher | Why do we not reject Ho? | because the P value is higher | |||||||||||||||||||
Interpretation: | ||||||||||||||||||||||
Almost no significant difference in salaries for males in this company compared to all employees | ||||||||||||||||||||||
Almost no significant difference in salaries for females in this company compared to all employees | ||||||||||||||||||||||
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.) | ||||||||||||||||||||||
Since the samples are the same as they will be the same, both T-tests results are in the same statistic, the same P- v | ||||||||||||||||||||||
Ho: Two -sample test assuming that there are equal variances | ||||||||||||||||||||||
Ha: Two -sample test assuming that there are unequal variances. | ||||||||||||||||||||||
Test to use: | ||||||||||||||||||||||
Place B43 in Outcome range box. | ||||||||||||||||||||||
t-Test: Two-Sample Assuming Equal Variances | t-Test: Two-Sample Assuming Unequal Variances | |||||||||||||||||||||
male | female | male | female | |||||||||||||||||||
Variable 1 | Variable 2 | Variable 1 | Variable 2 | |||||||||||||||||||
Mean | 52 | 38 | Mean | 52 | 38 | |||||||||||||||||
Variance | 316 | 334.6666666667 | Variance | 316 | 334.6666666667 | |||||||||||||||||
Observations | 25 | 25 | Observations | 25 | 25 | |||||||||||||||||
Pooled Variance | 325.3333333333 | Hypothesized Mean Difference | 0 | |||||||||||||||||||
Hypothesized Mean Difference | 0 | df | 48 | |||||||||||||||||||
df | 48 | t Stat | 2.7442189608 | |||||||||||||||||||
t Stat | 2.7442189608 | P(T<=t) one-tail | 0.0042530089 | |||||||||||||||||||
P(T<=t) one-tail | 0.0042530089 | t Critical one-tail | 1.6772241961 | |||||||||||||||||||
t Critical one-tail | 1.6772241961 | P(T<=t) two-tail | 0.0085060179 | |||||||||||||||||||
P(T<=t) two-tail | 0.0085060179 | t Critical two-tail | 2.0106347576 | |||||||||||||||||||
t Critical two-tail | 2.0106347576 | |||||||||||||||||||||
P-value is: | 0.008506 | |||||||||||||||||||||
Is P-value < 0.05? | Yes | |||||||||||||||||||||
Reject or do not reject Ho: | Yes | |||||||||||||||||||||
If the null hypothesis was rejected, what is the effect size value: | 0.0368 | |||||||||||||||||||||
Meaning of effect size measure: | 64% | |||||||||||||||||||||
Interpretation: | ||||||||||||||||||||||
b. | Since the one and two tail t-test results provided different outcomes, which is the proper/correct apporach to comparing salary equality? Why? | |||||||||||||||||||||
The P value- 0.008 is less than Alpha =0.05, it implies that there is enough evidence to indicate that the overall population average salaries of Males and females within the company do differ. | ||||||||||||||||||||||
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.) | |||||||||||||||||||||
Ho: | ||||||||||||||||||||||
Ha: | ||||||||||||||||||||||
Statistical test to use: | ||||||||||||||||||||||
Place B75 in Outcome range box. | ||||||||||||||||||||||
t-Test: Two-Sample Assuming Equal Variances | t-Test: Two-Sample Assuming Unequal Variances | |||||||||||||||||||||
male | female | male | female | |||||||||||||||||||
Variable 1 | Variable 2 | Variable 1 | Variable 2 | |||||||||||||||||||
Mean | 1.05624 | 1.06872 | Mean | 1.05624 | 1.06872 | |||||||||||||||||
Variance | 0.0070206067 | 0.0049483767 | Variance | 0.0070206067 | 0.0049483767 | |||||||||||||||||
Observations | 25 | 25 | Observations | 25 | 25 | |||||||||||||||||
Pooled Variance | 0.0059844917 | Hypothesized Mean Difference | 0 | |||||||||||||||||||
Hypothesized Mean Difference | 0 | df | 47 | |||||||||||||||||||
df | 48 | t Stat | -0.5703690595 | |||||||||||||||||||
t Stat | -0.5703690595 | P(T<=t) one-tail | 0.2855721176 | |||||||||||||||||||
P(T<=t) one-tail | 0.2855439182 | t Critical one-tail | 1.6779267216 | |||||||||||||||||||
t Critical one-tail | 1.6772241961 | P(T<=t) two-tail | 0.5711442353 | |||||||||||||||||||
P(T<=t) two-tail | 0.5710878364 | t Critical two-tail | 2.0117405137 | |||||||||||||||||||
t Critical two-tail | 2.0106347576 | |||||||||||||||||||||
What is the p-value: | 0.5710878364 | |||||||||||||||||||||
Is P-value < 0.05? | no | |||||||||||||||||||||
Reject or do not reject Ho: | reject | |||||||||||||||||||||
If the null hypothesis was rejected, what is the effect size value: | 0.0368 | |||||||||||||||||||||
Meaning of effect size measure: | 64% | |||||||||||||||||||||
Interpretation: | ||||||||||||||||||||||
4 | Since performance is often a factor in pay levels, is the average Performance Rating the same for both genders? | |||||||||||||||||||||
Ho: | ||||||||||||||||||||||
Ha: | ||||||||||||||||||||||
Test to use: | ||||||||||||||||||||||
Place B106 in Outcome range box. | ||||||||||||||||||||||
What is the p-value: | 0.29702594 | |||||||||||||||||||||
Is P-value < 0.05? | no | |||||||||||||||||||||
Do we REJ or Not reject the null? | reject | |||||||||||||||||||||
If the null hypothesis was rejected, what is the effect size value: | 0.1504 | |||||||||||||||||||||
Meaning of effect size measure: | 54% | |||||||||||||||||||||
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? | ||||||||||||||||||||||
The two T- Tests do offer a different conclusion given the parameters. | ||||||||||||||||||||||
Why is this? The Compa variables degrade or null the grade | ||||||||||||||||||||||
Ultimately , using the Compa lets us remove the degree of impact of grade. | ||||||||||||||||||||||
Week 3
Week 3 | ||||||||||||||
At this point we know the following about male and female salaries. | ||||||||||||||
a. | Male and female overall average salaries are not equal in the population. | |||||||||||||
b. | Male and female overall average compas are equal in the population, but males are a bit more spread out. | |||||||||||||
c. | The male and female salary range are almost the same, as is their age and service. | |||||||||||||
d. | Average performance ratings per gender are equal. | |||||||||||||
Let's look at some other factors that might influence pay - education(degree) and performance ratings. | ||||||||||||||
1 | 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.) | A | B | C | D | E | F | ||||||||
Null Hypothesis: | ||||||||||||||
Alt. Hypothesis: | ||||||||||||||
Place B17 in Outcome range box. | ||||||||||||||
Interpretation: | ||||||||||||||
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: | ||||||||||||||
2 | 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? (Assume equal variance, and use the analysis toolpak function ANOVA.) | ||||||||||||||
Use the input table to the right to list salaries under each grade level. | ||||||||||||||
Null Hypothesis: | ||||||||||||||
Alt. Hypothesis: | A | B | C | D | E | F | ||||||||
Place B55 in Outcome range box. | ||||||||||||||
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: | ||||||||||||||
Interpretation: | ||||||||||||||
3 | The table and analysis below demonstrate a 2-way ANOVA with replication. Please interpret the results. | |||||||||||||
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 | Ho: 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 salaries are equal for all grades | Ha: Average salaries 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: | ||||||||||||||
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 decisions mean in terms of our equal pay question: | ||||||||||||||
4 | Many companies consider the grade midpoint to be the "market rate" - what is needed to hire a new employee. | Midpoint | Salary | |||||||||||
Does the company, on average, pay its existing employees at or above the market rate? | ||||||||||||||
Null Hypothesis: | ||||||||||||||
Alt. Hypothesis: | ||||||||||||||
Statistical test to use: | ||||||||||||||
Place the cursor in B160 for correl. | ||||||||||||||
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: | Since the effect size was not discussed in this chapter, we do not have a formula for it - it differs from the non-paired t. | |||||||||||||
Meaning of effect size measure: | NA | |||||||||||||
Interpretation: | ||||||||||||||
5. | Using the results up thru this week, what are your conclusions about gender equal pay for equal work at this point? | |||||||||||||
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. How do they compare with the findings in the week 2 one sample t-test outcomes (Question 1)? | |||||||||||||||
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)? | |||||||||||||||
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 degrees compa 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.) | |||||||||||||||
What are the hypothesis statements: | |||||||||||||||
Ho: | |||||||||||||||
Ha: | |||||||||||||||
Note: You can either use the Excel Chi-related functions or do the calculations manually. | |||||||||||||||
Data input tables - graduate degrees by gender and grade level | |||||||||||||||
OBSERVED | A | B | C | D | E | F | Total | Do manual calculations per cell here (if desired) | |||||||
M Grad | A | B | C | D | E | F | |||||||||
Fem Grad | M Grad | ||||||||||||||
Male Und | Fem Grad | ||||||||||||||
Female Und | Male Und | ||||||||||||||
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? | |||||||||||||||
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: | |||||||||||||||
What does this correlation mean? | |||||||||||||||
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 in Output range box): | ||||||||||||
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. | ||||||||||||
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 | ||||
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: | ||||||||||||
Is the p-value < 0.05? | ||||||||||||
Do you reject or not reject each null hypothesis: | ||||||||||||
What are the coefficients for the significant variables? | ||||||||||||
Using 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 hypotheses (one to stand for all the separate variables) | ||||||||||||
Ho: | ||||||||||||
Ha: | ||||||||||||
Put C94 in output range 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: | ||||||||||||
Is the p-value < 0.05? | ||||||||||||
Do you reject or not reject each null hypothesis: | ||||||||||||
What are the coefficients for the significant variables? | ||||||||||||
Using only the significant variables, what is the equation? | Compa = | |||||||||||
Is gender a significant factor in compa: | ||||||||||||
If so, 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? | |||||||||||
If so, which gender gets paid more? | ||||||||||||
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? | ||||||||||||