# NURSING

## 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 | Female | |||||

In the first 3 questions use alpha = 0.05 in making your decisions on rejecting or not rejecting the null hypothesis. | 45 | 34 | 1.017 | 1.096 | |||||

45 | 41 | 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 | 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 | 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 | 1.134 | 1.000 | |||||

Males | Females | 45 | 42 | 1.149 | 1.050 | ||||

Ho: Mean salary = 45 | Ho: Mean salary = 45 | 45 | 24 | 1.052 | 1.043 | ||||

Ha: Mean salary =/= 45 | Ha: Mean salary =/= 45 | 45 | 24 | 1.175 | 1.043 | ||||

45 | 69 | 1.043 | 1.210 | ||||||

Note: While the results both below are actually from Excel’s t-Test: Two-Sample Assuming Unequal Variances, | 45 | 36 | 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 | 1.043 | 1.096 | |||||

Male | Ho | Female | Ho | 45 | 57 | 1.000 | 1.187 | ||

Mean | 52 | 45 | Mean | 38 | 45 | 45 | 23 | 1.074 | 1.000 |

Variance | 316 | 0 | Variance | 334.6666666667 | 0 | 45 | 50 | 1.020 | 1.041 |

Observations | 25 | 25 | Observations | 25 | 25 | 45 | 24 | 0.903 | 1.043 |

Hypothesized Mean Difference | 0 | Hypothesized Mean Difference | 0 | 45 | 75 | 1.122 | 1.119 | ||

df | 24 | df | 24 | 45 | 24 | 0.903 | 1.043 | ||

t Stat | 1.9689038266 | t Stat | -1.9132063573 | 45 | 24 | 0.982 | 1.043 | ||

P(T<=t) one-tail | 0.0303078503 | P(T<=t) one-tail | 0.0338621184 | 45 | 23 | 1.086 | 1.000 | ||

t Critical one-tail | 1.7108820799 | t Critical one-tail | 1.7108820799 | 45 | 22 | 1.075 | 0.956 | ||

P(T<=t) two-tail | 0.0606157006 | P(T<=t) two-tail | 0.0677242369 | 45 | 35 | 1.052 | 1.129 | ||

t Critical two-tail | 2.0638985616 | t Critical two-tail | 2.0638985616 | 45 | 24 | 1.140 | 1.043 | ||

Conclusion: Do not reject Ho; mean equals 45 | Conclusion: Do not reject Ho; mean equals 45 | 45 | 77 | 1.087 | 1.149 | ||||

Is this a 1 or 2 tail test? | Is this a 1 or 2 tail test? | ||||||||

– why? | – why? | ||||||||

P-value is: | P-value is: | 45 | 55 | 1.052 | 1.145 | ||||

Is P-value > 0.05? | Is P-value > 0.05? | 45 | 65 | 1.157 | 1.140 | ||||

Why do we not reject Ho? | Why do we not reject Ho? | ||||||||

Interpretation: | |||||||||

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: | |||||||||

Ha: | |||||||||

Test to use: | |||||||||

Place B43 in Outcome range box. | |||||||||

P-value is: | |||||||||

Is P-value < 0.05? | |||||||||

Reject or do not reject Ho: | |||||||||

If the null hypothesis was rejected, what is the effect size value: | |||||||||

Meaning of effect size measure: | |||||||||

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? | ||||||||

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. | |||||||||

What is the p-value: | |||||||||

Is P-value < 0.05? | |||||||||

Reject or do not reject Ho: | |||||||||

If the null hypothesis was rejected, what is the effect size value: | |||||||||

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? | ||||||||

Ho: | |||||||||

Ha: | |||||||||

Test to use: | |||||||||

Place B106 in Outcome range box. | |||||||||

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: | |||||||||

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? |

## 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? |