# NURSING

## 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? |