Statistics Assignment

Assigned Exercises: Block 4

Introduction to Statistical Inference

1. What are the assumptions underlying the use of parametric statistics?

2. For the following descriptive information:

__ __

X1 = 36.8 X2 = 35.8 n = 157 t = 1.002

Provide the following:

df = ______

p ____ .05

English Answer (Was there a significant difference?) __________

The remaining items relate to the following two research results:

A. t = 2.445 B. t = -3.123

df = 98 df = 48

p < .05 p < .01

3. For which situation is the absolute magnitude of the difference greater?

4. For which situation is the power of the statistical tool greater?

5. In which situation is the probability of Type I error smaller?

6. Which of the two situations will “probably” have more clinical significance?

7. Assuming equal distribution of subjects to each of two groups, how many subjects were enrolled in Study A? _______ in Study B? _______

8. What is the confidence interval associated with Study A? _____ Study B?_____

9. What is the probability of error in rejecting the null hypothesis associated with Study A? _____ Study B? _____

Assigned Exercises: Block 5

Selection of Inferential Procedures: The Use of a Statistical Decision Tree

Identify the appropriate statistical procedure for each of the following:

1. Children raised in single-parent families graduate from high school less frequently than children raised in “intact” families.

2. Stress, as measured by a 50 item questionnaire yielding a stress score, is higher among children living in urban settings than children living in rural settings or children living in suburban settings.

3. Acuity scores are good predictors of length of stay among ICU patients.

4. Women who smoke are more likely to have miscarriages than women who do not smoke.

5. Married post-MI patients have lower diastolic blood pressure than divorced or single post-MI patients.

6. VLDL blood values are good predictors of blood pressure and weight.

7. Class rankings of African-American students differ from class rankings of Asian students.

8. Physicians have higher incomes than nurses.

9. Age is a function of self-esteem, measured on an interval level scale, among adult diabetic patients.

10. There is an interaction between gender and room placement on patient satisfaction scores measured on an interval scale. (Note: this is a tricky one….if puzzled, check out “factorial designs” in the Block 1 reading.)

11. Height is a predictor of IQ among school-aged children.

12. Rank ordering on GRE scores is a good predictor of class rank at graduation among MSN students.

13. Nurse practitioners are less competent in interpreting research, as measured on a

categorical continuum, than clinical specialists.

14. Nurses have more positive attitudes toward the elderly, as determined by a 25 item inventory, than physicians.

Assigned Exercises for Block 6

Estimation and Measures of Difference

Estimation of Population Parameters

1. In a research situation involving multiple measures relating to burnout and employee turnover, a sample of 1,000 nurses was assessed on their attitudes toward hospital administration. The instrument used was an interval level device yielding scores from 1 to 100, with 100 being the most positive. The mean score of the group was 68 with a standard deviation of 12.5.

What is the best single estimate of the population mean (the point estimate)?

What is the “standard estimate of the population mean?”

Assuming the need to be more confident, what is the interval estimate of the population mean at the 95% confidence interval?

Comparing Samples to Populations: The z Statistic

2. A nurse educator wants to know if her students’ scores on the NCLEX are “higher” or “lower than the national average. Her 30 students averaged 869 on the NCLEX and she knows that the national average is 850 with a standard deviation of 75. At the 95% confidence interval, are her students’ scores significantly different from the national average?

Chi Squared (χ2) Test

3. A nurse educator wishes to determine whether pre-licensure education influences performance on certain advanced clinical examinations. She acquires the ACLS (Advanced Cardiac Life Support) data which indicate the pass/fail rates for 100 Associate Degree Nurses and 100 BSN Nurses. Sixty-eight percent of the Associate Degree and 73% of the BSN nurses passed the exam on the first attempt. Was there a significant difference in the pass rates between the two groups?

4. A nurse researcher wishes to know if attitudes toward HIV positive patients differ among selected ethnic groups. She identifies an instrument which yields categorical scores of “positive,” “neutral,” and “negative” attitudes which she administers to 30 white males, 30 Hispanic males and 30 African-American males. The African-American subjects were evenly divided among the three categories, while among the Hispanic men, only 5 indicated positive attitudes and 10 indicated neutral attitudes. The white subjects scored 15 positives and 10 negatives. Was there a significant difference in the attitudes of these groups?

5. A clinical researcher wished to know if there were differences in reported levels of pain between post-operative patients who were given pre-operative teaching and those who were not. Pain was reported on a nominal scale including 3 categories: “Little or No Pain,” “Moderate Pain,” and “Severe Pain.” One hundred subjects were randomly assigned, 50 to a group, to “Teaching” and “No Teaching” conditions. Twenty-five of the teaching and 20 of the no teaching subjects reported little or no pain post-operatively. Twenty of the teaching subjects reported moderate pain and 5 of the no teaching subjects reported moderate pain. Was the teaching effective in helping to control post-operative pain?

t-Test

6. A nurse educator wants to know if self-paced instruction is preferable to lecture-discussion as an instructional technique for teaching students about the elderly. She divides her 100 students evenly and assigns them to one or another of the conditions. She identifies an instrument which measures knowledge of the elderly and administers the tool following the instruction. Given the following data, was one technique preferable to another at the .01 level of significance?

_ _

X1 = 58.5 X2 = 63.7

sd1 = 6.7 sd2 = 8.5

7. In a study to determine the effect of pre-operative teaching on patient satisfaction, 30 patients were given specific pre-operative teaching before surgery. Another group of 20 patients were not given the pre-operative instruction, but all 50 patients were administered an interval level satisfaction instrument. At the 95% confidence interval, was there a difference between the groups based on the following data?

Teaching Group Control Group

_ _

X = 23.5 X = 27.6

sd = 4.5 sd = 5.0

Analysis of Variance (the F ratio)

8. A researcher is interested in the effect of specialty on burnout among nurses. She selects subjects from three identified specialty areas—critical care, pediatrics, and obstetrics. She administers a valid and reliable measure of burnout which yields interval scores from 0 to 100 where high scores indicate high levels of burnout. Based on the following data, does clinical specialty influence burnout?

Pediatrics Critical Care Obstetrics

n = 10 n = 10 n = 10

38 52 40

42 50 50

40 60 45

45 55 40

44 62 50

36 65 48

30 58 45

35 60 50

40 68 53

30 70 50

9. For the data in the problem above (# 8—burnout and clinical specialty), answer the following:

a. Which groups, if any, were significantly different?

b. If you wished to compare each group to each of the other groups, what would be required?

10. In another study, patients undergoing three treatments for ESRD were studied for life satisfaction. The outcome measure was a tool yielding interval scores from 0 to 10, with 10 representing the highest level of satisfaction. The three treatments were: Kidney transplantation, center-based hemodialysis and continuous ambulatory peritoneal dialysis (CAPD). Based on the following data, are there significant differences among the groups in terms of life satisfaction?

Transplant Center-based Hemo CAPD

n = 6 n = 6 n = 6

8 5 7

8 6 5

9 3 6

7 6 5

8 7 8

8 4 4

11. The following ANOVA table was generated in a study to test the following hypothesis: “Ethnic background significantly influences biomechanical ability based on a 20 point scale.” The study compared groups of students of different ethnic backgrounds at a large Midwestern university.

Source df SS MSS F p

Among 4 16833 4208.3 4.338 <.05

Within 245 237650 970

Total 249 254483 5178.3

a. How many groups were compared?

b. How many subjects were in each group (assuming equal distribution)?

c. The researcher concluded that biomechanical ability was influenced by ethnic background. Do you agree with this conclusion?

c. Based on this table alone, the researcher further concluded that black students had higher biomechanical abilities than oriental and white students. Is this conclusion justified? Why or why not?

Assigned Exercises: Block 7

Correlation and Regression

Correlation: Pearson’s “r” and Spearman’s ρ (rho)

1. A researcher wishes to know whether scores on a standardized instrument (instrument A) are related to a shorted form of the instrument (instrument B). To do this she selects 10 subjects and administers both instruments. The following are the paired observations. Determine the strength and direction of the relationship and report its statistical and practical significance.

Subject # Instrument A Instrument B

1 84 42

2 90 45

3 88 49

4 80 38

5 78 40

6 82 41

7 85 41

8 79 36

9 75 38

10 100 49

2. Another researcher wishes to know whether didactic rank is related to clinical rank among nurses students enrolled in clinical and didactic coursework. For twenty (20) students, the following are the ranks given by didactic and clinical instructors. Determine the strength and direction of the relationship and report the statistical and practical significance of the relationship.

Student # Didactic Rank Clinical Rank

1 1 4 2 2.5 2

3 2.5 3

4 5 6

5 5 6

6 5 6

7 7 1

8 9 10

9 9 12

10 9 8

11 11 9

12 12.5 15

13 12.5 11

14 14 15

15 15 13

16 16 17

17 17 15

18 19 18

19 19 19.5

20 19 19.5

Regression

For the following data set of paired observations, perform the identified statistical analyses and/or answer the questions indicated:

x y

14 21

14 22

12 22

11 23

11 20

10 18

9 17

9 21

8 15

7 12

3. Calculate the correlation coefficient and report its statistical significance.

4. Report the percent of variance (the coefficient of determination) shared between the known values for x and y.

5. Using the linear regression equations provided, calculate and report the slope of the regression line.

6. Using the linear regression equations provided, calculate the y intercept for the regression line.

7. Calculate the standard error of estimate for the regression equations completed. (note: you’ll need to calculate the standard deviation of y to complete this. If you’ve forgotten how, review Block 3.

8. Predict the value of “y” for a known value of x = 15.

As a point estimate:__________

As an interval estimate:___________

Assigned Exercises: Block 8

Interpreting SPSS (Statistical Package for the Social Sciences) Output

This little exercise is based on your ability to interpret SPSS output. In this instance, the exercise includes two pages of questions that deal with a few pages of output that follow the questions. The calculations performed include: Two (2) t-tests, on (1) Chi-squared, one (1) F Ratio or Analysis of Variance (Oneway ANOVA) and one Pearson r.

The first few questions deal with the output of the t-test. These analyses compared men and women on two variables –the number of children they had and their ages.

1. Was the t-test the appropriate statistical device for these comparisons?

2. For the comparison of ages:

a. Report the appropriate test statistic.

b. Report the appropriate df.

c. Report the appropriate p value.

e. Were there significant differences between men and women on the variable of age?

3. The “Crosstabs” output is the format for conduct a Chi-squared analysis. In this case, different ethnic groups were compared on a categorical measure of happiness.

a. Was the appropriate statistical test used?

b. What percent of white respondents reported being “very happy?”

c. What percent of those reporting general happiness as “Not Too Happy” were Black?

d. What is the appropriate test statistic for a comparison of the groups?

e. What is the appropriate df?

f. What is the appropriate p value?

g. Was there a difference in general happiness according to racial background?

4. For the Oneway ANOVA:

a. How many groups were compared?

b. How many subjects were enrolled?

c. Was there a difference among the groups

5. The bivariate correlation examined the association between age of the respondent and the highest year of school completed.

a. Was there a statistically significant correlation?

b. What was the percent of shared variance between age and highest year of school completed?

c. In looking at the general trend, did older subjects tend to have more years of school, or less years of school, than their younger counterparts?