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Hand Calculations

A retrospective comparative study examined whether longer antibiotic treatment courses were associated with increased antimicrobial resistance in patients with spinal cord injury (Lee et al., 2014). Using urine cultures from a sample of spinal cord–injured veterans, two groups were created: those with evidence of antibiotic resistance and those with no evidence of antibiotic resistance. Each veteran was also divided into two groups based on having had a history of recent (in the past 6 months) antibiotic use for more than 2 weeks or no history of recent antibiotic use.

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The data are presented in Table 35-1. The null hypothesis is: “There is no difference between antibiotic users and non-users on the presence of antibiotic resistance.”

TABLE 35-1

ANTIBIOTIC RESISTANCE BY ANTIBIOTIC USE

	Antibiotic Use	No Recent Use
Resistant	8	7
Not resistant	6	21

The computations for the Pearson χ2 test are as follows:

Step 1: Create a contingency table of the two nominal variables:

	Used Antibiotics	No Recent Use	Totals
Resistant	8	7	15
Not resistant	6	21	27
Totals	14	28	42	←Total n

Step 2: Fit the cells into the formula:

χ 2 =n[(A)(D)−(B)(C)] 2 (A+B)(C+D)(A+C)(B+D)

χ 2 =42[(8)(21)−(7)(6)] 2 (8+7)(6+21)(8+6)(7+21)

χ 2 =666,792158,760

χ 2 =4.20

Step 3: Compute the degrees of freedom:

df=(2−1)(2−1)=1

Step 4: Locate the critical χ² value in the χ² distribution table (Appendix D) and compare it to the obtained χ² value.

The obtained χ² value is compared with the tabled χ² values in Appendix D. The table includes the critical values of χ² for specific degrees of freedom at selected levels of significance. If the value of the statistic is equal to or greater than the value identified in the χ² table, the difference between the two variables is statistically significant. The critical χ² for df = 1 is 3.84, and our obtained χ² is 4.20, thereby exceeding the critical value and indicating a significant difference between antibiotic users and non-users on the presence of antibiotic resistance.

Furthermore, we can compute the rates of antibiotic resistance among antibiotic users and non-users by using the numbers in the contingency table from Step 1. The antibiotic resistance rate among the antibiotic users can be calculated as 8 ÷ 14 = 0.571 × 100% = 57.1%. The antibiotic resistance rate among the non-antibiotic users can be calculated as 7 ÷ 28 = 0.25 × 100% = 25%.

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SPSS Computations

The following screenshot is a replica of what your SPSS window will look like. The data for subjects 24 through 42 are viewable by scrolling down in the SPSS screen.

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Step 1: From the “Analyze” menu, choose “Descriptive Statistics” and “Crosstabs.” Move the two variables to the right, where either variable can be in the “Row” or “Column” space.

Step 2: Click “Statistics” and check the box next to “Chi-square.” Click “Continue” and “OK.”

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Interpretation of SPSS Output

The following tables are generated from SPSS. The first table contains the contingency table, similar to Table 35-1 above. The second table contains the χ² results.

Crosstabs

The last table contains the χ² value in addition to other statistics that test associations between nominal variables. The Pearson χ² test is located in the first row of the table, which contains the χ² value, df, and p value.

Final Interpretation in American Psychological Association (APA) Format

The following interpretation is written as it might appear in a research article, formatted according to APA guidelines (APA, 2010). A Pearson χ² analysis indicated that antibiotic users had significantly higher rates of antibiotic resistance than those who did not use antibiotics, χ²(1) = 4.20, p = 0.04 (57.1% versus 25%, respectively). This finding suggests that extended antibiotic use may be a risk factor for developing resistance, and further research is needed to investigate resistance as a direct effect of antibiotics.

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Study Questions

1. Do the example data meet the assumptions for the Pearson χ² test? Provide a rationale for your answer.

2. What is the null hypothesis in the example?

3. What was the exact likelihood of obtaining a χ² value at least as extreme or as close to the one that was actually observed, assuming that the null hypothesis is true?

4. Using the numbers in the contingency table, calculate the percentage of antibiotic users who were resistant.

5. Using the numbers in the contingency table, calculate the percentage of non-antibiotic users who were resistant.

6. Using the numbers in the contingency table, calculate the percentage of resistant veterans who used antibiotics for more than 2 weeks.

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7. Using the numbers in the contingency table, calculate the percentage of resistant veterans who had no history of antibiotic use.

8. What kind of design was used in the example?

9. What result would have been obtained if the variables in the SPSS Crosstabs window had been switched, with Antibiotic Use being placed in the “Row” and Resistance being placed in the “Column”?

10. Was the sample size adequate to detect differences between the two groups in this example? Provide a rationale for your answer.

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Answers to Study Questions

1. Yes, the data meet the assumptions of the Pearson χ²:

a. Only one datum per participant was entered into the contingency table, and no participant was counted twice.

b. Both antibiotic use and resistance are categorical (nominal-level data).

c. For each variable, the categories are mutually exclusive and exhaustive. It was not possible for a participant to belong to both groups, and the two categories (recent antibiotic user and non-user) included all study participants.

2. The null hypothesis is: “There is no difference between antibiotic users and non-users on the presence of antibiotic resistance.”

3. The exact likelihood of obtaining a χ² value at least as extreme as or as close to the one that was actually observed, assuming that the null hypothesis is true, was 4.0%.

4. The percentage of antibiotic users who were resistant is calculated as 8 ÷ 14 = 0.5714 × 100% = 57.14% = 57.1%.

5. The percentage of non-antibiotic users who were resistant is calculated as 7 ÷ 28 = 0.25 × 100% = 25%.

6. The percentage of antibiotic-resistant veterans who used antibiotics for more than 2 weeks is calculated as 8 ÷ 15 = 0.533 × 100% = 53.3%.

7. The percentage of resistant veterans who had no history of antibiotic use is calculated as 6 ÷ 27 = 0.222 × 100% = 22.2%.

8. The study design in the example was a retrospective comparative design (Gliner et al., 2009).

9. Switching the variables in the SPSS Crosstabs window would have resulted in the exact same χ² result.

10. The sample size was adequate to detect differences between the two groups, because a significant difference was found, p = 0.04, which is smaller than alpha = 0.05.

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Data for Additional Computational Practice for Questions to be Graded

A retrospective comparative study examining the presence of candiduria (presence of Candida species in the urine) among 97 adults with a spinal cord injury is presented as an additional example. The differences in the use of antibiotics were investigated with the Pearson χ² test (Goetz, Howard, Cipher, & Revankar, 2010). These data are presented in Table 35-2 as a contingency table.

TABLE 35-2

CANDIDURIA AND ANTIBIOTIC USE IN ADULTS WITH SPINAL CORD INJURIES

	Candiduria	No Candiduria	Totals
Antibiotic use	15	43	58
No antibiotic use	0	39	39
Totals	15	82	97

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EXERCISE 35 Questions to Be Graded

Name: _______________________________________________________ Class: _____________________

Date: ___________________________________________________________________________________

Follow your instructor’s directions to submit your answers to the following questions for grading. Your instructor may ask you to write your answers below and submit them as a hard copy for grading. Alternatively, your instructor may ask you to use the space below for notes and submit your answers online at http://evolve.elsevier.com/Grove/statistics/ under “Questions to Be Graded.”

1. Do the example data in Table 35-2 meet the assumptions for the Pearson χ² test? Provide a rationale for your answer.

2. Compute the χ² test. What is the χ² value?

3. Is the χ² significant at α = 0.05? Specify how you arrived at your answer.

4. If using SPSS, what is the exact likelihood of obtaining the χ² value at least as extreme as or as close to the one that was actually observed, assuming that the null hypothesis is true?

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5. Using the numbers in the contingency table, calculate the percentage of antibiotic users who tested positive for candiduria.

6. Using the numbers in the contingency table, calculate the percentage of non-antibiotic users who tested positive for candiduria.

7. Using the numbers in the contingency table, calculate the percentage of veterans with candiduria who had a history of antibiotic use.

8. Using the numbers in the contingency table, calculate the percentage of veterans with candiduria who had no history of antibiotic use.

9. Write your interpretation of the results as you would in an APA-formatted journal.

10. Was the sample size adequate to detect differences between the two groups in this example? Provide a rationale for your answer.

(Grove 409-420)

Grove, Susan K., Daisha Cipher. Statistics for Nursing Research: A Workbook for Evidence-Based Practice, 2nd Edition. Saunders, 022016. VitalBook file.

The citation provided is a guideline. Please check each citation for accuracy before use.

Need answers of questions to be graded at the end of each exercise.