# Understanding Pearson Chi-Square

Statistical Technique in Review

The Pearson Chi-square (χ2 ) is an inferential statistical test calculated to examine differences among groups with variables measured at the nominal level. There are different types of χ2 tests and the Pearson chi-square is commonly reported in nursing studies. The Pearson χ2 test compares the frequencies that are observed with the frequencies that were expected. The assumptions for the χ2 test are as follows:

- The data are nominal-level or frequency data.
- The sample size is adequate.
- The measures are independent of each other or that a subject’s data only fit into one category (Plichta & Kelvin, 2013).

The χ2 values calculated are compared with the critical values in the χ2 table (see Appendix D Critical Values of the χ2 Distribution at the back of this text). If the result is greater than or equal to the value in the table, significant differences exist. If the values are statistically significant, the null hypothesis is rejected (Grove, Burns, & Gray, 2013). These results indicate that the differences are probably an actual reflection of reality and not just due to random sampling error or chance.

In addition to the χ2 value, researchers often report the degrees of freedom (df). This mathematically complex statistical concept is important for calculating and determining levels of significance. The standard formula for df is sample size (N) minus 1, or df = N − 1; however, this formula is adjusted based on the analysis technique performed (Plichta & Kelvin, 2013). The df formula for the χ2 test varies based on the number of categories examined in the analysis. The formula for df for the two-way χ2 test is df = (R − 1) (C − 1), where R is number of rows and C is the number of columns in a χ2 table. For example, in a 2 × 2 χ2 table, df = (2 − 1) (2 − 1) = 1. Therefore, the df is equal to 1. Table 19-1 includes a 2 × 2 chi-square contingency table based on the findings of An et al. (2014) study. In Table 19-1, the rows represent the two nominal categories of alcohol 192use and alcohol nonuse and the two columns represent the two nominal categories of smokers and nonsmokers. The df = (2 − 1) (2 − 1) = (1) (1) = 1, and the study results were as follows: χ2 (1, N = 799) = 63.1; p < 0.0001. It is important to note that the df can also be reported without the sample size, as in χ2(1) = 63.1, p < 0.0001.

TABLE 19-1

CONTINGENCY TABLE BASED ON THE RESULTS OF AN ET AL. (2014) STUDY

` Nonsmokers n = 742 Smokers n = 57*`

No alcohol use 551 14

Alcohol use† 191 43

*Smokers defined as “smoking at least 1 cigarette daily during the past month.”

†Alcohol use “defined as at least 1 alcoholic beverage per month during the past year.”

An, F. R., Xiang, Y. T., Yu., L., Ding, Y. M., Ungvari, G. S., Chan, S. W. C., et al. (2014). Prevalence of nurses’ smoking habits in psychiatric and general hospitals in China. Archives of Psychiatric Nursing, 28(2), 120.

If more than two groups are being examined, χ2 does not determine where the differences lie; it only determines that a statistically significant difference exists. A post hoc analysis will determine the location of the difference. χ2 is one of the weaker statistical tests used, and results are usually only reported if statistically significant values are found. The step-by-step process for calculating the Pearson chi-square test is presented in Exercise 35.

Research Article

Source

Darling-Fisher, C. S., Salerno, J., Dahlem, C. H. Y., & Martyn, K. K. (2014). The Rapid Assessment for Adolescent Preventive Services (RAAPS): Providers’ assessment of its usefulness in their clinical practice settings. Journal of Pediatric Health Care, 28(3), 217–226.

Introduction

Darling-Fisher and colleagues (2014, p. 219) conducted a mixed-methods descriptive study to evaluate the clinical usefulness of the Rapid Assessment for Adolescent Preventative Services (RAAPS) screening tool “by surveying healthcare providers from a wide variety of clinical settings and geographic locations.” The study participants were recruited from the RAAPS website to complete an online survey. The RAAPS risk-screening tool “was developed to identify the risk behaviors contributing most to adolescent morbidity, mortality, and social problems, and to provide a more streamlined assessment to help providers address key adolescent risk behaviors in a time-efficient and user-friendly format” (Darling-Fisher et al., 2014, p. 218). The RAAPS is an established 21-item questionnaire with evidence of reliability and validity that can be completed by adolescents in 5–7 minutes.

“Quantitative and qualitative analyses indicated the RAAPS facilitated identification of risk behaviors and risk discussions and provided efficient and consistent assessments; 86% of providers believed that the RAAPS positively influenced their practice” (Darling-Fisher et al., 2014, p. 217). The researchers concluded the use of RAAPS by healthcare providers could improve the assessment and identification of adolescents at risk and lead to the delivery of more effective adolescent preventive services.

Relevant Study Results

In the Darling-Fisher et al. (2014, p. 220) mixed-methods study, the participants (N = 201) were “providers from 26 U.S. states and three foreign countries (Canada, Korea, and Ireland).” More than half of the participants (n = 111; 55%) reported they were using the RAAPS in their clinical practices. “When asked if they would recommend the RAAPS to other providers, 86 responded, and 98% (n = 84) stated they would recommend RAAPS. The two most common reasons cited for their recommendation were for screening (n = 76, 92%) and identification of risk behaviors (n = 75, 90%). Improved communication (n = 52, 63%) and improved documentation (n = 46, 55%) and increased patient understanding of their risk behaviors (n = 48, 58%) were also cited by respondents as reasons to recommend the RAAPS” (Darling-Fisher et al., 2014, p. 222).

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“Respondents who were not using the RAAPS (n = 90; 45%), had a variety of reasons for not using it. Most reasons were related to constraints of their health system or practice site; other reasons were satisfaction with their current method of assessment . . . and that they were interested in the RAAPS for academic or research purposes rather than clinical use” (Darling-Fisher et al., 2014, p. 220).

Chi-square analysis was calculated to determine if any statistically significant differences existed between the characteristics of the RAAPS users and nonusers. Darling-Fisher et al. (2014) did not provide a level of significance or α for their study, but the standard for nursing studies is α = 0.05. “Statistically significant differences were noted between RAAPS users and nonusers with respect to provider types, practice setting, percent of adolescent patients, years in practice, and practice region. No statistically significant demographic differences were found between RAAPS users and nonusers with respect to race, age” (Darling-Fisher et al., 2014, p. 221). The χ2 results are presented in Table 2.

TABLE 2

DEMOGRAPHIC COMPARISONS BETWEEN RAPID ASSESSMENT FOR ADOLESCENT PREVENTIVE SERVICE USERS AND NONUSERS

Current user Yes (%) No (%) χ2 p

Provider type (n = 161) 12.7652, df = 2 < .00

Health care provider 64 (75.3) 55 (72.4)

Mental health provider 13 (15.3) 2 (2.6)

Other 8 (9.4) 19 (25.0)

Practice setting (n = 152) 12.7652, df = 1 < .00

Outpatient health clinic 20 (24.1) 36 (52.2)

School-based health clinic 63 (75.9) 33 (47.8)

% Adolescent patients (n = 154) 7.3780, df = 1 .01

≤50% 26 (30.6) 36 (52.2)

50% 59 (69.4) 33 (47.8)

Years in practice (n = 157) 6.2597, df = 1 .01

≤5 years 44 (51.8) 23 (31.9)

5 years 41 (48.2) 49 (68.1)

U.S. practice region (n = 151) 29.68, df = 3 < .00

Northeastern United States 13 (15.3) 15 (22.7)

Southern United States 11 (12.9) 22 (33.3)

Midwestern United States 57 (67.1) 16 (24.2)

Western United States 4 (4.7) 13 (19.7)

Race (n = 201) 1.2865, df = 2 .53

Black/African American 11 (9.9) 5 (5.6)

White/Caucasian 66 (59.5) 56 (62.2)

Other 34 (30.6) 29 (32.2)

Provider age in years (n = 145) 4.00, df = 2 .14

20–39 years 21 (25.6) 8 (12.7)

40–49 years 24 (29.3) 19 (30.2)

50+ years 37 (45.1) 36 (57.1)

image

χ2, Chi-square statistic.

df, degrees of freedom.

Darling-Fisher, C. S., Salerno, J., Dahlem, C. H. Y., & Martyn, K. K. (2014). The Rapid Assessment for Adolescent Preventive Services (RAAPS): Providers’ assessment of its usefulness in their clinical practice settings. Journal of Pediatric Health Care, 28(3), p. 221.

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Study Questions

- What is the sample size for the Darling-Fisher et al. (2014) study? How many study participants (percentage) are RAAPS users and how many are RAAPS nonusers?
- What is the chi-square (χ2) value and degrees of freedom (df) for provider type?
- What is the p value for provider type? Is the χ2 value for provider type statistically significant? Provide a rationale for your answer.
- Does a statistically significant χ2 value provide evidence of causation between the variables? Provide a rationale for your answer.
- What is the χ2 value for race? Is the χ2 value statistically significant? Provide a rationale for your answer.
- Is there a statistically significant difference between RAAPS users and RAAPS nonusers with regard to percentage adolescent patients? In your own opinion is this an expected finding? Document your answer.

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- What is the df for U.S. practice region? Complete the df formula for U.S. practice region to visualize how Darling-Fisher et al. (2014) determined the appropriate df for that region.
- State the null hypothesis for the years in practice variable for RAAPS users and RAAPS nonusers.
- Should the null hypothesis for years in practice developed for Question 8 be accepted or rejected? Provide a rationale for your answer.
- How many null hypotheses were accepted by Darling-Fisher et al. (2014) in Table 2? Provide a rationale for your answer.

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