Chi-Square and Nonparametric Tests
Example of a Friedman test:
Rungreangkulkij and Wongtakee (2008) evaluated the psychological impact of
Buddhist counseling for Thai patients suffering from anxiety. They measured anx-
iety before the intervention, after it, and then 2 months later using the Friedman
test. Anxiety declined over the course of the study, and differences were signifi-
cant (x2 ϭ 42.0, p < .001).
TIP: Each of the nonparametric tests we have described tests the existence
of a relationship between an independent and dependent variable. It is
beyond the scope of this text to describe indexes for measuring the
strength of the relationship for situations in which these nonparametric
tests would be used, but such indexes do exist. For further information,
you can consult Jaccard and Becker (2001).
RESEARCH APPLICATIONS OF NONPARAMETRIC TESTS
Except for the chi-square test for independence, nonparametric tests are infrequently
used in nursing research. In large part, this is because parametric tests are more pow-
erful than their nonparametric counterparts and are fairly robust to violations of
many underlying assumptions. Yet, nonparametric tests are often appropriate, espe-
cially if there is evidence that the assumptions for parametric tests cannot possibly
be met (e.g., a markedly skewed distribution of the dependent variable). This section
examines some of the major applications of nonparametric tests and discusses meth-
ods of effectively displaying results from these tests in a research report.
The Uses of Nonparametric Tests
The nonparametric tests we have discussed in this chapter are, for the most part, used
in much the same applications as those for t tests and ANOVA, except for differences
in how the outcome variables were measured. Thus, we provide only a few illustra-
tions.
1. Answering research questions As with most inferential statistics, the pri-
mary use of nonparametric tests is substantive—that is, they are used mainly to
test hypotheses and to answer research questions. Throughout this chapter we
have illustrated the wide array of research questions that have relied on the use
of nonparametric tests, using actual examples from the nursing literature.
2. Testing biases Nonparametric tests are also used to examine the nature and
extent of any biases that need to be considered in interpreting substantive
results. For example, Nyamathi and colleagues (2008) studied the effective-
ness of a nurse case-managed intervention for latent tuberculosis among the
homeless. First, however, they compared the background characteristics of
those in the intervention and control groups to assess selection bias. They used
chi-square tests to assess the equivalence of the two groups with respect to
such characteristics as ethnicity, marital status, and sex.
3. Variable selection for multivariate analyses As you know, researchers
sometimes undertake complex multivariate analyses to assess the contribution
of multiple independent variables, taken simultaneously, in predicting an
outcome. They often begin by looking at each potential predictor in relation
to the outcome of interest in a bivariate fashion, to see if some should be
eliminated from further consideration. When outcomes of interest are
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Chi-Square and Nonparametric Tests
dichotomous (e.g., had a fall versus did not have a fall), chi-squared tests or
bivariate odds ratios are likely to be used in these preliminary analyses. For
example, Certain, Mueller, Jagodzinski, and Fleming (2008) developed a
model to identify predictors of domestic abuse in postpartum women. Each
possible independent variable or predictor, such as marital status, employment
status, and alcohol use, was tested for its relationship to abuse status using chi-
square tests. Variables that had a p < .10 were placed in the final model.
Presentation of Nonparametric Tests in Research Reports
Like other statistical tests, nonparametric tests usually are summarized in the text of
a report when there are only one or two tests, but are presented in a table if there are
more. The standard convention is to provide information about the name of the test,
the value of the test statistic, degrees of freedom, sample size, and significance
level. Here is a fictitious example: “A chi-square test indicated that diabetic patients
who had regular inspection of their feet by a nurse or other healthcare professional
were significantly more likely than those who did not to regularly inspect their own
feet for foot complications and ulcers (x2 [1, N ϭ 653] ϭ 45.3, p < .001).”
For tests with a nominal-level dependent variable, such as the chi-square test
of independence, multiple tests can be reported in a table in much the same fashion
as a table for t tests, except that the descriptive information is group percentages
rather than group means. Table 9 presents an example of such a table that elaborates
on our earlier example of heparin lock placement time groups. For four separate com-
plication outcomes, the table shows the percent in each group with the complication,
the value of the chi-square statistic, and the p-value. The table illustrates how
Fisher’s exact test was reported for an outcome for which the expected frequency for
some cells was less than five.
When a table is used to summarize multiple tests, the text highlights key
results. Here is an example of how the text corresponding to Table 9 might read:
The table shows that the rates of various complications in the two he-
parin lock placement time groups were comparable for every type of
complication considered. Overall, 18.0% of the 72-hour group, com-
pared to 22.0% of the 96-hour group, had a complication, a difference
that was not statistically significant. Although none of the differences
was significant, there was a modestly higher rate of complications in the
96-hour group for every complication. A post hoc power analysis re-
vealed that the power of the statistical tests was quite low, and therefore
replication with a larger sample of participants seems warranted.
TABLE 9 Example of a Table for Chi-Square Test Results
Complication Heparin Lock Placement Time Group
72 Hours 96 Hours x2 p
(n ؍50) (n ؍50)
Phlebitis 12.0% 16.0% .38 .54
Blocking/Leaking 8.0% 12.0% .44 .51
Purulence/Septicemia 0.0%
Any complication 2.0% a 1.00
18.0% 22.0% .25 .62
a Fisher’s exact test, expected frequency Ͻ 5 in two cells
Percentage of Patients with Various Complications, by Length of Time
Heparin Lock was in Place
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