Fit Y by X is the appropriate platform to conduct a chi-square
test for independence. For this analysis, the column containing the
responses to a survey question is the Y and the variable Org Level
is the X, as shown in
Figure 3.7 Completed Fit Y by X Dialog. .
The large mosaic plot shows the proportion of responses
in each rating category by each of the organization levels. The small
mosaic plot to the right shows the proportion of responses in each
rating category for both nurse professionals and leaders combined.
This represents the null hypothesis of independence, i.e., both organization
levels have the same proportion in each rating category. If the mosaic
plots by organization level are similar, then this is consistent with
the null hypothesis of independence. Less similarity between the
mosaic plots for the two organization levels suggests the data is
not consistent with the null hypothesis.
The contingency table displays the observed
counts and the counts that would be expected if the pattern of agreement
is independent of the organization level. The red triangle menu offers
a variety of options that can be shown in the contingency table, including
both conditional and unconditional relative frequencies. The chi-squared
test for independence compares the observed frequency (Count in the
JMP contingency table) to the expected frequency.
We can’t establish statistical significance through
visual comparison of graphs or comparing the counts in a contingency
table. The chi-square test statistic and the associated p-value (Prob>ChiSq)
are found in the Tests section. However, the warning at the bottom
of the JMP output indicates that the chi-square assumption for the
minimum number of cells with expected counts greater than 5 is not
satisfied. You can remedy this problem by combining some of the response
columns. In this case we can reduce the 5-point Likert scale to a
3-point scale by combining the strongly disagree and disagree categories
and the strongly agree and agree categories. JMP’s Recode
feature provides an easy means to create a column containing the levels
disagreement, neutral, and agreement. Rerunning the chi-square analysis
yields the results in
Figure 3.9 Chi-square Analysis for the Practicality and Workflow Question with a 3-point
Scale .
Note that the chi-square assumption is now satisfied
and we can safely use the p-value from the Pearson chi-square test
(0.0452) which tells us that at the 5% significance level the perception
of EBP with respect to practicality and workflow depends on whether
you are a leader or a nurse professional. P-values that are less
than the chosen significance level cause a rejection of the null hypothesis.
A p-value is the likelihood of obtaining the sample outcome, or something
more extreme, assuming the null hypothesis is true.
Figure 3.10 Categorical Response Analysis of the Practicality and Workflow Question
by Organizational Level shows the distribution
of the response for the two organization levels.
The leaders show a slight
majority in agreement while the nurse professionals most frequently
respond with neutral and have slightly more in agreement than in disagreement.
So for the proposition “All of the practice changes so far
have been practical and fit well with the workflow of the unit,”
the nurse professionals and nurse leaders differ in their patterns
of agreement.
For this survey question,
the chi-square assumption for the minimum number of cells with counts
of at least five is satisfied and the p-value of 0.0180 from the Pearson
test indicates that there is a statistically significant difference
at the 5% level in how leaders and nurse professionals view EBP in
relation to the limitations of their practice setting.
Figure 3.5 Categorical Response Analysis of Two Survey Questions shows the
differences in the support for the proposition with leaders generally
finding EBP is consistent with practice setting limitations while
the nurse professionals do not.
Finally, we address
the assumption of independence between survey respondents. This assumption
is best satisfied during the design and administration of the survey.
For example, sending the survey link to a respondent’s home
email rather than their work email may reduce the influence of co-workers.