I know this site is full of similar questions, but either their answers do not apply, or I'm missing something.
I have data from a questionnaire. Responses are in the form of Likert items, some of which can be used to construct a scale. I'm specifically interested in those that cannot be used to construct a scale and should therefore be treated as ordinal.
One of the statements probes an employee's job satisfaction: I enjoy working at the company (answer: Strongly Disagree, Disagree, Neutral, Agree, Strongly Agree).
Another statement probes the employee's organizational fit (for example): I have several friends at the company (answer: Strongly Disagree, Disagree, Neutral, Agree, Strongly Agree). I have defined a hypothesis: Employees with a strong organizational fit will experience greater job satisfaction.
My questions are:
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In order to reject (or not reject) my hypothesis, can I construct a contingency table and use either Pearson's Chi-square test or Fisher's exact test?
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If not, can I use this data to test my hypothesis and how should I go about it?
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If I can, how do I go about constructing the contingency table?: Should I take the response distribution to each statement (e.g. Job Satisfaction: SD = 35, D = 55, N = 40, A = …, SA =…) and end up with a 5×5 contingency table?
If it matters, I'll be using either R or SPSS to perform the calculations.
Best Answer
(1) Yes you can, but nothing in either test takes the ordering into account. The ordered scales are reduced to nominal. The tests are applicable, but ignore much of the information you have.
(2) Many researchers would be happy to use rank correlation here. At least it respects the ordering of the categories. Many ties are likely, but that's par for the course. Another test that might be helpful is the Jonckheere-Terpstra test. A more ambitious analysis would be to use an ordinal logit or probit model. I wouldn't put all the weight on a single measure or test of association. Looking at a mosaic plot (spineplot) or two-way bar chart may help you see structure that's not directly expressed by a correlation. For example, on questionnaires some people give almost the same grades regardless of the question.
(3) The contingency table is the same regardless of what tests you apply to it. It's a $5\times5$ table of counts, as you say. It's not clear why you're asking this, not least because producing it is a simple task in any software.