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Can I use chi square test with three variables ? The variables are organizational climate (11 dimensions), job satisfaction (7 dimensions) and customer satisfaction (5 dimensions). Likert scale. any suggestions.

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    $\begingroup$ Your variables are ordered, you'll potentially be losing a lot of information about ordered dependence (including but not limited to monotonic correlation) if you treat them all as nominal (whether you do so depends on how general the alternatives you most care about are) $\endgroup$
    – Glen_b
    May 15 at 1:07

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The short, not very useful answer, is YES.

However, it's probably not going to work very well or provide any meaningful statistics. I presume when you say each variable has $k$ "dimensions," you mean factor (or Likert*) levels. If so, then your 3-way table would have $11 \times 7 \times 5 =385$ frequency cells, requiring at least 2000 observations to get any reasonable expected values for the chi-square test (which likes the expected values to all be 5 or more).

You might get more insight into your data by looking at the three two-way scatterplots of your data (use jittered points or a density overlay--OK, because Likert) to look for associations. Pair this with the three possible Spearman correlations to test for possibly significant ones.

If you do find significant associations, you can dazzle the suits with a 3-d bubble chart, with bubble sizes representing frequency.

*Not sure how you define a Likert-scaled measurement for "organizational climate." This one may give you some trouble; think about stratifying its levels into sub-dimensions.

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