If you designed your questionnaire correctly you have form hypotheses between relations of constructs. For example I think you have implementation success as an Y variable dependent on manager involvement.
Now, you most probably have questions in your questionnaire which measure those variables somehow.
When you have the results of your questions you can make a scale (or index for that matter) to measure your construct. You can do this by using a few methods (be sure to invert negative questions in terms of scale)
When for example you measure implementation success with 5 questions. You may take the mean of those scores (again, rescale negative questions!) assuming they have equal weights for determination of the construct. Also, you could just give them weights by guesstimates.
What's more, you could extract factor scores to have a less arbitrary weighting. All of these methods have their (dis)advantages over the others.
Checking whether questions measure the same thing can be done by using reliability (Cronbach's) alpha. But be sure to know what it does.And also be sure to use other metrics, measures, tests and a healthy dose of face validity and common sense.
Finally you investigate the relationships between your constructs (measured by your developed scales) with for example correlations or regressions.
I hope this helps, good luck!
When you say 'quartile' - are those things based on the quartiles in this data (if so, how) or one some external criterion?
Assuming it's some externally determined cut-off point, this simply looks like a comparison of proportions rather than just raw counts ... which is, as you suggest, a chi-square.
Best Answer
It is usually advised to treat responses from individual Likert items as ordinal data. It requires an additional assumption about the spacing of the response categories in order to treat the responses as interval. Also, data from Likert items are likely to not approximate a continuous distribution for tests that make this assumption.
Ordinal regression is a flexible approach for analyzing ordinal data. Some modern software makes ordinal regression relatively easy.
For simple designs, some nonparametric tests, such as Mann-Whitney and Kruskal-Wallis, appear to behave well with ordinal data.
An appropriate post-hoc test for Kruskal-Wallis is Dunn test (1964).
There are a few appropriate effect size statistics for K-W. I think my favorite right now is pairwise Vargha and Delaney's A. VDA can be interpreted as the probability of an observation from one group being larger than an observation from the other group. I think this is relatively easy to understand relative to other choices for effect size statistics.