If I understand you correctly, that depends on whether you want to compare on an individual level or on a group level. In the first case, first of all of course you need a variable that helps you to identify the individual - e.g. a code. Afterwards you might treat the Likert scale as a metric scale and calculate correlations or t-tests. On a group level you do not need such a code and might calculate t-tests to compare the means. However, I am not sure whether or not you describe two different scales (governance issue and competence) or just two sets of independent items?

It seems like you are using the repeated measure design to compare the means of same group at two different point of time on the same instrument.instrument. Repeated measure t-test will the used in this case.

 I think that if you are interested in measuring the measures of the same population at different times then you should have more than two times to see the difference more clearly.

I'm not sure about using the repeated measures t-test (also known as the dependent measures t-test) because it is usually used to compare two related groups on the same dependent variable (such as the same people at two points in time or people in two different experimental conditions).

Perhaps someone can provide an example where the repeated measures t-test was used for this situation?

Beyond that, you can certainly examine the correlation to see how strongly the two variables are related. And along with that you could do regressions where one predicts the other, which would allow you to bring in other variables as additional predictors.

Right, t-tests make no sense if you compare two incomparable, totally independent variables, even if they have the same variance and are both normally distributed. A difference between distributions needs interpretation. But in this case it seems to be just the repeated measurement of two constructs with two scales, so the t-test could be a method of choice. Of course only if you want to find differences, if you want to find relationships you would certainly use correlations or regressions.

what i understand is you want to measure people before and after certain intervention . use  paired sample t test . , on spss follow are the codes.

analyse , compare means ,paired sample t test , tranfer the resp variable , click ok

Just to offer a different idea, it sounds very much like what you want to know is the level of agreement between the two sets, which is what the Kendall's coefficient of concordance (W) will tell you.  You can find a description here:

  http://www.real-statistics.com/reliability/kendalls-w/

You can run it in SPSS under "Reliability" in the "Statistics" subcommand.  If you google it, you will also find the R coding.

I dug a bit deeper on this and  found that repeated measures t-tests are the same thing as paired comparisons t-tests, which is a more familiar term to me. Here is a list of examples from the SAS statistics guide about when you might want to use a paired comparisons t-test.

* pre- and post-test scores for a student receiving tutoring

* fuel efficiency readings of two fuel types observed on the same automobile

* sunburn scores for two sunblock lotions, one applied to the individual’s right arm, one to the left arm

* political attitude scores of husbands and wives

Looking over the formulas for doing this kind of t-test makes it clear why the repeated measures example is used so frequently: because one of the variables is being subtracted from the other. In the case of repeated measures, this produces a change score, and the null hypothesis is that there is no change (i.e.., the difference in means between the two variables is zero).

I take this to mean that a paired comparisons t-test only makes sense when you are want to subtract one variable from the other to test the ill hypothesis that they have the same mean scores. In the present case, I don't think that it makes sense to compare importance and competence in this manner.

There is need for more information about this question. Do you intend to know the relationship between governance issues and competence ranking or how one predicts the other? If this is the case, then Correlation or Simple Regression will do it.

Since both time and question content vary over the repeated measures, untangling those things would be pretty complicated. Did you just do this a two time points for logistical reasons (e.g., it was too long for one survey)? If so, and if you're willing to assume that time doesn't make a difference, you could just treat them as if they were measured at the same time point, and treat them as measures of two constructs at a single point in time (e.g., correlation, cross-tab, etc). 

Use either repeated measure ANOVA or paired (correlated groups) t-tes. 

T-test or Wilcoxon