I have a 13 item likert scale with 5 responses on each question. I am using the same questionnaire before and after intervention on the same group of people. What is the best way of analysing this data. Is it a t-test? I am struggling here please can someone help point me in the right direction?
I must admit to not being a fan of Likert measures (and other quasi-ordinal researcher constructs). Whether you agree with Steven's taxonomy or not, you need to have a conceptual basis for creating a meaningful system of measurement, you can't just cross your fingers and hope you measure something and then decide what it is later. Even 'underlying variables' that show up during statistical methods need to have some basis in reality applied to them eventually, otherwise how are the having an 'noticeable' effect? And if they have some basis in reality then we have to construct a consistent conceptualization to understand and compare such things. Better to have a closer look at your factors and transparently define relevant combinational rules yourself, than arbitarily assume ordinal, interval or ratio operations have any relevance to analyses. The real world is a lot more complex than that.
If you're interested in the total sum of the scale, you can just add the score on each item. If you don't want to control for other variables, I think you should use the Wilcoxon signed-rank test for pair samples because the data probably doesn't follow a normal distribution.
I would start by plotting the data and observing what the actual distribution looks like. Visualizing data can be really powerful and can help to identify bias or other issues in ways that summary statistics cannot.
If you are summing your scale you should be safe in using a t-test and typical analysis of variance methods, especially if you have a large number of respondents. I'm assuming from your description that the likert scale is a proxy for the dependent variable.
A Likert scale produces numbers, just as a thermometer produces numbers. HOWEVER with a thermometer, we know that the difference between 20 deg and 21 deg is the same as the difference between 10 and 11 deg. That is NOT the case with the Likert scale. At best, we can order the numbers from a Likert scale. Hence data like these are called "ordinal". The standard wisdom is that ordinal data require special analysis procedures, and procedures (e.g. t-test) developed for degrees, inches, etc should not be applied. This is why the Wilcoxon Signed-Ranks Test was suggested. You have paired data, and this test uses only ordinal information from the data.