# Shapiro-Wilk normality test - how to interpret this?

So, I'm having data which represent two groups, one that used tool 1 and the other that used tool 2. I asked a series of questions (10 questions) and I recorded the time as well. Afterwards I calculated the productivity based on the data and now I want to analyse if the productivity of tool 1 is significantly different than the productivity of tool 2. To achieve this, I need to run either T Test or nonparametric tests; however, in order to decide which one should I use, I need to firstly ran the normality test, which I did in SPSS. Since I have 80 participants, I used Shapiro-Wilk normality test.

The results are something like this:

QS1 ... tool1 0,000

QS1 ... tool2 0,000

as can be seen from the example, the sig. is 0,000 which means that data is not normally distributed and I should use nonparametric tests. However, what should I do in case of this:

QS2 ... tool1 0,047

QS2 ... tool2 0,586

In this case QS2 and tool 1 the sig. is < 0,05, which calls for nonparametric tests. However, QS2 and tool 2 are > 0,5, which means I should use T Tests. How should I interpret these results and which tests for comparing the means should I choose?

• I would use the non-parametric throughout. That way you don't have to worry so much about the shape of the distribution, and I am guessing your questions have ordinal characteristics. The non-parametric test is a good one. As an aside, look into the problem of multiple tests if your p-values are not small. Commented Feb 2, 2016 at 23:38
• How does "productivty of tool" have to do with the answers to the 10 questions? What are the questions recording (/how are they represented?). Much about this question is unclear Commented Feb 2, 2016 at 23:43
• Excellent point, I will update the main question to make it more clear. Commented Feb 3, 2016 at 10:40