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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?

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  • $\begingroup$ 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. $\endgroup$
    – mandata
    Feb 2, 2016 at 23:38
  • $\begingroup$ 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 $\endgroup$
    – Glen_b
    Feb 2, 2016 at 23:43
  • $\begingroup$ Excellent point, I will update the main question to make it more clear. $\endgroup$
    – uglycode
    Feb 3, 2016 at 10:40

1 Answer 1

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If your data are not normally distributed you should use a non parametric test.

You can use the Wilcoxon-test for paired data: here is a guide R Wilcoxon Test

For unpaired data, use the Mann-Witney U test of location in SPSS.

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  • $\begingroup$ I don't think Wilcoxon-test is the right way to go, since (as far as I know) it is intended for dependent data, i.e. values PRE and values POST. However, in my case, I have two separated groups (one that used tool-1 and the other that used tool-2; one participant did not use both tools, but just one, randomly assigned). I think Mann-Whitney U Test is more appropriate here, since I have two independent groups. $\endgroup$
    – uglycode
    Feb 3, 2016 at 13:18
  • $\begingroup$ Sorry didn't fully understand the situation $\endgroup$
    – GGA
    Feb 3, 2016 at 13:21
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    $\begingroup$ No problem, I just hope that I understand it well enough to provide a solid argument. My original question addressed the situation where data from one group is not normally distributed whereas the other group has normally distributed data - which tests should I use? I think the basic T-Test cannot be used in this case, even though one group has normally distributed data. So, non-parametric tests are the way to go, I believe. mandata confirmed this as well in his response. $\endgroup$
    – uglycode
    Feb 3, 2016 at 13:24

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