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# Finding a appropriate statistical test

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### #1 Ikar

Ikar

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Posted 30 July 2011 - 12:18 AM

Hello,

I have a problem to figure out which statistical test is appropriate to deal with my measured data.
It is really important for my bachelor thesis (that has to be finished in 2 weeks). Unfortunately I figured out that I have a lack of statistical
background. Good news is that I have already chosen 2 statistic courses for my graduate study,

I've also asked several people in my lab, but nobody could give me a satisfying answer. Some of them said
that I should do a Student's t test. So I did. But other people said that a t test requires a at least three-digit
n value. My n is only 30.

So here is a example of the data that I want to analyse

Negative control:
2.225519288 -1.553398058 4.872881356 3.504672897 5.780346821 0.92449923 -1.873935264 -0.970873786 1.054852321 -6.340057637 2.415458937 -4.115226337 2.30125523 4.627249357 8.266666667 -7.692307692 6.534954407 0.690846287 2.34741784 -6.240713224 -0.591715976 -5.166051661 3.20855615 5.322128852 -0.653594771 -1.533742331 2.828282828 2.282157676 -7.766990291 2.964959569

Experiment1
4.414587332 4.414587332 2.117647059 -1.282051282 -1.030927835 -8.359133127 -10.13333333 -0.425531915 5.361930295 0.429184549 3.886925795 -4.333333333 2.06185567 7.462686567 -0.466200466 6.64893617 6.64893617 5.336426914 -1.909307876 3.314917127 -4.8 4.402515723 2.444444444 -0.584795322 -3.244837758 -9.685863874 -4.854368932 2.228412256 -3.389830508 4.456824513

Experiment2:
3.202846975 0.974025974 0 -2.985074627 -7.407407407 2.69541779 0.451467269 -3.146853147 0.588235294 5.053191489 3.157894737 5.167173252 2.686567164 1.680672269 1.245551601 7.142857143 2.079722704 4.166666667 -3.738317757 3.050108932 1.216545012 0.555555556 -0.36101083 4.368932039 1.80878553 3.166226913 2.305475504 0 -0.579710145 1.634877384

Positive control:
28.15656566 26.86980609 23.70517928 31.14640884 29.01353965 24.51861361 25.25724977 27.24902216 31.66421208 33.06358382 37.05882353 38.10861423 35.19494204 48.19967267 32.02072539 29.02408112 48.08629088 36.80981595 18.61074705 26.78405931 33.07984791 33.81443299 27.44680851 35.59577677 35.46666667 30.26467204 36.15023474 33.4038055 30.72970195 37.47228381

What I want to test now is if there is a significant difference between the negative control and experiment 1 ; the negative control and experiment 2.

I know that a higher n would make the things more easy, but unfortunately 1 experiment requires at least 1 week of preparation and the measurement itself takes up to 10 hours and
I did not have the time anymore.

I would be really really thankful for any kind of idea and help!

Best regards,
Ikar

### #2 hobglobin

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Posted 30 July 2011 - 10:01 AM

You should know if you have dependent data or not. And you should know something about the distribution of the data (e.g. a normal distribution), here box-whisker plots can help, or a test like Kolmogorov–Smirnov test. Usually for a comparison of two independent data sets with normal distribution, a t-test is good. If the variables are dependent, the t-test for paired samples works.

If you are unsure about your data, use a non-parametric test such as the Wilcoxon rank sum test (= Mann-Whitney U-test) for independent variables and the Wilcoxon signed-rank test for dependent ones.

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### #3 Ikar

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Posted 30 July 2011 - 03:10 PM

You should know if you have dependent data or not. And you should know something about the distribution of the data (e.g. a normal distribution), here box-whisker plots can help, or a test like Kolmogorov–Smirnov test. Usually for a comparison of two independent data sets with normal distribution, a t-test is good. If the variables are dependent, the t-test for paired samples works.

If you are unsure about your data, use a non-parametric test such as the Wilcoxon rank sum test (= Mann-Whitney U-test) for independent variables and the Wilcoxon signed-rank test for dependent ones.

I already made box plot charts. The data should be normal distributed and independent. I think I will have a look at the other tests and how they work. Thanks for your help!

### #4 bob1

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Posted 30 July 2011 - 08:47 PM

If the data is normally distributed and independent you can use ANOVA. 30 samples should be enough for ANOVA, though it is right at the limit of usefulness for parametric tests. You will probably also want to do a post-hoc test of some sort to determine which of the groups are significantly different to the others. Tukey's test is the common one for ANOVA.