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I have two 'samples'.

  1. The first consists of approx. 400 physical measurements of a quantity (taken over one hour, and the real situation is not a steady state). They show a very skewed distribution for which the theoretical model is not known, and the values can lie between 0 and (theoretically) +inf.
  2. The second 'sample' unfortunately consists of only one data point, as it is derived by modelling the physics of the scenario pretending it is a steady state in this hour. (I am not really sure if I should consider this as a mean for this hour, or as just one measurement in the hypothesis testing).

I want to find ways to quantify if the model describes the data well enough. I thought I could maybe use hypothesis testing, but I am not sure if the information I have here is sufficient. I first thought I'd do a Mann-Whitney U test, but (I think) one data point is too little. Would this be a case where I can just use the t-test even if the data is skewed? Would the One Sample Sign Test be appropriate? Is there a totally different approach I could consider?

I am new to this, feel like I am lost with this zoo of existing hypothesis tests.

Subhash C. Davar
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Mars
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1 Answers1

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You can apply t-test assuming modelled mean as a population mean calculated under the assumption that a steadystate existed. The observed sample data (n = 400) for speed of wind can be used to compute sample-mean. If you have highly skewed data, you may remove outlier data in the sample. Mann-Whitney U test is a non_parametric test- probability-based test. Your data does not meet its condtions

Subhash C. Davar
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