Shapiro-Wilk Test – Interpretation of Shapiro-Wilk Test Results

distributionsgoodness of fitinterpretationnormality-assumptionshapiro-wilk-test

I'm pretty new to statistics and I need your help.
I have a small sample, as follows:

      H4U
      0.269
      0.357
      0.2
      0.221
      0.275
      0.277
      0.253
      0.127
      0.246

I ran the Shapiro-Wilk test using R:

shapiro.test(precisionH4U$H4U)

and I got the following result:

W = 0.9502, p-value = 0.6921

Now, if I assume the significance level at 0.05 than the p-value is larger then alpha (0.6921 > 0.05) and I cannot reject the null hypothesis about the normal distribution, but does it allow me to say that the sample has a normal distribution?

Best Answer

No - you cannot say "the sample has a normal distribution" or "the sample comes from a population which has a normal distribution", but only "you cannot reject the hypothesis that the sample comes from a population which has a normal distribution".

In fact the sample does not have a normal distribution (see the qqplot below), but you would not expect it to as it is only a sample. The question as to the distribution of the underlying population remains open.

qqnorm( c(0.269, 0.357, 0.2, 0.221, 0.275, 
          0.277, 0.253, 0.127, 0.246) )

qqplot

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