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I have read somewhere that W values above 0.9 are considered normal. So I wanted to use that as a cutoff for normality. However, upon running various scenarios I have come up with the result of W = 0.888429, p = 0.254888.

Clearly, this is a borderline case. W is less than 0.9 so my cutoff considers this non-normal. However, if I rounded to one decimal place it would be 0.9 and therefore normal. Also, the p-value indicates the null hypothesis is not rejected eg. it is normal.

When I look at the histogram it is heavily skewed to the left.

How would others interpret this? I am tempted to take a hard line and consider this non-normal as the W is less than 0.9 but perhaps others would consider the p-value more important?

The data is:

0.65, -1.37, -1.22, 2.2, 0, -1.5, 1.1, -1.5, -0.5

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    $\begingroup$ With just nine data points, any test for normality will have very little power. A histogram is not very useful, because most bins will have only a few observations, and the shape heavily depends on how you chose the bin boundaries. Why are you interested in the normality of this dataset? $\endgroup$
    – Stephan Kolassa
    Commented Aug 2 at 20:30
  • $\begingroup$ While you consider how you respond to Stephan's question (which perhaps several people are waiting for you to answer), you might like to search through some of the many previous sets of answers to questions about normality and more generally about testing assumptions particularly with very small or very large sample sizes. One point: no matter how large your W statistic or its p-value, this does not imply that the population of values is normally distributed. $\endgroup$
    – Glen_b
    Commented Aug 4 at 22:27
  • $\begingroup$ Further, I see no evidence of left skewness in your data. The sample is mildly right skew (short left tail, longer right tail). Are you sure you have the terms correctly understood? Perhaps you could include the display you looked at (not that I'd suggest using a histogram with a small sample but if that's what you're basing it on, best to include it) $\endgroup$
    – Glen_b
    Commented Aug 4 at 22:55

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