Hi everybody
I hope you are doing great. I have little experience in SPSS and tried to do a normality test. Since my sample size was small and less than 50, I used Shapiro-Wilk test. Once I took a look at the table produced by software, I really confused. I saw three fields in the mentioned table. First one was: statistic = 0.865, and second: df=30, and last one was: Sig. =0.000
I know that "df "means "degree of freedom" and here is equal to my data size. Also, Sig = 0.000 implies that the samples comes from non-normal distribution. But, for first field "Statistic=0.865" i could not find any meaning for that. Could you explain what does "statistic" means in the mentioned context?
Regards,
Vahid
Hello Vahid,
The statistic in question is the Shapiro-Wilk test statistic ("W"). In general, smaller values indicate worse fit of the sample data to a normal distribution, whereas larger values indicate better fit. How small and how large to trigger "significant" results depends on sample size [Edited to fix failure to proof initial post.]
Here's a link that describes the computation of W: https://www.itl.nist.gov/div898/handbook/prc/section2/prc213.htm
Good luck with your work.
Hello
Data normality test in SPSS is used to ensure that the distribution of the collected data is normal for performing parametric tests.
David Morse: in the link you gave it is said: "Small values of W are evidence of departure from normality" (emphasis mine), what seems correct. The maximum W-statistic is 1, and the null distribution left-skewed, peaked close to 1. Thus, lower values indicate more misfit.
The statement of Jochen Wilhelm is confirmed in the original paper of Shapiro & Wilk.
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