Hi The shapiro.test function outputs a value of the W statistic, which should be 1 if the distribution is normal, and a p-value for the test (as the documentation states). I'm a bit confused with some results. I'm getting a W=0.9977 and a p-value=0.1889. I was expecting that a W of 0.9977 would tell me that the distribution is normal so p-value should be small ... What am I missing ? Thanks EJ
shapiro.test
4 messages · Ernesto Jardim, Rick Bilonick
Ernesto Jardim wrote:
Hi The shapiro.test function outputs a value of the W statistic, which should be 1 if the distribution is normal, and a p-value for the test (as the documentation states). I'm a bit confused with some results. I'm getting a W=0.9977 and a p-value=0.1889. I was expecting that a W of 0.9977 would tell me that the distribution is normal so p-value should be small ... What am I missing ? Thanks EJ
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You have it backwards. The null hypothesis is that the distribution is
Normal. You reject this null when the p-value is small. If the
distribution is Normal, the p-value will tend to be large.
> shapiro.test(rnorm(100))
Shapiro-Wilk normality test
data: rnorm(100)
W = 0.9877, p-value = 0.4894
Rick B.
Ok, let me put it the other way around. On another test I have W = 0.9907, p-value = 6.024e-06. The same question stands, with such huge W should it be expected to be normal ? EJ
On Mon, 2003-02-10 at 14:47, Richard A. Bilonick wrote:
Ernesto Jardim wrote:
Hi The shapiro.test function outputs a value of the W statistic, which should be 1 if the distribution is normal, and a p-value for the test (as the documentation states). I'm a bit confused with some results. I'm getting a W=0.9977 and a p-value=0.1889. I was expecting that a W of 0.9977 would tell me that the distribution is normal so p-value should be small ... What am I missing ? Thanks EJ
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You have it backwards. The null hypothesis is that the distribution is Normal. You reject this null when the p-value is small. If the distribution is Normal, the p-value will tend to be large.
> shapiro.test(rnorm(100))
Shapiro-Wilk normality test
data: rnorm(100)
W = 0.9877, p-value = 0.4894
Rick B.
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Ernesto Jardim wrote:
Ok, let me put it the other way around. On another test I have W = 0.9907, p-value = 6.024e-06. The same question stands, with such huge W should it be expected to be normal ? EJ
You have it backwards. The null hypothesis is that the distribution is Normal. You reject this null when the p-value is small. If the distribution is Normal, the p-value will tend to be large.
shapiro.test(rnorm(100))
Shapiro-Wilk normality test
data: rnorm(100)
W = 0.9877, p-value = 0.4894
Rick B.
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______________________________________________ R-help at stat.math.ethz.ch mailing list http://www.stat.math.ethz.ch/mailman/listinfo/r-help
It depends on how non-Normal the distribution and the size of the
sample. A t-distribution with df = 30 isn't Normal but it is close to
being Normal. A small sample size probably won't detect it:
> shapiro.test(rt(100,30))
Shapiro-Wilk normality test
data: rt(100, 30)
W = 0.9927, p-value = 0.8708
But a large enough sample size will:
> shapiro.test(rt(2000,30))
Shapiro-Wilk normality test
data: rt(2000, 30)
W = 0.9968, p-value = 0.0003097
You haven't told us your sample size.
Rick B.