# What is the role of the test statistic? [I'm not talking about the p-value]

#### Magnetar

##### New Member
For example when Shapiro-Wilk test shows the statistic .945, df=12, p-value=.563 I know it's 'not significant' and I retain the H0 hypothesis, but I also have to write about the test statistic (.945), so what does it mean, when is it high, when is it low, comparing to what?

Regards,
Chris

#### Dason

Are you specifically interested in the spairo-wilk test statistic? It sounds like you don't understand the point of test statistics in general - is this the basis of the question?

#### noetsi

##### No cake for spunky
The test statistic, whichever one you use, normally is a test of the null hypothesis. It is constructed to test a specific set of hypothesis and (assuming the null is true) has an associated distribution most commonly a t, f, or chi square one.

#### Magnetar

##### New Member
Yes, I am the beginner and just would like to know what the Shapiro-Wilk test statistic means, I don't need to know the equation and how it is calculated, just what it means. Thanks.

#### Magnetar

##### New Member
The user may reject the null hypothesis if W is too small.[3] -what does it mean it's too small ? when is it too small?

#### Magnetar

##### New Member
Yeah -like I don't know about Wikipedia

#### noetsi

##### No cake for spunky
Normally too small or too high (a highly subjective definition) means when the test statistic yields a p value below the alpha level you have chosen. Commonly .05. When your p value is below alpha it means that the results you got are extremely unlikely if the null hypothesis is accurate.

#### Magnetar

##### New Member
Dude, no offence but are you drunk? I can't figure out from your reply when is W too small (when the statistic level yields a p value below the alpha level or otherwise?) In every definition of Shapiro-wilk test they only talk about the p value and alpha, but what means the W value, why is it there in the SPSS output for what sake?

#### noetsi

##### No cake for spunky
Dude, no offence but are you drunk? I can't figure out from your reply when is W too small (when the statistic level yields a p value below the alpha level or otherwise?) In every definition of Shapiro-wilk test they only talk about the p value and alpha, but what means the W value, why is it there in the SPSS output for what sake?
If you can't manage basic curtesy good luck on discussing this issue with other posters. SPSS prints the statistic because individuals want to know what it is; the specific value is not critical for analyzing the null just the resulting p value. There is no such thing as "too small" or "too large", it is that value relative to your hypothesis that generates a specific p value that causes the null to be rejected or not.

Alternately, some argue that p values (hypothesis tests) are invalid and that the effect size is what matters. What is large enough to make a difference is not an absolute value. It depends on the question, your assumptions, and the like.

#### Magnetar

##### New Member
"The fact, that W cannot take a value bigger than 1 is an important property of the W statistic.
We will discuss later that a value of W near one is an incidence that the underlying sample is
actually normally distributed, while by getting a small value of W we tend to reject the null
hypothesis of a normal distribution."

Finally I 've found it, it seems guys here know nothing about it. Naukowcy za grosze.

#### noetsi

##### No cake for spunky
lol that is exactly what people said

#### Dason

W is not too horrible to calculate (although for large sample sizes it's not necessarily a walk in the park...). But the sampling distribution of W isn't too nice. I don't know exactly how each program is calculating the p-value but W is constrained between 0 and 1 (actually there is a lower bound slightly higher than 0 that is dependent on the sample size but it's not pretty so I don't feel like typing it up) and under the null hypothesis W should be 'close' to 1. If the data isn't actually normal we expect W to be further from 1. This is by construction of W and if you don't want to look into the math or the original paper then you'll just have to take my word for it.

So the p-value is obtained by looking at the probability that W is less than or equal to the observed value of W. This can be computed through some approximation or possibly by simulation - it depends on how the program decided to implement it.

Why is the observed value of W included in SPSS output? Because it's calculated and some people might be interested in it. I can't provide any more information than that but I don't see why it shouldn't be provided.

I posted the wikipedia link because you just asked "what it means" and it talks about that slightly. You never really explained what you meant by that though and it's hard to read your mind. You don't seem interested in understanding what test statistics are actually used for so I figured I'd provide a link that gives some details and you might be able to answer some questions yourself since it wasn't clear to me exactly what you wanted.

#### Magnetar

##### New Member
You know sorry but I will not read your answer now since I've found the basic answer I needed, sure it would be very interesting 2 hours ago, you could have done it before instead of posting some short meaningless answers and riding a high horse - THAT'S RUDE by me

#### trinker

##### ggplot2orBust
I agree Dason is rude. Finally someone who's reasonable and sees through Dason.

#### noetsi

##### No cake for spunky
I agree Dason is rude. Finally someone who's reasonable and sees through Dason.
You're just upset trinker he ate your meta analysis.