P-value is 0.05 - Normal or non-normal data?

O

Oskar_S

#21
You are correct. A p-value > 0.05 means the null hypothesis (that the distribution is normal) is accepted. A p-value < 0.05 means that the null hypothesis is rejected and the distribution is not normal.
This is what I remember from college. Maybe I´m wrong!!

Maybe of topic but a p-value < 0.05 means that the null hypothesis is rejected but it doesn´t mean that the distribution is not normal. I means that you have no statistical evidents for a normal distribution, but if you get a bigger sample it might turn into a normal distribution.
 
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#22
This is what I remember from college. Maybe I´m wrong!!

Maybe of topic but a p-value < 0.05 means that the null hypothesis is rejected but it doesn´t mean that the distribution is not normal. I means that you have no statistical evidents for a normal distribution, but if you get a bigger sample it might turn into a normal distribution.
This is not off-topic. You are correct.

If your p-value = .01, this means that you could obtain similar results from a true normal distribution ~ 1% of the time due to random chance alone. This is the meaning of alpha risk, which is 0.05 in this case.
 

bobdoering

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#23
... but if you get a bigger sample it might turn into a normal distribution.
Conversely, it may also turn into another distribution other than the normal distribution. Small samples can infer a normal distribution based on sampling error. As more samples are analyzed, the sampling error that masked the true distribution is reduced, and the true distribution - whatever it is - can become apparent.
 
E

Ehsan Heidari

#25
Hey guys!!!!
I don`t get my answer? I want to know the analysis of each graph in normality test in minitab. for example when I recieved a normality test with AD=3.164 what can I say????

Please look at attachment!
 

Attachments

B

Barbara B

#26
Hey guys!!!!
I don`t get my answer? I want to know the analysis of each graph in normality test in minitab. for example when I recieved a normality test with AD=3.164 what can I say????

Please look at attachment!
The p-value in this case maybe misleading.

Usually a p-value below 0.05 means that the null hypothesis is rejected. In a test for normality the null hypothesis is "data is normally distributed", so p<0.05 will lead to "data is not normally distributed."

But as you can see in the probability plot, there are only 7 different values in n=125 measurements total. The rejection of the null hypothesis could simply be caused by a to small resolution of your measurement system and the process itself could be normally distributed, but you can't evaluate this with this measurement process.

Before starting with a capability analysis (like you posted here) it is advisable to evaluate your measurement process. If you want to rely on numbers, you have to be sure that the information contained in the numbers is sufficient enough to describe the process behaviour.

Regards,

Barbara
 

Statistical Steven

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#27
Hey guys!!!!
I don`t get my answer? I want to know the analysis of each graph in normality test in minitab. for example when I recieved a normality test with AD=3.164 what can I say????

Please look at attachment!
What happens if you remove the largest x values? They seem to fall off the linear line. The data is probably normal but you have a tail issue. Just a quick assessment.
 

bobdoering

Stop X-bar/R Madness!!
Trusted Information Resource
#28
Hey guys!!!!
I don`t get my answer? I want to know the analysis of each graph in normality test in minitab. for example when I recieved a normality test with AD=3.164 what can I say????

Please look at attachment!
Do you have the raw data? Is this different data from before? This chart alone is not sufficient in my mind to discern normality. If it is the same data that you presented before (the C3 data), it was already shown to be clearly non-normal.
 
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E

Ehsan Heidari

#29
Thanks for your answers! But I want to know how can I analysis a probability plot like that? I want the way of analysis the probability plot.
 
B

Barbara B

#30
But I want to know how can I analysis a probability plot like that? I want the way of analysis the probability plot.
If data is normally distributed the points in the probability plot all appear near or on the ideal line (blue). The points should be linear, mainly in the middle of the values measured. A rough test for normality with probability plots is called "fat pencil test": If (nearly) all points disappear if you put a fat pencil on the ideal line, the data can be considered to be normally distributed.

When stacked points appear (like in your plot) identical values among the measurements are present in the data. A common reason for the stacks is a small resolution of your gage.

The normal distribution is a continous distribution, so there is (theoretically) only a very small probability to get identical values within 125 values total. If the process outcome is in fact normally distributed but the resolution of your gage is too small to get the differences between the parts measured, you will alway reject the assumption of a normal distribution. Therefore it is required to have a gage with appropriate resolution for the interval measured to get reliable results out of the probability plot and test for normality.

Compare the individual value plots for your measurements and random normal data as well as the probability plots for both attached and you will get a clearer picture what an ideal state is and why the assumption of normality in your data is rejected.

Regards,

Barbara
 

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