# (Wilcox signed tank test)

#### javedbtk

##### New Member
Hi, I want to ask about the theory/concept behind the statistical significance tests to find out the p values. For instance, I got two types of data, one has the mean value of 75 and another 86 and the test shows there is no significant difference. How it is possible? These tests test depends on what? Mean, median or what?
Regards

#### Karabiner

##### TS Contributor
Well, what did you read about statistical significance tests and p values so far?

With kind regards

Karabiner

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#### javedbtk

##### New Member
That it gives us an idea if there is a difference between the set of values or not? If we get the p-value less than 0.05, then we can say that there is a significant difference, otherwise, we can not claim it.

#### Karabiner

##### TS Contributor
The tests are about the populations from which the sample data were drawn, not about about the sample data itself.
p-values are a means to decide whether the null hypothesis (such as "in the population, the mean difference between
measurements is exactely = 0") can be rejected, based on the evidence gained from the sample data.

Maybe you should do some introductory reading about inferential statistics, tests of significance, and p-values .

With kind regards

Karabiner

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#### javedbtk

##### New Member
Thanks a lot Karabiner

But when I perform the test, it says there is no (significant) difference though there is a clear difference between the mean/average of the two set of values. I am not sure what exactly I am doing wrong?

#### Karabiner

##### TS Contributor
The sample data at hand are used to decide whether the 2 populations (from which the data were drawn)
are different. If you have a very small sample size, then it is not easy to reject the Null hypothesis, even
if the sample data show a marked difference. With small sample size, even marked differences could
still be due to mere chance.

In addition, a mean of 75 versus 86 would not really indicate a large difference in the sample, if the data
are spread out widely (i.e. if they have a large standard deviation).

With kind regards

Karabiner

#### javedbtk

##### New Member
The sample data at hand are used to decide whether the 2 populations (from which the data were drawn)
are different. If you have a very small sample size, then it is not easy to reject the Null hypothesis, even
if the sample data show a marked difference. With small sample size, even marked differences could
still be due to mere chance.

In addition, a mean of 75 versus 86 would not really indicate a large difference in the sample, if the data
are spread out widely (i.e. if they have a large standard deviation).

With kind regards

Karabiner