# Help : in the data normality

#### Amina

##### New Member
Hello everyone, I am facing some problems concerning my data normality of my dependent variable, my results are contradicted and I couldn't make my conclusion. Which criteria should I based for to say if the data is normally distributed or not ?

#### obh

##### Well-Known Member
Hi Amina,

What statistical method do you use?
What is the sample size?

#### Amina

##### New Member
Here are the statistical descriptions. My sample is 21 subjects.*Shapiro wilk test equals 0.016 which is bellow 0.05*both skewness and kurtosis z values indecate a normal distribution of the data since ( 0.373) and (-0.991) are ranging between (-1.96) and (+1.96)The standard deviation equals (1.01653) is more than the mean half (1.3333/2) <1.011653The histogram shows a normal curve ( normal distribution) Q-Q plots shows that the data is not normally distributed.

#### obh

##### Well-Known Member
Hi Amina.

What do you want to do with the data ...?

#### Amina

##### New Member
Hi Amina.

What do you want to do with the data ...?
I want to know if my data is normally distributed or not

#### obh

##### Well-Known Member
Hi Amina,

If the SW test shows significant results with such a small sample size and also the QQ plot say not normal, so ... not normal
But with such a small sample size even one outlier may change to non-Normal data.
So if the data looks valid you may say it doesn't distribute normally.

Usually, a normal distribution is not a target by itself, but you need it to be able to use tools that are based on the normal distribution.
For example you may use this data for t-test ...despite your results since it is reasonably symmetrical and you run the test on the average (CLT)

#### Karabiner

##### TS Contributor
Hello everyone, I am facing some problems concerning my data normality of my dependent variable,
Why do you care? In almost every statistical analysis (except the statistical test for the
Pearson correlation) normality of the dependent variable is irrelevant. It is the
distribution of the residuals (prediction errors) which might be important in some
analyses, or in case of the t test the distribution within each group. But usually only if
sample size is small. If sample size is large enough (n > 30 or so) most analyses are
robust against non-normal residuals. You should have answered obh's question for
which actual purpose you need to know whether the variables are distributed normally
in the population.

With kind regards

Karabiner

#### Amina

##### New Member
Hi Amina,

If the SW test shows significant results with such a small sample size and also the QQ plot say not normal, so ... not normal
But with such a small sample size even one outlier may change to non-Normal data.
So if the data looks valid you may say it doesn't distribute normally.

Usually, a normal distribution is not a target by itself, but you need it to be able to use tools that are based on the normal distribution.
For example you may use this data for t-test ...despite your results since it is reasonably symmetrical and you run the test on the average (CLT)
Thank you so much Sir I really appreciate it

#### Amina

##### New Member
Why do you care? In almost every statistical analysis (except the statistical test for the
Pearson correlation) normality of the dependent variable is irrelevant. It is the
distribution of the residuals (prediction errors) which might be important in some
analyses, or in case of the t test the distribution within each group. But usually only if
sample size is small. If sample size is large enough (n > 30 or so) most analyses are
robust against non-normal residuals. You should have answered obh's question for
which actual purpose you need to know whether the variables are distributed normally
in the population.

With kind regards

Karabiner
I have answered him Sir .just to know if my tests are normally distributed or not.
Thank you so much sir I really appreciate it

#### Amina

##### New Member
Why do you care? In almost every statistical analysis (except the statistical test for the
Pearson correlation) normality of the dependent variable is irrelevant. It is the
distribution of the residuals (prediction errors) which might be important in some
analyses, or in case of the t test the distribution within each group. But usually only if
sample size is small. If sample size is large enough (n > 30 or so) most analyses are
robust against non-normal residuals. You should have answered obh's question for
which actual purpose you need to know whether the variables are distributed normally
in the population.

With kind regards

Karabiner
Sir, I am calculating the data normality in order to calculate the correlation (Pearson's) for my two variables the independent and the dependent

#### Karabiner

##### TS Contributor
With such a small sample size, have you perhaps considered using Spearman's rho instead
of Pearson. It does not represent linear relationships but rather monmotonous relationships,
but it is independent of distributional assumptions.

With kind regards

Karabiner

#### Amina

##### New Member
With such a small sample size, have you perhaps considered using Spearman's rho instead
of Pearson. It does not represent linear relationships but rather monmotonous relationships,
but it is independent of distributional assumptions.

With kind regards

Karabiner
I concluded that there is no relationship between my two variables it equals: 0.058

#### Karabiner

##### TS Contributor
I concluded that there is no relationship between my two variables it equals: 0.058
Is 0.058 the sample coefficient for rho, or is it the p-value associated with your coefficient?

With kind regards

Karabiner

#### Amina

##### New Member
0.058 is the value of Pearson's correlation between my two variables. It's near to zero and far from one so I concluded that there is no relationship.Sir, I really want to show you some documents but they are too large to be put here.

#### Karabiner

##### TS Contributor
Yes, 0.058 is a nearly zero relationship in the sample.

#### Amina

##### New Member
Yes, Sir thank you so much for your help I really appreciate it
Kind regards.