The skewness for a normal distribution is zero and the kurtosis for a standard normal distribution is three

@Samah Abo-El-Hadid: Usually I got skewness from 0-0.9 and kurtosis from 1-2, is it valid to run One Way ANOVA?

In fact, several kurtosis values ​​may indicate a normal distribution.

Between 0 and 1, are expected to behave more like a standard normal

to test Normality, you can use the Kolmogorov-Smirnov Test for Samples from a population or Shapiro-Wilk test for multiple samples of populations.

@Carlos Jimenez-Gallardo : you mean that both test are requirede or just one is enough to test normality

Just one, but depends on how the sample is chosen. for example: you have 12 people with the same physical and biological characteristics (approximate), but 6 of them apply them to a control treatment and other experimental treatment you apply, consider that the sample is selected from a population. Test then applied to a sample Kolmogorov Smirnov (KS of a sample in SPSS).

if you, your escojes a group of subjects with a biological characteristic "a", another with "b" and another with "c", and give them all the same treatment, the difference is in the subjects to be extracted from populations a, b, c (Shapiro Wilk test). It was understood?

I can understand from you explanation:

Kolmogorov Smirnov is suitable to use before we run paired or idenpendent t-test.

Shapiro Wilk test is suitbale to use before we run One way ANOVA and similar test

Has nothing to do with the test. Is a tool for analyzing probability distribution. Therefore it is independent of the test.

are used under different selection of replications

Abdualrahman, Just write in SAS System the following Code:

Proc Univariate NORMAL;

Var Y;

run;

This code will provide 5 tests of normality including SW and KS. Just verify the significance and go to your analysis. But, if your data set contain more than 1000 observation. The probability that it follows a Normal distribution is high.

thanks Thiago da Cunha. You mention that the data should contain 1000 observation. In fact, my data is small. I have groups of animals (50 rats in each group), and I want to examine if there is a sig difference in blood pressure, glucose, lipid , etc between these groups.

The statistical tests K-S for sample drawn from one population and Wilk-Shapiro are valid for any sample size. Like most statistical tests they are about the probability of the sample coming from a population, so if it does not reject it means you can assume normal distribution, if you reject you can't. About kurtosis, when I was trained kurtosis of 3 meant normal. Typically, now, the kurtosis figure reported has an expected value of 0 for normal. I also think you should look at a normal probability plot. I also do a histogram and a box plot when assessing normality. Bob

The problem is that the test is valid for show. is quite possible that a proven method normally but not with another test .. be careful.

and proposed by Robert, I fully share, p and q plot are valid alternatives.

Can you to explain your experiment?, indicating their independent (or fact) and dependent variables

1- I have two groups of animals (50 rats each) and I want to assess if there is any significant difference in their blood glucose level, LDL, HDL, ....

2- I have four groups of animals (20 rats each). Three groups received a treatment at different doses and one group was considered as a control group. The blood glucose, LDL and HDL were measured. I want to assess if there is a sig difference between the treated rats and the control groups. Also, I want to assess whether there is a sig diff between the treated groups by different doses.

Do I need normality test before I use ANOVA or t-test.

It would be really good practice to check, because the assumptions of your test, which lead to the p-values in the end are that your samples come from populations with normal distributions. One of the things I like about SYSTAT (www.systat.com), the package I use for all my basic stats, is that you can elect to turn on "quick graphs," which spits out default graph from most statistics that you run, which are usually quite helpful in giving a sense of whether your data comply with assumptions or not. It's easy to ignore such stuff, but in cases of real violation of assumptions, the conclusions can definitely be misleading. In the case of small samples things can go very wrong. If you are curious you can have a look at StatXact. I believe you will find some examples there. Bob

steps

1. apply the KS test (nonparametric test) for a sample

2. apply the Levene test for homoscedasticity analysis (this is used to decide the ANOVA post hoc test, in the homoscedastic if the test can be, Tukey, Scheffe, Bonferroni, SNK, LSD, in the case of heteroscedasticity, apply Dunnet T3 or Games Howell)

Abdualrahman! First of all lets verify your situation. Well, one of the assumptions of ANOVA is that Y has to be Normally distributed. If the Y values are not normally distributed, the confidence intervals and the significance tests will be inaccurate.

Then, before run any analysis, you should run a normal test of Y. In your case you have two Y's (Y1=LDL and Y2=HDL).

For that run the following SAS code (if you have a SAS System):

PROC UNIVARIATE NORMAL;

VAR Y1 Y2;

RUN;

QUIT;

Verify the Shapiro-Wilk significance test. If Y1 and Y2 follow a normal distribution the p-value will show a value greater than 0.05.

Next run the ANOVA using the following SAS cod:

PROC GLM;

CLASS GROUP;

MODEL Y1=GROUP;

MODEL Y2=GROUP;

RUN;

QUIT;

The variable GROUP has a discrete value to define which group are the animals.

To run the other ANOVA follow the SAS code:

PROC GLM;

CLASS TREATMENT;

MODEL Y1=TREATMENT / SS3;

MODEL Y2=TREATMENT / SS3;

RUN;

QUIT;

The variable of class TREATMENT are the dosis cluster.

If you have some doubts send me a mail.

Best regards.

Many thanks Thiago da Cunha... you gave me a nice explanation...I would be very grateful if you cont your explanation by adding more information on what to do if Y doesn't follow normal distribution.

Your major options are to use nonparametric tests that don't assume normal distributions, and to attempt to transform your variables to a normal distributions, typically these are such things as taking the natural log of the variable and so on (a taxonomy of the transformations is sometimes referred to as "Tukey's ladder of transformations" or "Tukey's transformation ladder"). For commonly used variables that are characteristically non-normall, such as household income, there is often a common transformation, such as natural log. For a small sample where there has been little work done with similar samples/populations, I would tend more toward nonparametric statistics than transformations.

careful, Shapiro-Wilk test, is recommended for sample size less than 50.

the recommendation from the literature to biological cases (involving human beings for the application of its results), advises restricting alpha. and not use the default or "popular" 0.05

To have normal distribution , you should have a bell shaped graph besides using continuous data