Dear Samihah,

Yes, you should generally test for normality before running an ANOVA, although it may still be possible to run it even if the data appears to be non-normal. Have a look at our worksheets:

https://www.researchgate.net/publication/274635267_One-Way_Analysis_of_Variance_ANOVA

https://www.researchgate.net/publication/274635464_One-Way_ANOVA_-_Additional_Material

Technical Report One-Way Analysis of Variance (ANOVA)

Technical Report One-Way ANOVA – Additional Material

Dear Peter,

Thank you for answers. I'm using prism software for data analysis. Why prism stated that my data which are three replicates (5 groups) are small for normality test?

The statistical power will be low when the number of observations is small. You could consider using a rank based analysis of variance in addition to the standard analysis of variance F test based on the raw data. If the results look similar, go with the F test. If they differ greatly, go with the rank based ANOVA.

Dear Raid Amin,

Did you mean the analysis can be done by the prism too? It would be helpful if you can show on how to do the rank based analysis. 

Does Prism have the Kruskal-Wallis test?

Yes, Prism have it.

How many concentrations do you have?

I do not agree with Peter:

Testing assumptions of tests is logically flawed and causes many problems. Normality tests are not invented to declare data as suited for other tests that assume a normal distribution. If you take such a test serious and you find that its result is "not significant", then you should conclude only that it is still unclear whether or not the assumption (e.g. normal distribution) is met. Logically, this is *no* reason to believe that it would be ok to use the data; this would be like "accepting the null hypothesis" - what is *not* allowed. So the only "useful" result such a test of assumptions can give you is that the data shows some "significant" deviation from the assumptions. Unfortunately, this finding is by per se not an indication that the data would be unsuited for the test, because the kind and the strength of violation of the assumption  can be negligible or even completely irrelevant for the test. So: no matter what the normality-test says: it is not useful to solve your problem.

The only solution is to understand your data and wisely argue about the (non-)sensibility of the assumptions. I know that this is often not easy, and often we do not really know much about the data (what is bad! Here we must invest work! As scientists we must have or aquire a thorough understanding of our data). Some firt aid is to visualize the data and eye-ball if there are striking reasons to discredit an assumption. Normality can be checked visually quite well using normal-quantile-quantile plots of the residuals (not of the data! - so you use all the data of the whole experiment and not only 3 values, separately for each group). I am quite sure that Prism can't do that. But there are many free web-tools that can do this, and it is even possible to do it in Excel (although this is a cumbersome pain in the neck!).

I also do not agree with Raid:

Firstly, rank-based tests test different hypotheses, and you should be clear what hypothesis you actually want to test. It doe not make much sense to perform some kind of test just becuse the "data would fit" to that test, but not to another. If I had to test the function of light bulbs and I recognize that the light intensity can't be measured with a weighing machine, would it make sense then to weigh them and conclude their functionality because of their weight?!

Secondly, rank.based tests use less information from the data, and therefore small sample sizes are particularily more problematic in rank-based tests!

Thirdly, analyzing ranks instead of quantitative values with ANOVA does not hold (i.e.: exceeds) the nominal false-positive rate, escpecially with low sample sizes.

We don't have to agree on our opinions on the usefulness of rank based tests, Jochen. It is good that there are different opinions and options available to us all. I prefer using rank based statistical tests. 

Dear Jochen,

There are almost same method used in biological research; assumption that data is normally distributed.   If this method is reliable, I would like to know if there is any justification for it. Thanks for your explanation. 

Dear Raid Amin,

I'm appreciate your opinions regarding this. Definitely, there are lots of choices to do statistical analysis.

Dear Samihah, what do you refer to?

The assumption of normality is not a reasearch question - it is a mathematical fact on which the most common statistical tests operate.* It is about a probability model of a random variable and not about the frequency distribution of data. When the shape of the frequency distribution of the data is *similar* (more or less) to the shape of the probability model of a random variable describing the data, then alpha and beta of a hypothesis test can be interpreted as the expected (approximate) frequencies of type-I and -II errors. Otherwise, such an interpretation is not justified.

* a simple example: you may know that velocity (speed) is defined as the ratio of distance and the time needed to move that distance (keep it simple: classical mechanics, not relativistic). If you give a velocity of something, then you assume that there is non-zero time period in which this something could move. For time periods of length zero, the velocity is not defined. The "non-zeroness" of the time period is a simply assumption underlying the concept of velocity. For a particular problem this assumption is either sensible or not.