To choose whether a parametric or a non-parametric test should be used to compare data on viability that emerge from an assay such as MTT, one should establish if the data are normally distributed. My question concerns to which group of samples a normal distribution test should be applied.
To be more clear I try to introduce an example.
Let's say I have to make a time and dose-response curve for two substances, A and B. I'd like to test both substances at 3 different concentrations ([1], [2], and [3]) and at three different time points (24h, 48h, and 72h). For each condition, I'd like to test 6 wells of a 96 mw plate. Obviously in each of my plates (let's say one per day) 6 wells will not receive any treatment and will thus represent my reference. This means that each plate would include 6x7 = 42 wells
As I said, after three days of data collection I would like to compare the treatments to understand if at any concentration or time point my molecules influence cell viability. Before choosing either a parametric (e.g., one way ANOVA) (e.g., Kruskal Wallis) I should establish whether or not the data are normally distributed.
I suppose that what I should test for normality are only those samples belonging to a single condition (let's say the 6 wells of untreated samples of the first plate), shouldn't I? Or maybe I should consider all the untreated samples of all plates together? Or even all samples together?
Thanks in advance
You are right. Results of samples (wells) belonging to each single condition (e.g., all untreated - reference samples) should be analysed separately. In my opinion, you can test the results of the three days altogether.
After searching Google for 'normality test', I found an article by Ghaseimi and Zahedeisl at Int J Endocrinol Metab 2012 10(2) 486-489. There is also an article in Wikipedia that came up as the first item in my search. I have used the Kolmogorov Smirnov test and the Shapiro Wilk test in my own work, a long time ago. They were relatively easy to perform. I hope this helps.
A new suggestion, you might want to look up ways to analyze time series data separate from other data. Time series results, of course, can not be independent.
Sorry, that I did not notice this earlier in your question. You might be able to use ANOVA methods to test results at single time points.
Hello Gianluca,
The assumptions for the general linear model (including regression, ANOVA, and ANCOVA) are that the errors (residuals) are normal and homogeneous (Eisenhart 1947, Seber 1966, Neter et al 1983 pp 31& 49, Quinn and Keogh 2002 pp 110 & 280). Evaluation of assumptions in advanced texts, where it occurs, often entails a residual versus fit plot (for homogeneity) and a normal score plot or Quantile-Quantile plot (for normality of the residuals).
The statistical literature warns against statistical tests to evaluate assumptions and advocates graphical tools (Montgomery & Peck 1992; Draper & Smith 1998, Quinn & Keough 2002). Läärä (2009) gives several reasons for not applying preliminary tests for normality, including: most statistical techniques based on normal errors are robust against violation; for larger data sets the central limit theory implies approximate normality; for small samples the power of the tests is low; and for larger data sets the tests are sensitive to small deviations (contradicting the central limit theory). SPSS tends to promote the practice of checking the response variable instead of the residuals.
That preliminary evaluation is not correct can come as a surprise, as can advice against statistical tests to evaluate assumptions. But I think best practice, as in the literature, needs to be put out therer..
To check assumptions for residuals see:
https://www.datanovia.com/en/lessons/anova-in-r/#check-assumptions-1
Good luck with your research,
~David S
Chatfield, C. 1995. Problem Solving: A statistician's guide, Second edition (Chapman & Hall/CRC Texts in Statistical Science) 2nd Edition,
Draper, NR and H. Smith 1998 Applied Regression Analysis, 3rd Edition. Wiley
Eisenhart, C. 1947. Biometrics 3:1-21
Gelman, A C Pasarica & R. Dodhia (2002) Let's Practice What We Preach, The American Statistician, 56:2, 121-130, DOI: 10.1198/000313002317572790
Läärä, E. 2009. Statistics: reasoning on uncertainty, and the insignificance of testing null. — Ann. Zool. Fennici 46: 138–157.
Montgomery, DC EA Peck, GG Vining 2012 Introduction to Linear Regression Analysis, 5th Edition. Wiley
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