Hi- in every experiment you can use of Anova or proc GLM, if your date is normal., after testing your normality if your data were not normal or you cant make normal your data (Log- arc sin or ...) you have to use of non-paramatric methods such as Kruskal Wallis.

Best wishes,

Mehdi

If your data are normally distributed then use One-Way Anova. If your data are not normally distributed then use Kruskal Wallis test. 

I agree - for normally distributed data one way Anova, otherwise Kruskal Wallis -  with dunn's post hoc test

Hi

Selection one way ANOVA or KW ANOVA depends on two things - sample size andnormality of distribution.  Your one group has only 10 n. Now you should first test the normalcy of distribution and if the data is normally distributed then go for one way ANOVA otherwise use KW ANOVA. 

Hi! The dicision of using an ANOVA or Kruskal-Wallis test is the distribution of data.

Normal / gaussian distribution should be analysed with ANOVA while a non-normal / non-gaussian distribution should be analysed with the Kruskal-Wallis. So it depends on your data, not on the number of groups (since you seem to consider to have just one independent variable).

As previously mentioned, you can run a  normality test like the D'Agostino Pearson (do not use Kolgomorov-Smirnov), BUT do not make decisions based on that test alone. Please read the link for more information on why! - great guide for biologists and biochemists by the way.

Note that parametric tests (for normal distributions) have more power than non-parametric tests (for non-normal distributions) - among other advantages and disadvantages. So even if your distribution is not gaussian, and all groups have the same profile of distribution, you can try to transform the data into gaussian. If nothing works, go ahead with the non-parametric test (Kruskal-Wallis). It's also a good idea to look at papers in your field with similar measurements to evaluate what is the standard analyses.

Good luck!

p.s.: Yogyakarta is a great place to visit, by the way!

http://www.graphpad.com/guides/prism/6/statistics/index.htm?stat_how_normality_tests_work.htm

Thank you very much everyone for your answers. I really appreciate it.

I have just done normality test by using Shapiro-Wilk test and the data distribution is normal.  Thank you

By the way, I'd like to do a D'agostino-Pearson test just to confirm. I searched on the internet, but i couldn't find a way how to conduct the test in SPSS. Do we have to do the test manually or is there a way in SPSS that it can be conducted? Thank you again 

I usually use Graphpad, although it´s paid. Download the free trial and you'll be able to do it.

Same thing with independent t test, if the sample has normal distribution you can used independent t test, if not you will use Mann Whitney test

First normality test should be performed. Is the data is normally distributed proceed for one way ANOVA followed by post hoc group comparisons by Newman Keuls test or Tucky's test. If the data us not normally distributed then proceed for Kruskal Wallis followed by Mann Whitney U -test for post hoc group comparisons. 

Dear everyone, my date is not normally distribuited and I run test (single factor ANOVA.)

but I don't know how I can use  non-parametric test (Kruskal-Wallis)?

The test you need to apply depends on your data. I recommend to follow the guidance given by Nuno J Machado.

First try to identify the distribution of the data set (normal, exponential etc.). Then based on the distribution of the data set decide the method of analysis. I would rrecommend General Linear Model over ANOVA due to its capability of indepth analysis of the interactions between parameters.

5 assumptions for Kruskal Wallis one-way ANOVA (Non-parametric ANOVA)

1. Independent variables are categorical variables ( more than 2 levels)

2. Dependent variables is continue variable.

3. Independence assumption = ok

4. Normality assumption = violation

5. Equality of variance assumption= violation

cheers,

To use a statistical distribution (t, F, chisquare, normal) to calculate Type I error (the p-value) we need to make assumptions. The statistical literature warns against statistical tests to evaluate assumptions and advocates graphical tools (Montgomery & Peck 1992; Draper & Smith 1998, Quinn & Keough 2002). See also (Chatfield 1998; Gelman, Pasarica & Dodhia 2002). La¨a¨ ra¨ (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).

Chatfield, C. (1998) Problem Solving: A Statistician’s Guide. Chapman & Hall, Boca Raton, FL

Draper, N.R. & Smith, H. (1998) Applied Regression Analysis, 3rd edn. John Wiley and Sons, New York

Gelman, A., Pasarica, C. & Dodhia, R. (2002) Let’s practice what we preach: turning tables into graphs in statistic research. The American Statistician, 56, 121–130.

La¨a¨ra¨, E. (2009) Statistics: reasoning on uncertainty, and the insignificance of testing null. Annales Zoologici Fennici, 46, 138–157.

Montgomery, D.C. & Peck, E.A. (1992) Introduction to Linear Regression Analysis. Wiley, New York.

Quinn, G.P. & Keough, M.J. (2002) Experimental Design and Data Analysis for Biologists. Cambridge University Press, Cambridge, UK

Zuur et al 2010 Methods in Ecology & Evolution 1: 3–14

What tests do you use to see if the data is normally distributed or not?

This query, now 3 years old, keeps popping up. So let's get back to the query:

One-Way ANOVA or Kruskal Wallis, which one should I use?

It is often assumed that non-parametric tests (e.g. Kruskal-Wallis) compare means. They don't. They don't even compare medians. So that is a good reason to prefer ANOVA.

ANOVA assumes homogeneous, normal, independent errors. It is often believed we check this *before* analysis. The assumption applies to the errors, so we can only check the assumptions after estimating the means and computing the errors. Graphical displays are preferable to using p-values to check assumptions. If the errors are *substantially* heterogeneous or *substantially* non- normal then the next step is a randomization test on the data. This is preferable to doing a randomization tests on ranks (I.e. Kruskal-Wallis). With ranks we lose information.

It is technically incorrect to do both. Once you have computed the p-value for one of them, the Type I error is no longer 5% on the 2nd test. This is called "data-peeking" except of course that it is not intentional.

Bottom line. Try the ANOVA and check the residuals. If residuals are *substantially* non-homogeneous or non-normal (outliers, etc) then do a randomization test on the data, not on the ranks (Kruskal-Wallis). If you don't know how to do a randomization test on the data, a search on "how to do a randomization test" will produce many helpful videos.

~David S

Nuno J Machado Thanks for your detailed answer, I learned a lot. Thanks!

David C Schneider This is the explanation I was looking for. Thank you! Could you please share a reference for this?

Hi! From what I have been reading lately, before applying ANOVA, you will have to test for normality and equal variance assumptions. To test for normality, Shapiro-Wilk test (along with skweness, kurtosis, Q-Q plots, boxplots and histograms) can be used and for equality of variances, Levene's test can be used. Several studies have shown that ANOVA can be applied even in case of non-normality and that the results remain robust, but not so in case equality of variance assumption is violated. In that case, either the Brown-Forsythe or Welch ANOVA can be used. Studies mostly show that Welch ANOVA is a better test.

As to choosing between ANOVA and Kruskal Wallis, parametric tests hold more power than non-parametric ones. Since Kruskal Wallis uses ranks of values instead of actual values from data, it loses some power there. However, if you opt for Kruskal-Wallis anyhow, post-hoc tests can be applied even then. The following YouTube link might be of some help in case you're using SPSS:

https://www.youtube.com/watch?v=YB5Eza6j-Lo&list=PLETgLGt3zDDieOwDc8ECS25qxEiC6f8l4&index=9&t=0s

I've read all the answers mentioned above. They are very helpful. I would like to look at this from a different perspective. Let's assume that in our study the data would not be normally distributed and there would be two independent variables, one within-subjects (time) and one between-subjects (treatment) . In this scenario, if you had to perform an analysis of variance between means, what steps would you take next?

Hello Gökhan

If I wanted to compare means I would never use Kruskal Wallis. It does not even test medians, let alone means. If you have the same time measurements across treatments and subjects I would write an ANOVA with Tr, Time, & Subj. Subject is usually taken as random. Tr is Fixed. Time is Fixed if you are interested in looking at trends. The Tr x Time term gets tested over the 3 ways term (Subj(Tr x Time)). The fixed terms get tested over the correct mixed terms: Tr tested against Subj(Tr). If you are using SPSS, that package will form the F-ratios correctly.

You can find examples of your design in textbooks on experimental design. Quinn and Keough is a good reference.

I would never check assumptions on the data, before obtaining the residuals. Checking before obtaining the residuals is a widely held misconception. It is like taking rabies shots before being bitten. If the residuals do not meet the assumptions I would use the same design, but then use randomization to obtain the p-value. If you do this you will usually find that violations don't affect the p-value very much. This is especially true if you have an adequate sample size.

I would never use a statistical test of assumptions on the data before obtaining the residuals (see above). Statistical tests of assumptions on the residuals have low power for small sample sizes (high Type II error). So they are not a good idea for small sample sizes, where violations matter. They detect unimportant violations with large sample sizes. So they are not a good idea for large sample sizes. That sounds complicated! It is. A simple solution is take measurements in duplicate or triplicate, take the mean across the duplates or triplicates, and use the mean. This often produces a well behaved variable that is normally and homogeneously distributed with respect to the parameters (ie, normal residuals).

Good luck,

David S

Dear Dr. David C. Schneider,

Thank you for your reply. It's been quite helpful. I understand that treatment and time are both fixed factors. In the experiments, we'll use adult male rats, which will be born very similar (genotype). The rats which will be housed in the same box during the experimental sessions will also have grown up among the same litter during their developmental period. They'll have very similar ages. That being said, they may have different weight. Sample size in each group will be very similar to each one (n=8-10). Given all this taken into account, since we can consider these adult rats as identical to each others, we think that we shouldn't define the 'subject' as a random factor. Besides that, even if we define it that way, we don't know how we are supposed to see the possible effects of the subject factor in our behavioral experiments (rota-rod, activity cage, water maze, etc.).

As to measurements in duplicate or triplicate, we don't know how to perform a behavioral test evaluating learning such as water maze or object recognition more than once, because for each time we take measurement, we may see the animal learn the test and do it even better than the initial trials. So, if we take the mean of three different measurements for a subject at a single time and use it, then I suspect if there may be flawed data in that subject's favor.

You said that obtaining residuals should come first. I would like to learn how to check if the residuals meet the assumptions. You said if they don't, we could perform a randomization test to obtain the p-value, and in general the p-value doesn't get effected by violations for larger sample size. However, our sample size (8-10 per group) is not large. You said that statistical approaches on residuals may not work well due to limited sample size. So, what would you suggest me ?

Kind regards,

Gökhan,

hi,

according to youre data distrubtion that is normal or not!, you can use diffrent tests.

Nuno J Machado thanks for your nice answer.

@Nausheen Sodhi

It is widely believed and frequently posted online that we test for normality before choosing a test. This leads us astray (as described above). It is not correct. For references see an earlier post by me in this thread, 9 April 2018. I recommend that readers of this thread check out the references. In particular I recommend the publication by

La¨a¨ra¨, E. (2009) Statistics: reasoning on uncertainty, and the insignificance of testing null. Annales Zoologici Fennici, 46, 138–157

Answers contrary to this and the other publications posted earlier in this thread show up in ResearchGate, sometimes near the top as popular. When frequent testimony online conflicts with consistent advice in the refereed literature, what are we to believe? I leave the decision to you.

Suum quique,

David S.

Dear Gökhan Gökhaner

In your reply you provided a series of explanations and posed further questions. I'd like to address four topics: control for body size, subject as random, means from duplicates or triplicates, checking the assumptions by examining residuals.

1. Body size, You can include this as a covariate in your model. If variance due to body size is substantial, removing the variance due to body size will improve the analysis (increase in statistical power and so better able to detect treatment differences).

2. Subject as random. The standard approach, widely used in the literature and central to experimental design, is to treat units such as rats, cages, quadrats, etc as random factors. The principal reason is that this will improve the analysis (better able to detect treatment differences) by increasing the statistical power of the test. A second reason is that we are usually not interested in the differences in means among these units. A third reason is that with random factors we are inferring beyond our particular set of units--the cages, quadrats, etc we use. So our results can be taken as applicable beyond the units we used.

3. Means from duplicate or triplicate are defensible for physical units (cages, quadrats, etc). They become less defensible for organisms, where repeated measurements of a single unit are not necessarily independent -- organisms learn, etc. So not applicable, I think, to your situation.

4. Graphical analyses of residuals. This strays from the current thread, which was posted in 2015 to the question: One-Way ANOVA or Kruskal Wallis, which one should I use? There's lots of good advice in the references that I posted earlier in this thread, where I noted that the statistical literature warns against statistical tests to evaluate assumptions and advocates graphical tools (Montgomery & Peck 1992; Draper & Smith 1998, Quinn & Keough 2002). See also (Chatfield 1998; Gelman, Pasarica & Dodhia 2002).

For each of the topics, you could follow up by posing a question on the topic in RGate to get advice beyond just mine.

Yours in getting it right,

David Schneider

Thank you for your reply, Dear David C Schneider and Dear Mehrab Atighi

First, I think I would follow the obtaining residuals approach. I would like to read the very information in the references Dear David C Schneider posted, and as far as I understand from the detailed explanations given by him, there'll be issues when directly evaluating the assumptions by using statistical tests.

Based on your statements, I consider I could assign 'Rat' as a subject factor. But, I don't understand why a rat should be assigned as a random factor despite the randomness we created by randomly assigning the animals into the cages .

Thanks for advice on units. I'll not take measurements in duplicate or triplicate, because, as you've said, a rat as a unit is an organism which can learn. So, when all the information and advice you gave, which are so precious to me, taken into account, I come to the conclusion: I'm not sure if I assign the 'subject' as a random factor. Nevertheless, I know the time and treatment will be both fixed factors. I think I won't add a covariate to the design, and after test runs completed, first of all, I'll check the residuals even if the sampling size is small (10 for each group, 4 groups). If the residuals meet the assumptions, I would use ANOVA. If not, I would perform same method, and then do a randomization test.

Thank you again, Dear David C Schneider

Note, as you suggest, I've posted some questions about mixed model ANOVA and two-way ANOVA before. However, I have not received any answers or suggestions yet.

Kind regards,

Gökhan Gökhaner

Hello Gökhan,

You asked about reasons for treating subject as a random factor. I am going to suggest that the question show up in a thread devoted to that topic. It is a fairly well read thread (6.6K reads). I have no idea how to paste a link to it. However, if you go to questions and paste the following, the thread should show up.

May 2018 Bruno Pinho How to define fixed and random factors in a linear mixed model?

Make sure it is the question posedby Bruno Pinho. Once you find it, pose your question there. Because I was one among several people who replied, I should get a notification to which I can write a reply, which will have to do with forming F-ratios where it is your intention that subjects be random. The thread has r code for mixed models, in case you don't have access to Minitab, SPSS, SAS, or other packages with less steep learning curves than r.

With kind regards,

David S

Thank you again. It's been quite helpful. I appreciate that, Dr David C Schneider

I'll post my question there. The issues raised in the thread are similar to my case. I,too, will try to define two fixed factors and maybe a random factor (subject as rats) for mixed ANOVA. I've been reading this thread since you've mentioned. It includes R codes, as you've already said. So, I'll keep following it. Thank you for your time.

Kind regards,

Gökhan Gökhaner

wich test is avaible to analysis mortality rate data in insecticidal experments? is probit analysis enough? thanks

Hello Abdelkader Harizia,

You will need to provide more information about your response variable.

It appears you are looking at a binomial variable - number living out of a number exposed, at different exposures or conditions. But perhaps it is time to mortality, not ndead/ntotal. Or perhaps the resonse variable something else.

In general, KW test is a last resort -- all you get is a p-value, which is not a measure of evidence. The KW test does not test effect size, the KW p-value does not apply to effect size, such as magnitude of the difference among treatments.

Good luck with your research,

David S

hello David C Schneider

thank you for your very much for your response. in the tests insect were expose to various concentrations and mortality was recorded across time exposures. for the time-mortality I applied survival analysis usine a kaplan meir and rank test,the results were significative. As the mortality rate is an anormaly distribution I wondered if the transformation of the data to arcsin and than make an anova follewed by a Tukey test is appropriate?. Or use the KW as you said wich is not enought....tjis last should be follewed but wich test to see the effect of the various concentrations on the mortality.

Hello Abdelkader,

Kaplan Meir produces survival curve estimates from your data. It does not display mortality rate. The log rank test tells you whether the *survival* curves overlap. There are many ways that two survival curves can fail to overlap, so this overlap test is not particularly informative (same problem with KW rank tests).

The more informative alternative to the rank test is the Cox proportional hazards test, which estimates the survival rate and then compares the rates. Stat package output should provide parameter estimates that you can report, in addition to the test statistic and p-value in comparing the curves. The parameter estimates display the effect size--how large is the difference in survival? The p-value does not tell us effect size, it is a useful addition when reporting effect size.

It is widely believed, but unfortunately untrue, that we check assumptions for parametric tests (e.g. CoxPH) before running the test. The assumptions apply to the residuals (difference between the model fitted values and the data). So we check the residuals by plotting them as a histogram (normal) or as a QQ plot (normal) and we check them by plotting the residuals against the fitted values.

Here is an article that covers the topic of checking assumptions. It has a section of software (routines in SPSS and R).

https://academic.oup.com/icvts/article/28/1/1/5053964

Here is another article, same topic, this time with SAS code.

https://stats.idre.ucla.edu/other/examples/asa2/testing-the-proportional-hazard-assumption-in-cox-models/

Bottom line: Tell the reader of your research how big the difference is (effect size), not just a p-value. Non-parametric tests based on ranks, or that compare overlap, do not test the effect size.

~David S

thanks a lot David for your help your response is very useful. thanks for the 2 articles too

It is widely believed that the Kruskal-Wallis test is a simple substitution for ANOVA. It is not. It does not compare means, so one cannot make a conclusion about means. It does not even compare medians-- no conclusion can be drawn about medians. There are better alternatives than doing a KW test. One is to do a randomization test instead of a parametric test. This can be set up to test for differences among means. Another is to use non-normal errors (e.g. gamma error) in a generalized linear model to tests for differences among means.