Assumptions for ANOVA

Basic Concepts

To use the ANOVA test we made the following assumptions:

  • The residuals are normally distributed
  • Group populations have a common variance
  • All samples are drawn independently of each other
  • Within each sample, the observations are sampled randomly and independently of each other
  • Factor effects are additive

The presence of outliers can also cause problems. In addition, we need to make sure that the F statistic is well behaved. In particular, the F statistic is relatively robust to violations of normality provided:

  • The populations are symmetrical and uni-modal.
  • The sample sizes for the groups are equal and greater than 10

Priorities

In general, as long as the sample sizes are equal (called a balanced model) and sufficiently large, the normality assumption can be violated provided the samples are symmetrical or at least similar in shape (e.g. all are negatively skewed).

The F statistic is not so robust to violations of homogeneity of variances. A rule of thumb for balanced models is that if the ratio of the largest variance to smallest variance is less than 3 or 4, the F-test will be valid. If the sample sizes are unequal then smaller differences in variances can invalidate the F-test. Much more attention needs to be paid to unequal variances than to non-normality of data.

Further Information

We now look at how to test for violations of these assumptions and how to deal with any violations when they occur.

Reference

Howell, D. C. (2010) Statistical methods for psychology (7th ed.). Wadsworth, Cengage Learning.
https://labs.la.utexas.edu/gilden/files/2016/05/Statistics-Text.pdf

175 thoughts on “Assumptions for ANOVA”

  1. Hi, i want to ask question for my examination. How to determine if a data set that have been collected from an experiment meets the ANOVA assumption?

    Reply

  2. Dear sir,
    In my research work Im considering PEG concentration (14-22, %w/w), salt concentration(12-20, %w/w) , Nacl addition (1-5, %w/w) and pH (5-9)as independent variables and extraction efficiency (%) of a protein as a dependent variable. All these variables seems to be continuous variables. But I have fixed the each independent variable concentration range to be analysed. I read that ANOVA can be appled only for categorical independent variables. For this type of data can I go for one way ANOVA with Tukey’s test ?

    Reply

  3. Hi Charles,

    As part of my dissertation, I conducted a study testing the effectiveness of an intervention (assessing participants at pre- and post- intervention) on 123 participants assigned to 3 conditions (2 intervention group and a control group). I have 40 , 41, and 42 participants in each condition respectively. Levene’s test value is significant for some of the variables, so I was wondering whether my sample is big enough and group sizes equal to say that the assumption of normality has not been violated?

    Thank you in advance for the help!

    Silvia

    Reply

    • Silvia,
      If I understand correctly, you have one fixed factor Condition with 3 levels and one repeated measures factor Time (before and after). Thus, you need to use Levene’s test to check whether the 3 groups have similar variances. where each group consists of the difference in the values (after minus before). Lack of homogeneity of variance is a concern especially with unequal samples (although
      It is likely that the central limit theorem holds re normality, but you should check just to be sure.
      Charles

      Reply

      • Hi Charles,

        Thank you for the super quick response!

        That’s correct, we have condition and year group (2 levels) as fixed factors, and time as within-subjects factor.
        Field (2013) said that according to the central limit theorem data is normally distributed if the sample is large enough. He said that in light-tailed distributions an N as small as 20 can be ‘large enough’, and in heavy-tailed distributions up to 100 or even 160 might be necessary. Our distribution does not have a lot of skew and kurtosis (we only had to transform one variable because it was negatively skewed), would you say that it is fine to disregard Levine’s and assume our data is normally distributed?

        Reply

        • Silvia,
          It is likely that your data is normally distributed, but Levene’s test doesn’t test for normality; it tests for homogeneity of variances which is a lot more important.
          Charles

          Reply

  4. Hi,
    What is the minimum required sample size of each group for a three groups ANOVA test? Is it required to always have same sample size for all the groups?

    Reply

  5. Hi, I just want to ask you if you could give me real research examples (events) that violate the independence assumptions. I have a problem of explaining convincingly with real examples.

    Reply

    • Kibrom,
      It would be difficult to give a real example, since no researcher would knowingly violate this assumption, so let me give you a made-up example.
      Suppose you are comparing the whitening capabilities of three types of toothpaste, and so create a sample consisting of 20 people for toothpaste A, 20 people for toothpaste B and 20 people for toothpaste C. If you started with 60 people and randomly assigned 20 people to each type of toothpaste, this would be a perfectly appropriate approach. If, however, one person got sick before the study started and had to drop out, and so you placed John Smith (one of the remaining 59 people) in both the toothpaste A sample (where he was randomly assigned) and also in group C (where the person who dropped out was assigned), then you would violate the independence assumption.
      Charles

      Reply

  6. Hi, I am currently writing my dissertation and need help with assumptions of normality.
    To give you a bit of detail, I ran a one-way anova

    My IV was Diet (consisting of omni, vegetarian, vegan groups)
    DV- Scores from PHQ-9, HADs (HADs was split into the items that measure anxiety and depression)
    – so three separate DV’s
    My test violated the assumption of homogeneity, so I ran an alternate test to report the results (Brown Forsyth). That’s all sorted now.

    However, my results have also violated normality.

    For the PHQ-9:
    omni – .004
    vegetarian – .008
    vegan – .001

    HADs anxiety:
    omni – .21
    vegetarian – .39
    vegan – .001

    HADs depression:
    omni – .003
    vegetarian – .12
    vegan – .000

    How do i report this in the results section of my dissertation?

    Reply

    • Lucy,
      1. With three dependent variables, MANOVA might be a better choice.
      2. When the homogeneity of variances assumption is violated (for ANOVA), Welch’s ANOVA is usually a better choice than Brown-Forsythe, although this may not be the case if normality is also violated. ANOVA (and perhaps also Welch’s ANOVA) are pretty robust to violations of normality especially if the data is reasonably symmetric.
      3. You should report your results just as you would for ANOVA, but you should also report that normality and homogeneity of variances was violated (and give the test results for these).
      Charles

      Reply

    • Ibrahim,
      It is pretty easy to create data which violates one of the assumption. Try it yourself. The usual problems are homogeneity of variances and normality.
      Charles

      Reply

    • Hi
      Does anyone know of an academic reference or text for the above comment, “normality assumption can be violated provided the samples are symmetrical or at least similar in shape”. I’ve hunted for hours.
      All my 4 groups are negatively skewed so I wanted to justify doing a 2 x 2 ANOVA for a dissertation (even though several assumptions are violated – using Levine’s test, skewness z scores & Shapiro-Wilks).

      Reply

    • Joana,
      Yes, the interactions need to be additive as well. This just means that the error terms need to have zero mean. I wouldn’t worry about this assumption and wouldn’t explicitly test for it.
      Charles

      Reply

  13. Hi,
    Can you please explain why the standard deviation of a measurement is not used in a Design of Experiments and thus only the averages are used in the ANOVA of the DOE?

    Very nice post!

    Reply

    • Manuel,
      ANOVA and DOE focus on detecting differences in the means (averages) between various groups. This is because the mean tends to be the more relevant statistics in many experiments. There are tools that do compare the standard deviation, such as Levene’s test. Note too that the standard deviation is used in DOE and ANOVA, but the objective of these tools is to compare means.
      Charles

      Reply

  15. Hi sir,

    my survey questions are based on five-likert scale and the distribution are never normal. but based on central limit theorem i have sample size more than 30, which means my sample mean is normally distributed.
    i have used t-test and ANOVA to perform the analysis. am i correct?

    Reply

    • Cheng,
      Without getting into all the details of the central limit theorem (esp. the fact that you need a continuous set of values), it is best to check that your data is really normally distributed by using a test like Shapiro-Wilk. Since your data will have a lot of tied values, in your case, it is better to use the d’Agostino-Pearson test for normality.
      If the data is at least symmetric the t test and ANOVA will perform pretty well even if the data are not normally distributed. In general, a 9-likert scale will perform better than a 7-likert scale (more like a continuous function) and a 7-likert scale will perform better than a 5-likert scale.
      Charles

      Reply

  16. I Have Scatter Data between (Y,X). I need to fit (Nonlinear Regression) between them. how I can read the interpretation of regression results. In other words, if the t-test of the Coefficient is significant, is it enough for my null hypothesis. And what is about the F-test in the Nonlinear Regression??!!! is it necessary or not.!??.

    Reply

  17. hi charlie,
    I read that anova is rhobust with violations of homogenity if the number of subject in grups are aproximately equal…what do u think?

    Reply

  18. Sir, I have a question.

    I am running a series of one-way ANOVA in a 3-group comparison.
    All groups are with sample size > 300, but are in unbalanced condition (eg. 300, 500, 600, or let say the ration is always around 1:1.5:2). Levene tests are significant in some comparisons (let’s say p<0.01), but i note that the ratios of largest: smallest variance are very small (eg. largest SD: smallest SD = 1:0.8). Could I say if ANOVA is still robust in this conditions even if it violates the the assumption of equal variance?

    or am i supposed to employ Welch's test?

    Thanks

    Reply

    • Hin Yan,
      Anova is not that robust to violations of equal variance, especially with unbalanced models. Welch’s Anova (or resampling) is probably a better choice.
      Charles

      Reply

    • I need an answer to this question and how they got the answer.
      Which of the following is NOT an assumption of the one-way randomized ANOVA?
      a. the data are interval or ratio
      b. the underlying distribution is skewed
      c. the variance among the populations being compared are homogeneous
      d. all of the alternatives are correct.
      Thank You, Pauline.

      Reply

  19. Hi Charles,

    I have a question related to repeated-measures ANOVA, basically I had a sample of 8 participants that were tested on three different conditions. I did get a significant result, is this valid?

    Reply

  20. I have some repeated measurements for the same sample at 4 time points and I want to test if the difference between their means is significant. The assumption of independent measurements is violated. How can I resolve this? What do you suggest?

    Reply

  21. Hi Charles,

    Forgive me if I have this confused, but I believe that you have made a mistake in stating that an assumption of ANOVA is that “Each group sample is drawn from a normally distributed population”. The link that you provided for correcting for this assumption encourages identifying this violation by plotting histograms. This link further says that the non-normality may be fixed by transformations of the response variable. I think this is being confused with the fact that transformations of the response variable are an approach correction when there is a violation of the assumption of linearity.

    From what I have learnt, the assumption is that the residuals are normally distributed, which can occur when the response variable is not normally distributed.

    http://stats.stackexchange.com/questions/6350/anova-assumption-normality-normal-distribution-of-residuals

    https://en.wikipedia.org/wiki/One-way_analysis_of_variance

    Reply

    • Luke,
      For one-way Anova with say 4 groups (aka levels), you need to make sure that each group is normally distributed.
      For two-way Anova with say 2 groups for factor A and 3 groups for factor B, you need to make sure that all 2 x 3 = 6 groups are normally distributed.
      Fortunately, Anova is pretty robust to violations of normality.
      Normality can be corrected (if necessary) by using a transformation (not just to address linearity) or by using a different test.
      Charles

      Reply

  22. Hi Charles,

    I work with bacteria in soil and water. I am running statistics (or trying to) on my data which constantly violates normality and equal variances. I know the Welch Anova is recommended for unequal variance and that the Kruskall-wallace anova is for non-normality. What can be done if both of these ANOVA assumptions are violated at the same time? I understand transformations are useful in combating variance issues but I’d like to keep that as a last resort. Do you have any recommendations?

    -Matt

    Reply

  23. Hi Charles,

    I have a convenience sample of size 60. My IV is major of study (three levels) and my DV is hours of study a week. I would like to run an ANOVA to determine differences in the means of these three groups. What are the consequences (both theoretical and practical) of the fact that my sample is not random? Will it “just” limit my ability to generalize my results? Or will it prevent me to use the test altogether? What do you suggest in these cases?

    Another, and related question: also other colleagues of mine use both ANOVA and the T-test with non-random samples (which can vary in size from 20 to 100) but, and this what puzzles me, they say that they do so without any inferential goal in mind… Basically they told me that all they want to do by using these tests is checking if the means are different among the groups in their sample. BUT, and this is my question, why running these tests if you do not have any inferential goal in mind? By inferential I mean to say smt about the population form your sample (even if non-random). In my understanding, these tests are made for inferential statistic. What do you think about it? Is there something I am missing here?

    I very much appreciated your website, and will greatly benefit from your advice. Thanks so much in advance for taking the time to answer my questions!

    Reply

    • Serena,

      The whole point of using ANOVA is to generalize your results from the random samples to the corresponding populations. If you are only interested in using the results for the given sample, then, as you have said, there is no point in doing any inferential analysis. You can simply compare the sample means and draw no conclusions about the population means.

      You say that the samples are not random, but how specifically were they drawn? Very often samples that are called random are not really random. E.g. in a lot of university research samples are drawn from the student body, based on students volunteering to participate. This is not really a random sample, but lots of research papers are written based on such samples.

      Charles

      Reply

      • Thank you very much! The sample I believe is convenient: I am asking people in my class (they come from different majors) how many hours a week they study using an online survey. I agree with you that sometimes we think we are collecting a random sample but we really aren’t. I guess my population can be my class in this case, as it is a very large class and I am only collecting a sample of 60 students in there?

        Reply

        • Serena,
          If you are sharing the results with other people, the important thing is to describe accurately the limitations of your sampling technique even if you use the standard analysis tool assuming random samples.
          Charles

          Reply

          • I have another quick question for another stats assignment. Thanks in advance for your help!

            I am working on a stats assignment for which I am required to design a little study, collect my data, and run an ANOVA. In my study, my IV would be “social media platform used”, with three levels being: Snapchat, Twitter, Facebook. The DV is the number of posts posted per day.

            The three categories of my IV are not mutually exclusive: should they be in order to run an ANOVA? If this is a potential issue, what is the best way to deal with it? Do I have to ask people to self-classify in one group to begin with? Or could I ask let’s say subject1 to provide an answer for each of the three groups, and then subsequently put subject1 in one of the three groups based on the highest score (for ex if subject 1 says Snapchat 2, Twitter 4, Facebook 6, then I would assign the subject to the Facebook group)? Is this theoretically correct? If I do so, would it be a within group research design (with the same subject measured three time)?

            My DV should measure the hours spent on each of these platforms (by the same subject) or the hours spent in general on social media?
            I wonder if I might violate the assumption of independency of the samples.

            Thanks so much!

          • Serena,
            I am reluctant to answer someone’s homework assignment, but the approach to use really depends on what the objective of the study is. One of your approaches might work for some situations, but not for most others. Another approach is to view this as a repeated measures ANOVA where you allow multiple types of measurements per subject.
            Charles

  24. I have a general question on your article – which I found very useful.

    A question that constantly comes up is related to the nature of the treatments in an experiment, and whether or not ANOVA and means separation is acceptable, or regression analysis should be performed. Following is the question:

    If treatment means are not independent of each other, is it still acceptable to do ANOVA and means separation, or is regression analysis the proper approach? For example, if treatments represent a continuum of concention, such as 0X, 05X, 1.0 X, 1.5X and 2.0X, to me the treatments are not independent and the samples are therefore not independent of each other. Am I reading your article correctly?

    I am sorry about my terrible grammar in the previous post. I failed to review before submitting. My bad!!

    Thank you so much for your time and trouble.

    Reply

    • John,
      In your example, you have 5 treatment groups. If you use a sample of 50 then as long as you assign 10 elements from this sample to each group at random, then you have independent group samples.
      Charles

      Reply

  25. Dear Dr. Charles,

    I have to perform a set of unpaired t-test on independent samples on a large number of endpoint variables (that is, I have to compare several male vs. female population characteristics).
    For some variable, normality assumption is violated; for some other, homogeneity of variances is violated; for some other variable, both assumptions are not met.
    The two samples are almost equal size (n about 50).

    What is the best non-parametric test to use for such cases?
    Do you think that, for a better consistency of all results, I should use the same method for testing all endpoint variables, independently from which assumptions are violated (if any) for each single variable?

    Thank you very much for your valuable help.
    Best Regards
    Piero

    Reply

    • Piero,

      You can use the t test even if the variances are unequal. The test is pretty robust even if normality is violated provided that the data is reasonably symmetric.

      If you meet the assumptions, the Mann-Whitney test is usually the best nonparametric test to use.

      Charles

      Reply

  26. Dear Mister Zaiontz,
    I would like to observe how physical performances outcomes are influenced by 2 categorical variables (1- physical activity level (low vs high) and 2-presence of a disease (0-1)). I would like to use a 2-way ANOVA where y= physical outcome, x1= presence of the disease, x2= sedentary/exercising.
    The problem: The sample size is then not the same in each subgroup. So the model is unbalanced. One of the assumptions for the use of this type of ANOVA is therefore not met.
    I read somewhere that we can get round this assumption by using type I sum of squares (sequential) instead of the usual type VI SS (unique). Is it true? Can we draw the same conclusions about the significance of the effects of the 2 variables and their interaction? I guess that it would be too easy and there must be some tricky considerations?
    What is your opinion? Should I rather reduce/match the sample size in order to get equal groups?
    It is not the first time that I find useful and clear answers to my questions on your website and I’m very grateful. I hope that my junk language was understandable for stat expert. Thx a lot.

    Reply

  27. Hi, you state that one of the assumptions are “Factor effects are additive” – is this an assumption that needs to be tested? How can I do that? Can you explain what this means a little?

    Reply

    • Additive just means that you can use the usual ANOVA equations to model what is going on (as described on the website). I don’t test for this assumption explicitly. I probably should drop this assumption from the list since it is confusing.
      Charles

      Reply

    • André,
      This is likely to be true, but you should check for normality just in case. As long as the data is not too far from normality you should be ok.
      Charles

      Reply

  29. Hi
    I am conducting a one way within subject Anova but my sphericity test is violated. I violated my Mauchler’s test and got a value of .702 so I guess I have to use the Greenhouse geisser. How would I report that in the results. Do I mention that the Mauchler’s test was violated and report the Greenhouse geisser instead?

    Reply

    • How you report the results really depends on the requirements for publications in your discipline, but in general I would report that Mauchler’s test was violated and report the Greenhouse-Geisser correction (and even the Huynh and Feldt correcction).
      Charles

      Reply

      • Thank you so much for your reply.
        I am writing my thesis and I have been reading around it and wasn’t sure on what to do . Will I still be okay to carry on with my ANOVA analysis even if I have this violation?

        Reply

  31. Outline the assumptions which underlie the analysis of variance (ANOVA) and the possible methods for their detection and remedy?

    I understand the first part of the question … the assumptions that underlie ANOVA but what are their possible methods of detection and remedy ?
    Thanks

    Reply

    • Don,

      The brief answer is as follows:

      Normality – ANOVA is quite robust to violations of normality, especially if each group is reasonably symmetric. If this assumption is strongly violated then you can use an alternative test (e.g. Kruskal-Wallis or Brown-Forsythe) or a transformation could be employed

      Outliers – If some data are outliers, then you should check to make sure that there wasn’t some error in measurement or in copying the data. If that is not the case, then you can use a rank-oriented test instead (e.g. Kruskal-Wallis), use a trasformation or go ahead and perform the ANOVA, once with the outlier and another time with the outlier removed.

      Homogeneity of Variances – This is covered on the website. See
      https://real-statistics.com/one-way-analysis-of-variance-anova/homogeneity-variances/dealing-with-heterogeneous-variances/

      Charles

      Reply

  33. Hello Charles,
    May I ask some questions about ANOVA and two sample t-test?
    1) For experiment 1, there are three experimental groups. Two group data sets passed normality test, one failed (P=0.045). I used Kruskal-Wallis One Way Analysis of Variance on Ranks to compare the three groups. Is this the right choice? Or I should use ANOVA, since the p values is close to 0.05? What if the P values for the third group is 0.014?
    2) For experiment 2, I have two sets of data. Group A: 1.12, 1.07, 1.12, normality test P<0.001. Group B: 0.05, 0.12, 0.35, normality test P=0.430. Because group A failed normality test, I used Mann-Whitney Rank sum test to compare the two groups, with P=0.077. However, if you look at the raw data, group A values are much bigger than group B values. It does not make sense that there is no significant difference between these two groups. Just for curiosity, I also run t-test to compare these two groups, with P=0.000542. In this situation (two data sets, only one pass the normality test), is the nonparametric test the correct test I have to use to compare these two groups?
    Thank you very much!

    Reply

    • Hello Xia,

      1) For data that is so close to normality (p = .045), generally I would just use ANOVA provided the homogeneity of variances assumption is met. ANOVA is much more sensitive to violations of this assumption and is pretty robust to violations of normality. Even if one group has p = .014 when testing normality probably ANOVA is the right way to go provided the data is relatively symmetrical and there aren’t problems with outliers. You can use a box plot to see whether the data is relatively symmetric.

      2) For two samples, if each group is relatively symmetric, I would use the t test. Without seeing your data I can’t say why the results from the MW test are so different from those of the t test; generally they would be similar if the data is symmetric.

      Charles

      Reply

      • Hello Charles,
        Thank you very much for your reply!
        1) For experiment 1, both data sets that failed the normality test (p=0.045 and p=0.014) are not symmetric, according to the box plot. Therefore, a nonparametric test should be used for the analysis, right?
        2) For experiment 2, there are two experimental groups. I only have three values for each group. The data for group A are: 1.12, 1.07, 1.12 (normality test P<0.001). The data for group B are: 0.05, 0.12, 0.35 (normality test P=0.430). The results from t-test (p=0.000542) and Mann-Whitney Rank sum test (p=0.077) are very different.
        Thank you!

        Reply

        • Xia,

          1) Yes you would normally use a nonparametric test.

          2) With only three data points in each group, I would expect too much from either statistical test. Given that the first group is symmetric (at least from what you can see from the box plot) and the second group is normal, I would use the t test result. Also just looking at the data indicates that the population means are likely to be different. Again, with such small samples I would be very cautious about any conclusions.

          Charles

          Reply

  34. Thank you very much Sir for your effort : I have 2 questions:
    1. How can I judge the factor effect and how could I judge is it additive or not …?
    2. if the assumption of homogeneity of variance is not met .. i.e. significant Levene test … what do you recommend to use Welch ANOVA or Brown-Forsythe test..?
    thank you very much again.

    Reply

  35. Can ANOVA still be used if most of the data sets show normality but not all of them? Out of 21 data sets, 3 don’t show normality according to shapiro-wilk and Kolmogorov-smirnov tests.

    Reply

    • Rae,
      ANOVA is quite robust for violations of normality. It should be valid provided the data in these three groups are not too skewed.
      Charles

      Reply

    • Raheem,
      A test is valid if it measures what it claims to measure. I don’t think that ANOVA is the type of test this definition is intended to apply to, but if I do apply it to ANOVA, I guess I have to conclude that when the assumptions of ANOVA are met then ANOVA does measure what it is supposed to subject to the type I and type II error rates.
      Charles

      Reply

  37. Do the samples have to be random or can you use this test on data collected from random samples?

    Also same question for chi-square and t-tests?

    Thanks
    L

    Reply

        • Lola,
          It depends on what you mean by random. For most tests, samples should indeed be collected in a random manner. That doesn’t make the numbers random. These values must be collected randomly from the population that we are studying.
          Charles

          Reply

          • I mean for example if we use survey data should the sample of respondents be for example stratified or systematic taken from a complete sampling frame whereby all members of the population stand an equal chance of selection. As opposed to say a convenience based or self select survey?

          • Lola,
            Obviously a random sample is better. Many study are conducted with self-selected participants because it is easier to get a sample in this way. Although statistical analyses can be made, the results may not be reliable since the sample is not random.
            Charles

  38. Before now, my major concern was the ”assumptions of the ANOVA”, but this your analysis has been of great help. I visited and was able to surprise my lecturer during ST 525 lecture and i did well even in exams. I’ve also developed interest for design of experiments in advancement. I REMAIN GRATEFUL.

    Reply

    • You should make sure the assumptions hold before you spend a lot of energy building and analyzing the model. ANOVA is pretty robust to violations of normality, but not so robust to violations of homogeneity of variances. Thus if the variances are very different, the results of ANOVA can be completely inaccurate.
      Charles

      Reply

  40. Am trying to using statistical analysis of anova in flood hazards . how do i use rainfall data and flood events to do my analysis , since there is no flood data in Africa.
    urgent attention sir
    Thanks

    Reply

  42. Could you please enlighten me on this; anxiety is assessed with the use of three groups of participants utilising differing amounts of resources, no resources, two resources and five resources. The groups are also assessed in terms of gender differences between male and female. Is this a one way anova, a factorial anova or something else? I something else what would it be?

    Reply

  43. Hello

    You say
    “All populations have a common variance”

    but you are calculating the variance SSB.
    Maybe it’s because the assumption is about the pupulation variance and you calculate the sample variance?

    Reply

    • As usual, inferential statistics makes inferences about populations based on the observed sample. Since there is some chance that what we conclude based on the sample is not indeed true of the population, the results are probabilistic in nature.
      Charles

      Reply

  44. There is this question I was ask to solve. It goes thus: “what are the assumptions required in the use of ANOVA for a regression analysis”. Does this mean Anova assumption or regression…I need an urgent answer

    Reply

    • It sounds like they want the assumptions for regression, but I don’t know the intention of someone else when they ask such a question.
      Charles

      Reply

  45. If my whole population is being used (so I don’t have sample). Can I use ANOVA for that? Could someone please let me know his/her idea, and also if knows any reference regarding that.

    Reply

  46. help me and provide answers to the following questions: (1) assumptions of analysis of variance? (2) implications of non parametrics?

    Reply

  47. Do you have any formal reference regarding the F statistic is relatively robust to violations of normality provided the two listed conditions? This reference would be valuable for a text I need to write for school.
    Thank you.
    Josue

    Reply

    • There are a number of references regarding robustness to violations to normality, with slight differences from one to the other. Here is one such reference:

      Zar. J. H. (2010) Biostatistical analysis 5th Ed. Pearson

      Charles

      Reply

  48. is there any data u provide to check the ANOVA assumptions , their violations and effect on results. kindly show these things on real data

    Reply

  50. Does a one-way ANOVA require that the responses be linear with group?
    Also is a one-way ANOVA applicable for analysis of data such as response to increasing doses of a drug?

    Reply

    • 1. There is no linearity assumption for ANOVA
      2. Yes, ANOVA can be used to compare responses to difference drug doses.
      Charles

      Reply

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