One-way Analysis of Variance (ANOVA)

Essentially Analysis of Variance (ANOVA) is an extension of the two-sample hypothesis testing for comparing means (when variances are unknown) to more than two samples. In this part of the website, we deal with the simple case, namely One-way ANOVA.

Topics

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

115 thoughts on “One-way Analysis of Variance (ANOVA)”

  1. Estimado profesor, una consulta.

    Para probar el supuesto de normalidad de residuales en la prueba de ANOVA no logro obtener los residuales de manera automática, lo estoy haciendo manual, ¿Existirá alguna pestaña u opción para hacerlo automático?
    Tengo 3 grupos con 10 datos cada uno.

    Muchas Gracias

    Reply

    • Hello Victor,
      1. The residuals for each group are the 10 data values minus the mean for that group (using the AVERAGE worksheet function). You can use any of the techniques described in Real Statistics website and software, especially QQ plots and Shapiro-Wilk tests (in the Descriptive Data and Normality data analysis tool, to determine whether the residuals of each of the groups are normally distributed.
      2. To make the job easier, you can test raw data in each group since the residuals are normally distributed provided the raw data in each group are normally distributed.
      Charles

      Reply

  2. Hi Charles,

    I have one doubt regarding ANOVA and dunnett’s test. Actually i have 4 groups ,in that one group is the control and other 3 are treatment groups. While doing ANOVA it do not came significant ( alpha = 0.05) .After that when i run dunnett’s test one group came significant. Came i know why this happened.

    Reply

    • Hi Sanjith,
      I need to see your data to explain why this might happen, but, in general, this is possible although usually this does not happen. ANOVA and Dunnett’s test have different assumptions and are based on different principles.
      Charles

      Reply

  3. Hi,

    I have several (12) results for 5 points in time (60 values in total). I have performed my statistics but want to add the effect size (cohens d). Where do I find that in XRealStats?

    Best regards,
    Tobias

    Reply

    • Hello Tobias,
      Cohen’s d is not the usual effect size for ANOVA. You can use it for the follow-up to ANOVA. It is usually used as an effect size for the t-test. Which version depends on the particular t-test of ANOVA follow-up test you use and which variable (or pair of variables) you are interested in.
      Real Statistics reports Cohen’s d for all the t-tests and many of the ANOVA post-hoc tests.
      Charles

      Reply

  4. Hello Charles,

    sorry if I bother you. I’d like to set up a pilot study to assess whether concentration of iron in the human brain (assessed through magnetic resonance examination) is associated with a certain disease, so only 10 Patients and 10 healthy controls are taken into consideration. A normal distribution of the data can be assumed for the healthy sample:
    a) what test would you suggest to test if there are differences in iron concentration between the two samples?
    b) how would you modify the test if normality is not statistically confirmed?
    c) would you choose a different test if sample numerosity was 100 vs 100 ?

    Thank you very much.
    Best Regards,

    Ivano

    Reply

    • Hello Ivano,
      a) If the differences are normally distributed, you could use the two-sample independent t-test.
      b) If the normality assumption is not met, the usual test is the Mann-Whitney test.
      c) With small samples a table of critical values is used for the Mann-Whitney test (and there is an exact test option as well). For large samples a normal approximation is used. The tests described on the Real Statistics website and included in the Real Statistics software take all of this into account and provide the various options.
      Charles

      Reply

  5. Hi, I’m struggling to perform the single factor ANOVA test by rows not column’s. transposing the table has not worked and performing the test like this results in missing one of the rows, is there a way to fix this?

    Reply

  6. Hi, would love some help on a question I have! I asked participants in a survey to rank a list of items. To present these data, I took the weighted average of each item using the formula (x1*w1+x2*w2+⋯+xn*wn)/(total response count), where: x=response count for item; w=weight of ranked position; and total response count=number of participants. Weights were applied in reverse order (i.e., item ranked 1 has a weight of 9, when there are 9 items).

    I took the weighted average for all participants, but I want to compare the ranks by group. Can I run a one-way ANOVA on this weighted rank average?

    Reply

  7. Hi Charles,
    I have to make an ANOVA for a data set from an experiment with a single factor and 3 levels (10 data points each). To test the normality of the data before ANOVA, do I need to test for normality of the three sets of data separately (for each level data: 10 data points) or test the normality for the whole data set (30 data points)? Thanks in advance.

    Reply

  8. Dear Charles
    Thank you for proposing such a great tool for free. I tried to calculate p-value using Dunnett T3 method after Welch’s ANOVA with your tool. However, I found different values compared to what I saw in Prism (my lab has this as statistical software). When I change from Welch’s to classical ANOVA, it did not change the result in Dunnett test. Do you have any comments ? I expected some changes because we have different sum of square. I am a novice so forgive if what I ask is the obvious.

    Reply

  9. Good day. I hope this finds you well. If you do not mind, I would like to humbly ask for your advice.

    I plan to propose conducting an experiment with 5 independent samples. As such, I planned to conduct one-way ANOVA to identify equality in all means. However, I am concerned that my sample size is too small. My sample size within one group is 3 and this is the same for all groups. The significantly small sample size concerns me as I believe this will certainly affect the validity due to a highly likely unequal variances. The thing is I can only have 3 scores as my sample size per group and I cannot increase it anymore due to certain constraints. As such, I plan instead to conduct Welch’s ANOVA or Brown-Forsythe F*. I remember being adviced that Brown-Forsythe F* leads to more valid results that Welch’s ANOVA when the sample size per group is incredibly small such as that lower than 7, so I plan to use it, along with Games-Howell. Am I on the right track with my decision? Or do you advice me to use the classic one-way ANOVA or Welch’s ANOVA instead? If the classic one-way ANOVA is applicable, I plan to run Hsu’s MCB instead as my post hoc test, as I see it more powerful in this case compared to Tukey’s HSD.

    Another question I have is regarding the FWER, because I believe that having 5 groups will cause alpha inflation (my target alpha is 0.05). Is having a post hoc test with simultaneous CI of 95% enough, even when I do an omnibus test with a=0.05? Or do I do an alpha correction (let’s say the Bonferroni correction for example, which will give a corrected alpha of 0.005) and apply that corrected alpha to my omnibus test, before proceeding with my post hoc test with simultaneous CI of 95%?

    I will patiently wait for your response. Thank you very much in advance.

    Julius

    Reply

    • Hello Julius,
      1. With only three repetitions you will be limited no matter what you do unless the results are overwhelming (i.e. the effect size is quite large). As far as Brown-Forsythe vs. Welch’s ANOVA, see
      https://www.graphpad.com/guides/prism/8/statistics/interpreting_welch_browne-forsythe_tests.htm
      Hsu’s MCB is more powerful than Tukey’s HSD, but I can’t comment on whether this is the correct follow-up test to use in your situation
      2. You shouldn’t need to adjust the alpha value for the omnibus test. Tukey’s HSD, Games-Howell and Hsu’s MCB do their own alpha correction and so you don’t need to use a Bonferroni correction.
      Charles

      Reply

  10. Many of the tests like Dunnett’s, Scheffe’s demand that the group size should be the same.
    Does it mean that these tests cannot be run if my trials vary in the number of samples?
    They vary between 4 to 6.
    In that case what should I do?

    I want to acknowledge that real-statistics has made my life so very simple, taking away all the anxiety of how to do post hoc ANOVA.
    I really want to express my gratitude to you for your generosity to share knowledge.

    Reply

    • Sujatha,
      Since the group sizes are different, you should avoid post-hoc tests that require balanced models (i.e. equal group sizes). Dunnett’s test is still valid even when the group sizes are different, but unfortunately, the table of critical values is not valid. Differences between 4 and 6 might still be ok, but I am not sure.
      A good choice when group sizes are different is usually Tukey-Kramer (a modification of Tukey’s HSD). If group variances are also different, then Games-Howell is better. These are all described on the Real Statistics website.
      Thank you for your kind words. I am pleased to help you.
      Charles

      Reply

    • Thanks Charles for your advice.
      I checked the homogeneity of the variance of various groups through Levens’s test and found that p-value is greater than alpha.

      I have been able to run Dunnett’s, Tukey-Kramer, Games-Howell and pairwise t test for academic interest to compare the results and almost are of it are consistent. However, in just one pair, their is discrepancy between the results of pairwise t-test and Games-Howell test.
      Is it legitimate to get such result?
      Though I have an explanation to offer why the two pairs are not equal as indicated in the t-test even though they are expected to be, can there be such variation in the results of the two tests?

      Reply

  11. Hello, Charles
    A quick question regarding alpha corrections that you present in the ANOVA: Single Factor dialog box. The default value is 1. I have been doing mostly Welsh’s test with Games-Howell as the follow up. Some of the intergroup comparisons are quite large. I’ve been using a standard alpha (p<0.05), which is the default.

    I presume that the value you enter for the alpha correction is the number of intergroup comparisons you make in the follow up test? So, I counted up the number of intergroup comparisons from the first run and entered that value in the alpha collection box, then re-ran the test. It didn't seem to do anything. My Welsh's test still said there was a significant difference in the groups. It didn't present me with an updated alpha or change any of the Games-Howell p value results. Am I doing something wrong? Please advise when convenient. Thanks!

    Reply

    • Hello Chris,
      Welsh’s ANOVA with a Games-Howell is often a good approach.
      The Alpha correction value (default 1) is only used with Contrasts. Games-Howell has its own built-in alpha correction and so doesn’t use the Alpha correction value.
      Charles

      Reply

  12. Dear Dr. Charles Zaiontz

    Cheerful greetings to you Sir.

    Your resources have been so helpful to me and have guided me so far in improving my understanding of statistics and statistical methods. I am grateful for that.

    I am at a critical point in my journey to a PhD and I really need urgent guidance and cross-checking of statistical methods, so I do not waste time and start all over again with my stats analyses , so please respond to me

    Currently I have a challenge and it is with violated assumptions of M/ANOVA.

    I have one independent variable called “Plant Specie” with 16 levels(16 different species) and each level(specie) has 5 replicates. I also have 4 dependent variables(4 different heavy metals).

    I initially wanted to use MANOVA for testing differences between mean concentrations of each of the 4 heavy metals across the 16 different species being investigated but several assumptions of MANOVA especially homogeneity of variance and sample size were violated .

    Log transformation of data had no effect on the outcome of equal variances as both the Box test and Levene’s test were still significant.

    So I decided to use ANOVA. However, with ANOVA I am faced with the challenge of violation of assumption of sample size for the groups being greater than 10, as I have a sample size of 5 replicates for 15 of the 16 species and 4 replicates for 1 of the 16 species.

    How do I proceed from here? What can I do to achieve this goal of meeting all assumptions of ANOVA?

    Thanks for your cooperation as I await your response.

    Reply

    • Hello Presh,
      I am not familiar with an ANOVA “assumption of sample size for the groups being greater than 10.” Please explain what the problem is. The sample sizes of the groups don’t need to be equal.
      Charles

      Reply

  15. Hi Professor Charles,

    How ANOVA and Regression are different?
    Is that any criteria when should I use ANOVA and When Should I use Regression?

    Thanks in advanced for my question.
    WIN

    Reply

    • Win,
      They are quite different concepts, as you can see by reading the ANOVA and Regression webpages on the Real Statistics website. However, regression can be used to perform the ANOVA test and an ANOVA table is used in the output from regression.
      Charles

      Reply

      • Win,
        They are quite different concepts, as you can see by reading the ANOVA and Regression webpages on the Real Statistics website. However, regression can be used to perform the ANOVA test and an ANOVA table is used in the output from regression.
        Charles

        Reply

  16. Hello Charles,

    Thanx for your response. I want to compare raw material composition of a medicine between 2 periods of 24 month each. For individual raw materials say RM1, for 2 periods, I have done the comparison using one way anova. How to compare the interaction between Raw materials of individual period, as there are 15 such raw materials

    Reply

    • I don’t completely understand the scenario that you are describing, but, in general, if you want to compare interactions, you would need to se two-way Anova.
      Charles

      Reply

  18. Hi Charles,

    I want to test a hypothesis that states that country of origin significantly influences the consumers’ price perception of electronics ‘Made in Country X’.

    In my data, i have four questions measuring this price perception. They are

    1. How high would you estimate the price of this Country X laptop given the image above? (6 price categories were given)

    2. How high would you estimate the price of this National laptop given the image above? (6 price categories were given)

    3. What is the max. amount you would be willing to pay for this Country X laptop? (open question)

    4. What is the max. amount you would be willing to pay for this National laptop? (open question)

    Can I conduct a one-way ANOVA to compare the means btw. the two first questions and then another one-way ANOVA to compare the means btw. the 3. and 4. question in order to answer my hypothesis?

    Which numbers to I have to put in the histogram to check for normal distribution?

    Thank you so much for your help.

    Reply

    • Sally,
      Before being able to answer your question, I need to understand the situation better.
      How many different countries are you evaluating? Are these the only countries you care about or are these taken at random from the list of countries producing electronic equipment? Does each participant evaluate only one country or multiple countries?
      So far, I think you need to combine the information from the 4 questions to produce a single measurement. Then depending on the answers you give to me I might be able to determine which type of test to use.
      Charles

      Reply

      • Hi Charles,

        thank you for the quick reply, I truly appreiate your help. The research is about how Chinese laptops are perceived by European consumers. Therefore, two identical laptops are shown and it is stated that one is ‘Made in China’ and one ‘Made in Europe’.
        Hence, each participant states
        – how much he/she is willing to pay for the Chinese laptop
        – how much he/she is willing to pay for the European laptop
        – max. amount they are WTP for a Chinese laptop
        – max. amount they are WTP for a European laptop

        I hope I could clarify the situation better and am looking forward to your response.

        Reply

  19. Sir,
    I have an ambient air data ( 5 gases) from three bus stations over a period of one year. I hypothesized that there is no significant difference in spatial distribution of the five gases on the bus stations. Can I use one way ANOVA. If yes, how?

    Reply

    • Hello Mike,
      Are the bus stations randomly selected?
      Do you measure the 5 gases in each of the 3 stations?
      When you say “over one year” do you have daily data for each of the 5 gases in each of the 3 bus stations?
      Charles

      Reply

  21. Please sir how can we calculate confidence interval and effect size for kruskal wallih test for three independent group

    Reply

  22. i want to determine if there is a significant difference in the assessment of the respondents in relation to their demographic can i use anova?

    Reply

      • in realstat how can i do this? i have 1 group of respondents 4 demographic each of it has levels.i apologize i know its like spoon feeding but i kept on researching how to proceed but i can”t seem to understand the process

        Reply

        • James,
          If you are not comparing different demographic categories, but only the levels within each of the 4 categories, then it appears that you have four separate one-way ANOVA tests, one for each category. This will allow you to make comparisons across 3 educational levels (high school, university, graduate school)
          If you do want to make comparisons across different demographic categories, then you need to specify which comparisons are of interest.
          Charles

          Reply

  23. Sir, I am cant getting. how will I use annova in my data to make it significant. Actually I am a beginner in this and want to know how our data will be under range TO MAKE THE READINGS BEST.

    Reply

    • Ahmed,
      If by count data you mean ordinal data (e.g. Likert scale data), then you can use ANOVA provided the distances between the scale values can be considered to be equal (e.g. a value of 4 is the same amount more than 3 as 5 is more than 4, etc.) and the other assumptions for ANOVA are met. With such data you may find that the assumptions are not met though.
      Charles

      Reply

      • Thanks, I have three concentration of insecticide and under each one of concentrate, i have three replications. I count a number of insects which die under each concentrate in each replicate so, I have nine reading. I ask if I can use one-way ANOVA to study if different between three concentrate significant or not and then I will LSD if sig.

        Reply

        • Ahmed,
          One-way ANOVA can be used for this purpose (assuming the assumptions are met). I would then use Tukey HSD instead of LSD as the follow up test. Keep in mind that your results will be limited since your sample size is so small.
          Charles

          Reply

  25. Charles,

    I am working through another scenario and have a question:

    Dr. Brown is a pediatric nurse practitioner. She would like to know the effectiveness of different HIV prevention programs on adolescences’’ sexual practices. She conducted a randomized clinical trial to see the differences between 3 different groups of high school students (attending one sexual education class, attending one sexual education plus one skills training class, and attending regular class- no sexual educational class provided). She used a safer sexual practice (SSP) questionnaire to measure the outcome of her study. The higher score on the SSP questionnaire indicates safer sexual practices. The students were randomly assigned to 3 different groups. The questionnaires were given to the participants of the study, 4 weeks after attending the classes.

    I’m not sure if I need to use a one way anova or two way anova. Part of my issue with understanding which test I need is being able to properly identify my dependent and independent variables. I start to work through each assumption for the one way anova and my variables are mixed up. The dependent variable I know is continuous and that my independent variable consists of 3 or more categorical and unrelated groups.

    I am writing my hypotheses like this:
    Ho: There is no significant difference in means of the interest variable among the three different groups.
    Ha: There is a significant difference in means of the interest variable among the three different groups.

    I lean more towards the one way anova, but I’m not really sure. Any help would be appreciated, you have been so great.

    Reply

    • Misty,
      It depends on what “the interest variable” is.
      You can use one-way ANOVA where the variable of interest (i.e. the dependent variable) is the score on the test. The group is the independent variable (categorical with three possible values). You would then compare the means of the three groups.
      If you tested each subject prior to the educational classes and then after, you could use two-way ANOVA with one fixed factor (Groups) and one repeated measures factor (Time).
      Charles

      Reply

  26. Hi.

    I have 23 variables collected at each of my 20 sites.

    I want to see if there is a significant difference of each variable between the 20 different sites.

    Can I do this in a one-way anova or do I need to do another test.

    Cheers

    Reply

  27. Hi Charles,
    Would like to ask for your help regarding our experiment. We have 3 different treatment or group namely: color, size and shape. What statistical tool is appropriate for this? Thank you.

    Reply

  28. Hello Charles,

    I have two groups and I want to compare three means of three parts of the website page (i.e three AOI’s).Can i use one way anova ???

    Your quick answer is highly appreciated.
    Thanks

    Reply

  29. Is there time difference in time spent on website between customer of 3 region , i have to apply multiple sample test here please help me with some idea

    Reply

  30. Dear Zaiontz

    I have data from 10 individuals over 24 points (i.e. every week for six months). As the data is not normally distributed I need to use Frieman’s ANOVA. My question is whether 24 points is to many to run one-way repeated measurement? I would really appreciated if you could reply me.

    Yours sincerely,

    Sam

    Reply

      • Hi Charles,

        Thank you for the prompt reply!

        I used SPSS to run the Friedman’s and the p-value came out significant, Chi-Square(23)=44.39, p=.005. Now, I think you would usually run Wilcoxon test with Bonferroni correction (in this case p-value of.002?), but there are 24 points…. What would you do?

        Kind regards,

        Sam

        Reply

  31. I have a question maybe you could help.
    I’ve conducted an outcome study using four groups, and want to analyze the data using a one-way ANOVA. I note that the variances for my four groups are: 5.4, 2.3, 1.5 and 2.1. Based on a quick check, have I violated any assumptions?
    the answer is No
    I need to figure out how to explain why it has not violated any assumptions

    Reply

    • Thank you for your time, I hope you can help me, I have spent so much time trying to understand the concept. I stumbled on this site and thought I would ask.

      Reply

    • Sean,

      Clearly the variances are not equal, but they are not wildly different either. You are probably at the borderline of acceptance of the homogeneity of variances assumption. You should conduct Levene’s test to make sure. See the following webpage for more information about testing this assumption:
      Homogeneity of Variances

      You haven’t provided any information about the other ANOVA assumptions, and so I can’t comment on these. For more information see:
      ANOVA Assumptions

      Charles

      Reply

  32. Thank for the intellectual exposure. I am currently working on the five metallic sample where am to know the effect of heat on the properties on the sample. With one of the samples being the control, can I use anova to compare the value of the Properties of the metals and how?

    Reply

  33. Hello Charles,

    Thanks for your helpful program.
    However, I have a problem when I want to do a test such as ANOVA with Levene option or any other tests, it says that there is a compile error in an hidden file….
    Do you have a solution for this ?

    Reply

    • Noz,

      The usual reason for this is that the addin wasn’t installed properly. These instructions are listed on the the following webpage:
      Download Resource Pack (or if using Excel 2007 or Excel for the Mac, click on the appropriate page).

      In particular, you need to make sure that Excel’s Solver is installed before you try to install Real Statistics Resource Pack.
      To check to see which addins are installed press Alt-TI and see which have a check mark next to them.

      Charles

      Reply

      • Charles,

        Thanks for your answer.
        I checked and Excel solder is installed. I’ve tried with another computer where it’s work without any problems.
        On my computer, when I want to install it as you said, it closes excel and say that there is a serious problem if it is installed in appdata. When I put it in Microsoft/office12/library/analyses I can open the tests window but it says error in an hidden module.
        Do you know why ?
        Noz

        Reply

  34. Good Morning Sir,

    quick question: How Do I choose my c-value during Games-Howell post-hoc?

    I’ve got 4 Groups of n=5 (1=17, 2=17, 3=10, 4=10).

    Do I just look it up in “the Critical Values of Studentized Range Distribution(q)”-Chart? And would it be the same for every row in your RealStats Excel-Sheet?

    Cheers,

    Martin

    Reply

    • Martin,
      It is much simpler than that. Just insert +1 and -1 (the contrasts) in the c column corresponding to the two groups you want to compare. You can compare any two groups. You can also change the rows where you put the +1 and -1 if you want to make multiple pairwise comparisons.
      Charles

      Reply

  37. Thank you very much sir. I got an idea about the selection of variables.please sir could you reply me whether its correct or wrong with my selection of variables for the analysis. I took between the age and level of satisfaction towards schemes as my study is about it

    Reply

  38. Sir I am using excel format for my analysis. I am not having clear idea to select the variables for one way anova. let us do ANOVA analysis between frequency of visit of the respondent and income per month of the respondent. please do reply me sir. Am awaiting for your answer

    Reply

  39. Dear Sir,

    I followed your suggestions in doing ANOVA and simply wish to clarify a doubt. My ANOVA result is significant at p<0.01 but a couple of pairs in post-hoc are insignificant. This won't challenge my finding that the variable influences the error count, will it?

    Meera.

    Reply

    • Meera,
      The significant result from ANOVA means that at least two of the variables have unequal population means. It does not mean that all the pairs of variables have significantly different means. Thus, the fact that some of pairs in post-hoc are insignificant, does not challenge your finding that the means of all the variance are not equal.
      Charles

      Reply

    • Sorry, but I don’t understand what you mean by a “likert scale average”. There is some risk in taking the mean of likert scale data, since you don’t necessarily know the distance between the sclae elements. If you can determine what these distances are, then you would take the weighted average. Most people simply take the simple average, and ignore this issue.
      Charles

      Reply

  41. Researchers desire a reliable predictor for Juvenile Idiopathic Arthritis flare ups. It is suspected that levels of phagocyte activation marker myeloid related proteins 8 and 14 hetercomplex (MRP8/14) are good markers. Known mean MRP8/14 in patients with JRA is 500 ng/ml with standard deviation of 200 ng/ml. A difference of 100 ng/ml is considered clinically significant. What sample size (per group) of patients with JRA is necessary to compare MRP8/14 measures between groups of with and without flare ups if the t test is to be used? Assume MRP8/14 is normally distributed in the population. (Foell D, et al, Methotrexate withdrawl at 6 vs 12 months in Juvenile Idiopathic Arthritis in Remission. … Could u break this down?

    Reply

  42. Dear Sir,

    I tried doing the post-hoc test but got no significant result. I’m confused. My ANOVA result was significant at p <0.01
    What to do?

    Meera

    Reply

      • Dear Sir,

        I went for Scheffe’s. Not using the Resource Pack though. When I tried it in the Resource Pack it said “Compile error in hidden module: frmAnova1”

        Meera

        Reply

        • Meera,
          That is not good. What version of Windows and Excel are you using? Are you able to use other Real Statistics Resource Pack capabilities?
          Depending on what you are trying to demonstrate, Scheffe’s is usually not the best post-hoc test to use. Usually Tukey HSD gives better results.
          Charles

          Reply

  44. Dear Sir,

    I didn’t quite get this part “If, however, you get a significant result, then usually you will want to better pinpoint what is causing the non-significant result, which is where the post-hoc tests come in to play.”
    I got significant results at p<0.01.

    Meera.

    Reply

    • Meera,
      If for example you had four groups, the significant result from the ANOVA test tells you that there is a significant differences among the means of the four groups, but it doesn’t tell you which groups(s) have different means. If you want to better understand this then you need to conduct some follow up test. See the website for more details and examples about this.
      Charles

      Reply

  45. Dear Sir,

    Is it mandatory to do a post hoc test after ANOVA? I need to prove that the variable ‘annual income’ influences error count. Can I simply do an ANOVA and leave it at that?

    Reply

    • Meera,
      If ANOVA gives you sufficient information for the test you are trying to make then you can leave it at that. Particularly if you get a non-significant result then you will typically want to leave it at that. If, however, you get a significant result, then usually you will want to better pinpoint what is causing the non-significant result, which is where the post-hoc tests come in to play.
      Charles

      Reply

  46. Thank you for your reply Charles.
    I will explain in a bit detail of what I am trying to do:
    1. I have a reactor and I am recording velocity data at different cross-sections.
    2. I have three heights where I am taking these datas.

    3. I am measuring the velocity using different instruments. I want to compare the difference between these instruments based on the time-averaged velocity values.

    So, now here are my questions:
    1. Should I take the instantaneous values or time-averaged velocity values for doing ANOVA.

    2. By doing Anova at three different heights, I will have 3 p- values. Is a way to combine these 3 p-values to get just one, which will represent the whole system.

    I hope that I conveyed the problem to you. Thanks very much in advance.
    Subhu

    Reply

  48. Hi Charles:

    Thank you very much for this website. I have been benefited from you website in a number of occasions.

    I have a question about the ANOVA test:
    1. Does it necessary to have the whole population to do Anova or we can as well use the average values of the population to do Anova.
    2. I have several p-values from a number of Anova tests. What is the possibility of combining all these p-values to come up with one p-value. Is there any way of averaging the p-value for one system.

    Thanks very much.

    Reply

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