Multivariate Analysis of Variance (MANOVA)

In the univariate case, we extend the results of two-sample hypothesis testing of the means using the t-test to more than two random variables using analysis of variance (ANOVA). In the multivariate case we will now extend the results of two-sample hypothesis testing of the means using Hotelling’s T2 test to more than two random vectors using multivariate analysis of variance (MANOVA).

ANOVA is an analysis that deals with only one dependent variable. MANOVA extends ANOVA when multiple dependent variables need to be analyzed. It is especially useful when these dependent variables are correlated.

Topics

References

Johnson, R. A., Wichern, D. W. (2007) Applied multivariate statistical analysis. 6th Ed. Pearson
https://www.webpages.uidaho.edu/~stevel/519/Applied%20Multivariate%20Statistical%20Analysis%20by%20Johnson%20and%20Wichern.pdf

Rencher, A.C., Christensen, W. F. (2012) Methods of multivariate analysis (3nd Ed). Wiley

128 thoughts on “Multivariate Analysis of Variance (MANOVA)”

  1. I have time series data on three variables: Unemployment (Independent Variable), Crime Rate (Dependent Variable), and Suide Rate (Dependent Variable). I want to determine the effect of the independent variable on the two DEPENDENT VARIABLES (DVs) using MULTIVARIATE REGRESSION. How do I go about this problem?

    Thank you.

    Reply

  2. Dear sir:
    I have 2 categorical variables for IV and 3 continuous variables for DV, and the correlation between dependent variables was over .90. How should I should the problem of multicollinearity? (PCA did not work).
    Thanks for your help!

    Reply

    • Dear Yingcong Chen,
      If the correlation between two DVs were 1 then you could simply drop one of them and use ANOVA. With a correlation near 1 you could combine the two DVs (e.g. weighted average) and use ANOVA. You could perform separate ANOVAs expecting the results to be similar. These are the approaches that I can think of. See also
      https://www.youtube.com/watch?v=A47-Rut5BZ0.
      Charles

      Reply

  3. Hello, Charles
    I had conduct a research about two different teaching methodologies on two different groups and want two see which teaching methodology is more effective to improve students perceptions of paragraph writing, use of paragraph writing strategies and performance of paragraph writing . I had taken their pre-test and then start to taches these 2 groups with different methodologies .then i took their post test .i have one independent variable that is teaching methodology and 3 dependent variable that is Witten and spoken .can i use MANOVA test for this analysis ?need your guidance thank you .

    Reply

    • Hello Amnauel,
      If you had only one dependent variables, then there are a number of possible approaches. With multiple dependent variables, then Repeated Measures MANOVA (or possibly the two-group version Paired Hotelling’s T-square test) is the way to go.
      Charles

      Reply

  5. sir kindly guide me about MANOVA and repeated measures ANOVA. My conducting topic is ” the effect of blended approach on EFL learners’ paragraph perceptions, writing strategy use and writing performance. This implies that one IV and 3 DVS. Can I use MANOVA or repeated measures ANOVA?

    Reply

  6. Hey Charles, could you help me: if I had a quasi-experimental design where I had one IV (experimental, control), and three DVs, could I run a MANOVA to see the group differences, then a regression analysis to see the relationships between the DVs? Or will the MANOVA tell me everything I need to know in terms of how much of the variation?

    Reply

  7. Thanks for your website. I have a question about a study I have conducted and how to analyze the results statistically.

    I have three independent variables (v1, v2, v3) and two sets of elements (dependent variables). The first set (set 1) consists of 19 elements and the second set consists of 30 elements (set 2). I have involved 11 participants. For each independent variable and each set of elements, I have asked each participant: Which element(s) contribute to independent variable v1, which element(s) contribute to independent variable v2, which element(s) contribute to independent variable v3. The participants could select per independent variable: no element, one or more elements.

    In total, I received six answers per participants with a list of elements. I’d like to calculate a correlation between each independent variable and selected elements.

    Question 1: Is the number of participants large enough to determine a correlation?
    Question 2: Which statistical method should I apply to determine a correlation?

    Reply

    • Hello Helmut,
      I don’t quite understand the values that you are trying to correlate. Are you trying to correlate each of the C(6,2) = 15 pairs of the 6 independent/dependent variable combinations? This would yield a 6 x 6 correlation matrix. For each participant and each of the 6 independent/dependent variables, does your data consist of the number of elements selected?
      Charles

      Reply

  8. I have a data with two group and 100 dependent variable. i had done a MANOVA test and p value is 0.00, which mean there is significance difference between two mean group, now i have to find the which dependent variable have maximum effect so what do next?

    Reply

  9. If I have one way repeated mearured manova and the time is the IV and the DVs are “Psychological Resilience” and “Mental Health” but the mental health is measured in 3 dimensions “Psychological”, “Emotional” “Social” and “Overall” then I have my DVs are 5?

    Reply

  10. I am doing a research study paper for school. This study seeks to better understand the effects of mental health medications on the people who take them. What MANOVA will be the test to use.

    Reply

  11. Hi Team,
    I am comparing the outcomes of few independent variables (IV) (a few are nominal and a few ordinal) between two groups (G1 and G2) which also have dependent variables (DV) ( 1 ordinal and 1 nominal). I need to see if the difference between the outcomes of IVs in both groups are confounded by unequal distribution of DV among the groups. Is MANOVA an apt application to use in this scenario?

    Reply

  12. Greetings. I am currently doing a research regarding how lactose content affects bacterial growth using pour-plate method (CFU). I have 3 IVs: the percentage lactose content in milk, the dilution factors of milk to the power of 7 and to dilution factors to the power of 8. My 2 IVs are: total plate count (TPC in CFU) for dilution factor to the power of 7 and TPC for dilution factor to the power of 8. Can I use MANOVA for this? If yes, then should I opt for 1-way, 2-way or 3-way MANOVA? (Thank you beforehand for your help).

    Reply

    • If I understand correctly, you have 3 IVs and 2 DVs, but the IVs are not categorical as would have to be for MANOVA.
      The stated objective “how lactose content affects bacterial growth?” can be studied via a regression model. If instead you are trying to test some hypothesis (or hypotheses), then you need to specify which hypotheses you want to test.
      Charle

      Reply

  13. Hi,

    I have two iv – (two psychology intervention groups. one face to face and one on the internet), i am measuring 3 related DVS and one overall cofounding ? if thats right. I have one measure PRE and POST intervention. How do i do the MANOVA showing the difference between the groups, my aim is to see which group is superior post therapy. do i need to do one MANOVA for pre and one for POST or can i do it all in one and code id pre1,pre2,poot1,post2 ect. or shall i just do a few anovas ?

    Many Thanks

    Reply

    • Josie,
      1. When you say that you want to show “the difference between the groups”, more specifically what hypothesis or hypotheses do you want to test? 2. If you care about improvement post over pre, then perhaps you can use the data for post minus pre. The devil is in the details, which is why I asked question#1.
      Charles

      Reply

  14. Hi Charles.

    Thank you for your excellent explanation. Although I have studied on my own a few of the statistical analysis methods, I am still confused about which method is more suitable and satisfy conditions/assumptions of my study.

    I conducted a phytoremediation experiment with 3 IVs (column type, study duration and media depth) with 5 DVs (N, P, Zn, Cu and Pb). I am interested to find the effect of the factors (IVs) on the removal efficiency of the pollutants (DVs). The issue is my columns were labelled separately into 4 different types of column (3 replicates for each type), with every column having 4 variations of media depth. That is altogether 12 columns for one week and I have the same number of columns for 3 different weeks (Week 0, 10 and 20). That means I have a total of 36 columns in my study.

    I am thinking of using MANOVA since there were more than 2 IVs and 2 DVs. The problems are:

    1. I don’t think theoretically there is a correlation within the DVs as it represents removal efficiency of each pollutant by the system.
    2. I am confused as to whether some of the factors e.g. week or media depth should be categorised as covariates, and what difference would it make other than I could not conduct a post-hoc test since I have fewer factors now.

    I am also considering using 3-way ANOVA as I am interested to see the differences in the factors rather than the effect on the DVs. In this case, do I have to conduct the 3-way ANOVA separately for each DV?

    Thanks and hope to hear from you soon.

    Reply

  15. Hello, Sir
    I’m currently on my research, I’m comparing 3 different methods to extract a substance of my samples to find which method is the most effective based on accuracy and precision parameters. In this case, I will have %recovery of 5 samples and relative standard deviations for each extraction method. I can’t decide if I should use ANOVA or MANOVA? or should I use different statistical method?

    Reply

    • Raspati,
      I would need more details to say for sure, but if you are comparing more than one parameter (accuracy and precision) then you would use MANOVA instead of ANOVA.
      Charles

      Reply

  16. Hi, I am currently conducting a research about the effect of the pandemic in consumer behavior, and the effect of the consumer behavior to local business entities. I wonder what statistical test should I use and what sample size do I need? Thank you.

    Reply

    • Jonah,
      You need to provide more information about the type of data you plan to collect and how you will characterize the effect before I could answer your question.
      Charles

      Reply

  17. Hi Charles sir
    I had conduct a research about two different teaching methodologies on two different groups and want two see which teaching methodology is more effective to improve students written and spoken narration ability . I had taken their pre-test and then start to taches these 2 groups with different methodologies .then i took their post test .i have one independent variable that is teaching methodology and 2 dependent variable that is Witten and spoken .can i use MANOVA test for this analysis ?need your guidance thank you .

    Reply

    • Presumably, you have a group factor with two treatment groups (simple teaching vs. special teaching) and two dependent variables (written and spoken). You need to determine what sort of measurements you use for the dependent variables. If this is the difference between the scores they received on some questionnaire post-treatment minus pre-treatment, then MANOVA looks to be a good fit
      Charles

      Reply

  18. Hey Charles, could you help me: if I had a research design where I had 1 IV (experimental, control), and 3 DVs that are theoretically related, could I run a MANOVA first to see the group differences, then a regression analysis to see the relationships between the DVs? Or will the MANOVA tell me everything I need to know in terms of how much of the variation in, say, DV3 is accounted for by DV1?

    Reply

  19. I have one group, one independent variable, one dependent variable with two measures. Is one-way MANOVA the correct test? How do I use G* Power to calculate my sample size?

    Reply

  21. Hello. Please I really need some help. I have a study examining the effect of stretching for knee ROM and knee swelling. Two groups is the intervention and control group with measurements of pre and post. However I have for knee ROM three sub measurements which make up the outcome measure: flexion , extension and total arc. For knee swelling I have again three areas of measurements on the knee joint: mid patella, distal and proximal. Thus how can I analyse these two outcome measures comprising of sub-measures without dong many separate tests? I want to see if they have improved for iteration compared to control group(if swelling decreases following stretching rehab compared to control standard treatment and pre and post for each group as well).
    Thank you In advance

    Reply

    • You can use MANOVA to see whether there are any significant results. If there are some significant results then you will need to perform a number of separate tests in any case (taking familywise error into account). What you do specifically depends on which sort of comparisons you are interested in and which you really don’t care about. This will simplify things for you.
      Charles

      Reply

  22. This is a great inspiring article. I am pretty much pleased with your good work. Thanks for sharing it & keep it up.

    Reply

  23. Hello sir,
    I want to ask. I have two dependent variables and one independent variable in my experiment so I use one-way manova to analysis. but before analyzing manova, are we must to find the correlation between the dependent variables? then how is the decision taken?
    thank you

    Reply

  24. I have a pilot study of two independent groups in which the populations are unknown; only data is from the control and intervention samples. Control group non-concussed subjects 17. Intervention is 45 concussion subjects (determined by a doctor). Each group speaks seven words, three times in which only the vowel sounds are analyzed. All subjects have at least two visits, some up to six. I wish to determine if the variation is the same or about the same between the groups Ho at the first and subsequent examination visits.

    There are five, dependent variables that are continuous (measurements taken on the seven spoken vowels); the variation is thought to be materially greater than the same dependent variables of the control group.

    There are seven independent variables that are labels (7 vowel spoken by subjects). Each of the vowels are spoken three times.

    So I have unequal sample sizes (17 vs. 45); control group speech acoustic measurements are thought to be a normal distribution; while the intervention speech acoustic measurements are thought to be non-parametric as compared to the control group. I want to compare the variation of speech acoustic measurements for each of the seven vowels at each point in time.

    I believe this analysis require a MANOVA with repeated measures and a post-hoc KS test and a Anderson-Darling test…is this correct? How do I conduct two temporally different repeated measures i.e. three repeats at each visit, then comparing all subsequent visits? It is probably proper to talk of data requirements for SPSS.

    Thank you,

    Matthew

    Reply

    • Matthew,
      1. Before deciding which tests to use, you need to decide specifically what null hypotheses you want to test. The choice of test(s) depends on this.
      2. It is easy to require tests that are quite complex, testing all possible combinations of variables, but this may not be necessary for your objectives. Also the more complicated the tests, the larger the sample that you will need. With samples of size 17 and 45, you should try to simplify rather than make things too complex, although it may be appropriate since this is a pilot study and the final study may have samples of suitable size.
      3. MANOVA is indeed possible, although it may turn out that you need some sort of Hotelling’s T-square test since you only have two samples and unequal sample sizes.
      4. I am not sure what sort of KS ad Anderson-Darling post-hoc tests you are referring to. These tests are used to test normality and are not typically used as post-hoc tests. Again, which post-hoc tests to use depends on the null hypothese you want to test.
      Charles

      Reply

      • Charles:

        I have some further information to share.

        The seven independent variables, from a speech acoustic perspective, have no correlation nor interactions. Each IV is considered from an individual perspective. Correspondingly, the dependent measurements have no correlation nor interactions either…same as IV. Since speech acoustic variables (IV & DV) correlations or interactions do not exist, if one is to use the Hoteling T2…do you just ignore the covariance matrix? What are the implications if a MANOVA is performed?

        Also, both gender and age are aspects that need to be taken into consideration (pilot study age range 6-21 yrs). The ages of many “concussed” subjects are teenagers, therefore, male subjects voice recordings have inherently more variability because their voices are changing. Thus one needs to group them and compare to those of the same age range (control group). Does the addition of gender and age preclude the Hotelling T2 test? How are gender and age accounted for in Hotelling T2 or MANOVA? How would age grouping be incorporated for Hotelling T2 or MANOVA?

        Lastly, at each examination of the “concussed” subjects, all seven words are repeated for a total of three recordings for each of the seven words. This is done to have more data points thus not relying on one data point. Does this require something specific in Hotelling T2 or MANOVA? I thought that this averaging of the three word sounds per word would be a separate activity with the single value used in Hotelling T2 or MANOVA.
        One of the seven words (IV) is a made-up word, it is of some interest to determine if the made-up word performs (based on the five measurement types) differently than the other six actual words. I think this would be a separate statistical analysis, is this correct? How should this be performed statistically? I realize this is outside the scope of the Ho but could lead to changing the made-up word to an actual word going forward.

        Many thanks,

        Matthew

        Reply

        • Matthew,
          What you are describing seems quite complicated, but it is not clear to me which are the essential things that you are trying to study. E.g. you seem to have one overall objective, but are probably trying to test multiple hypotheses. Once you clearly state these hypotheses (using precise terms based on measurable data), it will be easier to determine which tests are required.
          Charles

          Reply

          • Charles:

            You are correct. It is easy to get lost in the forest. Since this is an experimental study i.e. we do not know if subjects acoustic characteristics show variation from a concussion. We are simply seeking to establish if there is variation and how much is the variation. Since the first examination answers this question, the subsequent examinations would only further establish that the variation diminishes and ultimately returns to a normal variation (same as the control) group. We are seeking to establish that speech acoustics can reliably diagnose a concussion, thereby providing the basis for another study with a larger number of subjects.

            Matthew

  25. I have 9 years financial data of 5 companies and in order to find significant difference in their financial performance I have used ANOVA using SPSS. Please suggest which other statistical test can i apply

    Reply

  27. Hello Charles, and thanks a lot for your very helpful website.

    You write “In the univariate case, we extend the results of two-sample hypothesis testing of the means using the t-test to more than two random variables using analysis of variance (ANOVA).”
    Isn’t it “to more than two samples” rather than “to more than two random variables” or did I misunderstand something?

    Reply

  30. Hi all,
    Could you tell me how many dependant variables this tool can handle? I have tried with about 20 dependant variables and it gives me weird values like #VALEUR

    Reply

    • Anthony,
      I don’t believe there is a fixed limit. If you send me an Excel file with your data and the analysis that you have run, then I will try to figure out why you are getting these error values. You can find my email address at Contact Us.
      Charles

      Reply

  31. Hi Charles,
    I’m wondering if a MAN(C)OVA would be appropriate for my situation. I’m looking at speech production data of vowels in three different contexts (e.g. A, B, C). For each vowel I have continuous values from about 5 different measurements (e.g. vowel duration, etc.). I’d like to see if a combination of those 5 measurements is able to distinguish a given word (e.g. ‘bank’) as a member of categorical context (e.g. the aforementioned A,B,C). In other words, do the words in context B look different from the words in context C (in a statistically significant way), given the values of measurements 1,2,3,4,5?

    Reply

    • Adam,
      If I understand the scenario, MANOVA could be used to determine whether there is a significant difference between words in groups A, B and C based on the 5 measurements.
      Charles

      Reply

  32. Dear Charles,
    I intend researching on the IMPACT OF INTERNALLY GENERATED REVENUE ON STATE FINANCES.
    a) Can I use MANOVA?
    b) What is going to be my likely DV and IV.

    Reply

    • I would need a lot more information about what sort of hypotheses you are trying to test before I would be able to answer your question.
      Charles

      Reply

  33. I am trying to figure out which analysis to use. I have 1 DV (dichotomous) ,3 IVs (test scores, which are all ratio), and three covariates (gender, actual age, and past offenses-categorical). I know MANCOVA will not work, as I only have one DV. I thought an ANCOVA would work, but does not because I do not meet the first three assumptions. Please help.

    Reply

    • Yvonne,
      Sorry but I don’t understand your scenario. You say that you would use ANCOVA except that the assumptions are not met, but let’s put this issue aside for a moment. To use ANCOVA you would have 3 categorical independent variables (which could be dichotomous) and one dependent variable which would be numeric (and not dichotomous).
      Please describe the situation better.
      Charles

      Reply

  34. Dear Charles,
    Could you please help me with the interpration of the following?

    1. If one, in order to have a Wilcoxon test with N=12, gives G-power the values “effect size = 0,8, a=0,05, power=0,8, it means that: they have a probablity of 80% to find statistical significant differences that really exist, only if these differences are big enough (large size effect). Do I get it right or not?

    2. I can have N=12 with two ways:
    (a) 1-tail: “effect size = 0,8, a=0,05, power=0,8”
    (b) 2-tails: “effect size = 0,95, a=0,05, power=0,8”
    What does 1-tail/2-tails mean and more importantly which might be ‘better/more acceptable’ or at least ‘less bad’: (a) or (b)?

    Thank you very much.

    Reply

  35. Your work with Real Statistics seems to me excellent, monumental and very useful. I would like suggest you to include individual tests for comparing the means of each variable in the MANOVA. Thanks!

    Reply

  36. Dear Charles,
    G-power gives N=12 for a Wilcoxon, if I give these values:
    – Tail = 1
    – effect size=0,8
    – a = 0,05
    – power = 0,8
    What do you think about it? Could it be acceptable to procced this way or it does not have any meaning at all?

    Just grateful for your help,
    Maria

    Reply

    • Maria,
      If these are the values reported, then you need to make sure that a one-tailed test is appropriate and you only need to detect such a very large effect.
      Charles

      Reply

  37. Dear Charles,
    i used the G-power you recommended and I found out that the minimum sample needed for MANOVA in the case of having questionnaires with 6 dependent variables (=5 sub-scores of Likert questions groups+1 total score) and a unique independent variable (= a didactic intervention) is 42. (The values I gave to the G-power were alpha= 0.05, power=9.80, large size effect f=0.40. Since I am not familiar with this procedure, these values came from http://www.statisticssolutions.com/manova-2-levels-and-2-dependent-variables/).
    Moreover, I tried to estimate the minimun sample for Wilcoxon signed-ranked test, but G-power requires to provide values for parameters I don’t really know.

    So, i need to ask you this: is there any test one can do with just 12 pre-questionnaires and 12 post-questionnaires with Likert-type questions, in order to have a clue about whether their didadctic intervention had any effect on students’ scores?

    Thank you very much.

    Reply

    • Dear Maria,
      I am not surprised that you will need to have more than 12 elements to perform MANOVA with any power. It is not likely that another test which is suitable will require a sample as small as 12.
      Regarding the minimum sample for Wilcoxon signed-ranked test, to get at least some idea of the sample size requirement use G*Power (or the Real Statistics Power and Sample Size data analysis tool) for the equivalent paired t test. It shouldn’t be a lot different from the sample size requirement for the Wilcoxon test.
      Charles

      Reply

      • Thank you very much, Charles.
        In order to use G-power for estimatating the minimun sample for Wilcoxon, I need to give info about tails (options: 1, 2) and parent distribution (options: normal, laplace, logistic, minARE), but I don’t really know what to choose. So, even if I keep the “default values” for the other parameters (effect size=0.5, a=0.05, power=0.95), I don’t know what to do with tails and parent distribution. Could you please give me a clue? Thanks again.

        Reply

        • Maria,
          Generally you should choose the 2 tailed test. I would choose the normal distribution, but see how much the sample size changes if you try the other values. As I said in my previous response, I would find out the sample size required for the paired t test and assume that the sample size required is probably similar to that value.
          Charles

          Reply

          • Dear Charles,
            Could you please tell me what you think about the following? Is it ok to procceed ths way?

            1. For Wilcoxon with 2 tails, parent distribution=normal, effect size=0,5, alpha=0,05, power (1-β error prob) = 0,3, G-power gives N=11. Is it ok to lower power so much? (0,95 became 0,3 in order to lower the sample at a convenient size).

            2. For t-test with 2 tails, effect size=0,5, alpha=0,05, power= 0,8, G-power gives a N=34. If I lower the power to 0,3, then N=11 as well.

            Thank you very much.

          • Maria,
            Power of 30% is quite bad. It means that you have a high possibility of a type II error.
            The best you can do is to increase the effect size, which means that you test will only find very large effects (not great either).
            Charles

  38. Dear Charles,
    What is the minimum number of questiionnaires one should have in order to perform MANOVA? Can they do the test with 12 pre/post questionnaires in case they have (a) one categorical independent variable (didactic intervention) with 2 occasions of measumeremnt (before and after), and (b) six dependent variables (the scores of the 5 sub-scales of the questionnaire that includes Likert-questions and the total score)?

    Thank you very much for your time,
    Maria

    Reply

      • Thank you very much, Charles. And something more. In the case I described before, namely if someone has 12 pre and 12 post- questionnaires with 6 dependent variables (=5 sub-scores of Likert questions groups+1 total score) and the unique independent variable is a didactic intervention, would it be a good idea to perform a Wilcoxon test (a) for each sub-score before and afer, (b) for the total score before and after, instead of performing MANOVA?
        Thank you very much once more.

        Reply

        • Maria,
          If there is a fair amount of correlation between the dependent variables, then MANOVA is generally preferred, but if there is little correlation then there isn’t any reason to do MANOVA. In this case you could perform a paired t test or if the assumptions for a t test are not met, then Wilcoxon’s signed ranks test.
          One other thing, you look at the following webpage since you seem to have a repeated measures test:
          Multivariate Repeated Measures
          Charles

          Reply

  39. Hi Charles,

    I know I have to use multivariate regression with my 1 dependent variables and 4 independent variables. All variables are correlated with the minimum number 0.3. Some says i need to use discriminate function analysis to analyze it completely. But i dont even familiar with it. I read that manova is the reverse of it. Can u advise me wether i can benefit manova from it? Thank you

    Reply

    • Hi Juliana,
      If you only have 1 dependent variable then you don’t need to use MANOVA. The correct tool depends on the specific questions you want to answer or hypotheses you want to test.
      Charles

      Reply

      • Thanks Charles,

        I need to create model/equation from it. Do you think multiple regression is enough? Adjusted R 0.834, F and P value less than 0.05. It looks ok right? ????????. Thank you in advance sir for your kind help.

        Reply

        • Juliana,
          I don’t have enough information to say for sure, but multiple regression may indeed be the way to go.
          Charles

          Reply

  40. Hello Professor !

    My objective is to study the impact of gender and income group (2 categorical predictors) on 5 continuous variables (factors obtained by PCA).

    I am using two-way MANOVA (using SPSS) for the same.

    I obtained statistical significance (p-value alpha.

    Interpretation:
    Factors differ significantly for different income group, while there is no significant difference between Factor for male and female.

    Am I using the right test?
    Is my interpretation correct?
    Please suggest. Thanks

    Reply

    • I realized that some how I missed some text in my earlier comment:

      I obtained statistical significance (p-value alpha).

      So for income group, what kind of post-hoc test I should apply? [If my approach and interpretation is correct]

      Reply

    • Learner,
      Since you have multiple dependent variables and multiple categorical independent variables, MANOVA seems to be a reasonable test to use.
      Without seeing your results, I cannot comment on whether your interpretation is correct.
      Charles

      Reply

      • Thanks a ton for your response.

        I was just worried about applying 2-way MANOVA as my response variables are uncorrelated (as, I’ve obtained them from PCA).
        Is this a problem? If yes, What are the alternatives for multiple response and predictor variables. Please suggest.

        I realized that there is some typo in my text again [I’ve written the results obtained by me]. I’ll try to learn and ask again, in case of any difficulty regarding interpretation.

        Reply

        • Learner,
          If the dependent variables are uncorrelated, then there really isn’t any point in using MANOVA. You might as well use separate ANOVAs (and/or their follow-up tests).
          Charles

          Reply

    • Irsalan,

      I show two types of follow up tests on the website: ANOVA and contrasts. The contrasts case is described on the webpage
      MANOVA Follow up using Contrasts

      I believe that you can modify the contrasts approach to create Tukey’s HSD test in the same manner as you do as a follow up to ANOVA.

      Charles

      Reply

  42. Dear Sir,
    I am trying to analyze and use post hoc test to find if there is a significant differences in the performances of four different multi class( three different classes) classifiers for single data set. From the literature, I understand an ANOVA followed by post will differentiate the classifiers. Which ANOVA should I use? Kindly help me.
    ?

    Reply

  43. Kindly suggest me best statistical method based on the following details.

    I want to analyze distribution of mosquitoes in six different locations based on the physico-chemical parameters, climatic variabilities, spatio and temporal variabilities.

    Reply

  44. Hi Charles,

    I want to compare change in tree volume with change in elevation. I also want to test if tree species is a factor, and if maybe a certain species is affected more at a specific elevation. I have further (possibly co-variates) i want to add in, but for now i want to run that analysis. Help please!

    Thanks

    Reply

  45. I have a fatigue questionnaire in my experiment with constructs like alertness, concentration difficulty, irritability etc. 15 subjects filled it out at four different times (T1, T2, T3 and T4) on two different days (i.e. Day 1 and Day 2). I am trying to see if there is any difference between the ratings at the four different times. Which ANOVA should I be using? Can you please help.

    Reply

    • Abdul,
      MANOVA and multiple regression are not the same. MANOVA is like ANOVA (which can have multiple independent variables, but only one dependent variable) but MANOVA can support multiple dependent variables. Multiple regression is related to ANOVA and it too supports multiple independent variables but only one dependent variable. Analogous to MANOVA is multivariate multiple regression.
      Charles

      Reply

  48. Hello, sir
    I wonder if I could get the right way to calculate multiple regression with two dependent variables. Does MANOVA substitute it?

    Reply

    • Getash,
      Multivariate regression is the tool that performs multiple regression with multiple dependent variables. I plan to add this to the Real Statistics Resource Pack and website shortly, probably sometime in January.
      Charles

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    • Excel does not have a MANOVA function or data analysis tool. If you install the Real Statistics Resource Pack you will be able to get access to various MANOVA functions and the Single Factor MANOVA data analysis tool. Installation is free.
      Charles

      Reply

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