Studentized Range q Table

The following tables provide the critical value for q(k, df, α) for α = .10, .05 and .01 and values of k up to 20. Following these tables, we provide additional tables for α =.05, .025, .01, .005 and .001 and values of k up to 40, but with less granularity for higher values of df. See Unplanned Comparisons for ANOVA for more details.

First group of tables

Alpha = 0.10

Studentized Range q, alpha = .10 Alpha = 0.05

Studentized Range q, alpha = ..05

Alpha = 0.01

Studentized Range q, alpha = .01Second group of tables

Alpha = 0.05

 Studentized Range q, alpha = .05Alpha = 0.025

Studentized Range q, alpha = .025

Alpha = 0.005

Studentized Range q, alpha = .005Alpha = 0.001

Studentized Range q, alpha = .001

28 Responses to Studentized Range q Table

  1. Sonja Ahlberg says:

    Can you please tell me what the Q statistic is for alpha 0.05, df 21 and k 3? The numbers are so small I’m not sure I am reading them correctly.

  2. Sarthak says:

    This question is regarding to one of the components of Tukey’s HSD procedure which is studentised range statistic i.e.q(k, df, α). Here I have k=9, df=441 and α=0.05.So in order to find q, I need to refer the critical values table and look for k=9 and df=441. But all the tables I get have values of df till 120 or 240 and then infinity. Since i am looking for df=441 which row of df should I use: 240 or Infinity? Hope my conveyance of the question is clear to you. Please help. Thanks

    • Charles says:

      After 240 you should use infinity. In the next release of the software you will be able to enter df = 441, but there will only be a small difference between that value and the value for infinity.

  3. nano says:

    Can you please tell me what the Q statistic is for two way anova (25×2), alpha 0.05, and df 200 ? Thx :D

  4. binxu says:

    Can anyone please tell me what the Q statistic is for alpha 0.05, df 75 and k 23? I have not found it in any reference table.

  5. Adeniran Seyi says:

    how can i get df 45, i can only see 40 and then 60. thanks

  6. hemn says:

    how found Second group of tables 0.05 k=40

  7. hemn says:

    Second group of q tables 0.01 k=40

  8. Sarah says:

    Can someone please tell me what the Q statistic is for alpha=0.05, df=156 and k=4? I can’t find it in the reference table.

    • Charles says:


      You would need to interpolate between the table values for df = 120 and df = 240. Q-crit for df = 120 is 3.685 and the Q-crit for df = 240 id 3.659. A linear interpolation would give the value 3.6772, which can be calculated using the Real Statistics formula =QCRIT(4,156,0.05,2).

      The Real Statistics formula =QINV(0.05,4,156,2), which does not use the table, will usually give a more accurate answer, which in this case is 3.6726.


  9. Lina Nur Hayati says:

    thanks a lot prof. i can finish my task about this :).

  10. hemn says:

    what mean of tukey HSD and tukey-b

  11. Gurumani says:

    Thank you for your service! I am interested to known about ANOVA post-hoc Q test. Is it possible to run this test for more than 20 treatments (groups)? Where do I get a Q table that provides values for a>20? Can I calculate table Q value? How? Is there an “infinite a” Q value? Will you please help me?

    • Charles says:

      The Real Statistics Resource Pack provides the function QINV(p, k, df, tails) which calculates the table value for any value of k (= # of groups), even for k > 20. The values of Q for infinite df are given in the table on the referenced webpage. You can download the Real Statistics Resource Pack for free from the website.

  12. Jess says:

    Are these tables also applicable to games-howell post hoc tests?
    Currently my df values are below 4 and a similar table I found only went to 5 as a minimum, which proved hard finding the correct Q value.
    If so, when choosing the the Q value for example if the df was 4.65, would 4 or 5 on the table be most accurate?
    I understand with games howell, you must first calculate the df, between each pair, followed by the qcrit value for each pair, before using in the final equation (see link): to get the minimum significant difference.

    Can someone please confirm if this equation is correct?

    I followed the guidelines from this website:

    However in the final calculation of minimum significant difference for games howell, (down the bottom of the webpage) I noticed in place of their qcrit, they used the calculated df value instead, despite in the formula saying q crit. I wonder if this is a mistake, or if this is what one is meant to do.

    Any guidance would be greatly appreciated and if anyone has a better calculations example for games-howell please share.

    Warm regards, Jess

    • Charles says:

      Yes, these tables are applicable to Games-Howell. If your df is between 4 and 5 you can interpolate between the values in the table.
      Sorry but I haven’t had time to look at the references you provided regarding your other questions.

      • Jess says:

        Dear Charles,
        Thank you kindly for that!
        I have since downloaded the program onto my mac and have attempted to use QCRIT formula, however every time I type the function with the values, separated by commas, it shows up as #NAME and says ‘compile error in module: look up’.
        Any guidance please?

        • Jess says:

          Apologies the message is #VALUE!, not name that shows up.

        • Charles says:

          I have just checked on my Windows.based computer and the QCRIT function works fine. I can’t think of any reason why it wouldn’t work on the Mac, but
          unfortunately, since I don’t own a Mac I can’t test the QCRIT on the Mac until the next time I borrow a Mac from a friend. In any case, you can try to use the QINV function which estimates the value of the inverse Studentized Range value without doing a table lookup.

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