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

32 Responses to Studentized Range q Table

  1. Myra Villaflor Gutierrez says:

    good day. i have this little question. How can be the q critical value be computed without depending on the tukey’s distribution table? Is there an existing formula that can be used? what is it? thanks for your response :)

  2. Iris Jimenez says:

    How can i get the critical value if my df=42 and n=3, with alpha=0.05? I can see 40 and 60 but I don’t know how I can get the exact value for that? What is my critical value then? Thanks!

    • Charles says:


      I can offer you two choices:

      (1) interpolate the values in the table between the values for 40 and 60. Since 42 is a lot closer to 40 than 60, the appropriate value should be closer to the value in the table for 40.

      (2) Install the Real Statistics Resource Pack. You can then use either the QCRIT or QINV function. QCRIT will do the interpolation for you and QINV will directly calculate an estimated value for df = 42.


  3. 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.

  4. 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.

  5. hemn says:

    what mean of tukey HSD and tukey-b

  6. Lina Nur Hayati says:

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

  7. 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.


  8. hemn says:

    Second group of q tables 0.01 k=40

  9. hemn says:

    how found Second group of tables 0.05 k=40

  10. Adeniran Seyi says:

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

  11. 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.

  12. 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 😀

  13. 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.

  14. 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.

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