224 thoughts on “Durbin-Watson Table”

  1. Morning mr charles, May i know what is the Dupper and Dlower critical value for:
    n=206, k=12, alpha=5%

    because my computer had a problem when installing real statistics,
    thank you so much for your help

    Reply

  2. Hello,

    I used the dLowercrit and dUppercrit but I’d like to know the calculations behind the formula. How are the critical value calculated? I don’t find anything in the internet regarding this. Could you send me the formula or where I can look for that?

    Thanks

    Alex

    Reply

  3. May i know what is the upper and lower critical value for:
    a) n=50, k=8, alpha=2.5%
    b) n=60, k=6, alpha= 2.5%
    c) n=100, k=20, alpha= 2.5%

    Reply

    • Hello Ben,
      I will try to expand the table to include higher values for n.
      In the meantime you can use the Real Statistics DLowerCRIT and DUpperCRIT functions. They are available when you download the Real Statistics software (it is free).
      Glad that you are getting value from the website.
      Charles

      Reply

  7. Hi Charles,

    Thank you very much for your introduction to the Durbin-Watson Table; this is very useful.

    Can you kindly please let me know dl and du for 250 samples, 3 independent variables, and alpha 0.5?

    If it is possible, can you please also show me the formula for dl/du calculation?

    Thanks a lot.

    Reply

    • Hi Albert,
      I assume you mean alpha = .05. The values are 1.76851 and 1.81706.
      These values are based on a table of critical values, probably compiled via simulation. It is likely that there is no simple formula.
      Charles

      Reply

  9. Hi Charles,

    Would you help me to get dl and du for 134 samples, 12 independent variables, and alpha 0.5?

    k would be 12 or 11?

    Thank you, I love your website!

    Reply

    • Hi Laura,
      Thank you for your kind words about the website.
      k = 12
      To get the dl and du values just interpolate between the values in the table for 100 and 150 (125 would be about half-way between these values, and so favor 150 slightly more). See Interpolation
      Alternatively, you can use the Real Statistics DLowerCRIT and DUpperCRIT functions.
      Charles

      Reply

  13. my data size 115 alpha =0.05 can you help me to find du and dl i can’t find it because i don’t have real data i just know number of data and d.w. = 1.8571

    Reply

  14. Halo data saya memiliki 279 pengamatan dan 6 variabel independen. Untuk nilai dU dan dL nya berapa ya? Saya ingin tahu cara penghitungan menggunakan Excel. Terima kasih.

    Reply

  16. Halo,
    data saya memiliki 204pengamatan dan 5 variabel, bisa tolong beri tahu saya nilai dl
    dan du. Saya mencari perangkat lunak tetapi saya tidak bisa menemukannya.

    Reply

    • The table values for a sample of size 200 for 5 variables at alpha .05 are 1.623 and 1.725. The value at n = 204 won’t be very different.
      If you download the Real Statistics software you can use DUpperCRIT and DLowerCRIT to get the values you are looking for.
      Charles

      Reply

  17. Hi, my data have 15 observations and 7 variables, could you please tell me the values of dl e du. I looked for the software but i couldnt find it.

    Reply

  18. Hi, my data have 228 observations and 2 variables, could you please tell me the values of dl e du. I looked for the software but i couldnt find it.

    Reply

    • Hello Davi,
      If alpha = .05 and k = 2 then you can find the values that you are looking for using the formulas =DLowerCRIT(228,2) and =DUpperCRIT(228,2). These take the values 1.765387 and 1.800752.
      Charles

      Reply

  19. hi the nummber of observation of my data are 146 and i have 9 independent variables so pls tell the du and dl of my data by durbin watson test

    Reply

  20. if the sample number is 231, the same as the number k = 2, what is the value of dL with the same dU? for the alpha 5%

    Reply

  21. hey hello..
    my sample size is 300 with one independent variable , but in durbin watson table there is 200 obs then according to my sample size what is my dL and Du in it?
    kindly reply

    Reply

    • The Real Statistics software can calculate values up to 2,000 observations using the DUpperCRIT and DLowerCRIT functions. For 300 observations, one independent variable and alpha =.05, the lower and upper critical values are 1.80398 and 1.81375.
      Charles

      Reply

  22. Hi,

    I have a sample size of 3019 do I take n=200? or is there a way that I can obtain the value for n=3019, please?

    Thank you in advance

    Reply

    • Maria,
      Unfortunately, the largest tables that I have seen only go up to a sample size of 2,000. This is higher than 200 shown in this table, but still less than n = 3019. The Real Statistics DLowerCRIT and DUpperCRIT handle values up to n = 2,000. E.g. for n = 2000 with 3 independent variables and alpha = .05, dL = 1.92347 and dU = 1.92947.
      For higher values you need to use a normal approximation. For n > 200, when the null hypothesis that there is no serial correlation is true the test statistic z = (2-d)*sqrt(df)/2 has a standard normal distribution, where df = n-k-1 (n = sample size and k = # of independent variables) and d = Durbin-Watson statistic. Thus, if |z| > z-crit at alpha/2, then you reject the null hypothesis (two-sided test).
      I will eventually add this to the website, but for now if you need more information, you can look at the following technical paper:
      Lee, M-Y. (2016) On the Durbin Watson statistic based on a Z-test in large samples, Int. J. Computational Economics and Econometrics, Vol. 6, No. 1, pp.114-121.
      Charles

      Reply

  23. Good Morning,

    I have three predictors, a sample size of 196 and the sig level of 0.05.
    After running analysis on SPSS, the Durbin-Watson stat is 2.00. I would like to know the dL and dU critical values. I would also like to know if autocorrelation has been met.

    Please could you assist?

    Reply

  24. Good Morning,

    Please guide me, I have a sample of 196. The Durbin Watson statistic is 2.00. There are three predictors. Is autocorrelation present with reference to dL and dU?

    Reply

    • Ishtiaq,
      For values larger than those shown in the table, you can use the Real Statistics DLowerCRIT and DUpperCRIT functions, as described at
      Durbin-Watson Test
      In any case, for 3 predictors, sample size of 196 and alpha = .05, dL = 1.7352 and dU = 1.79731.
      Charles

      Reply

  25. hi , please guide me. i have 200 + sample. have done questionnai survey on 5 point likert scale. Dw is 1.4 .Does this represent insignificance and what to do to sort this matter as the data is collected one point in time. alpha=5%
    regards

    Reply

  27. Hello charles, I have 31 obversations, 3 parameters p=5% and DW =1.3 How could i know that my model is suffering serial correlation. Noted is time series

    thank you.

    Reply

    • Eronika,
      I have not seen any tables that have more than 20 independent variables.
      Perhaps the following is a property of the Durbin-Watsin statistic can be used instead: For large n, the following is true d ~ N(2,2/√n). In this case, the normal approximation of the critical value d-crit is NORMINV(α,2,2/SQRT(n)). Values of d < d-crit indicate a significant autocorrelation. Charles Charles

      Reply

  31. Hi Mr. Charles,
    I want to ask you something. If n=100 , k=4 and DW statistics is 2.310, is there an autocorrelation? how to determine it? thanks

    Reply

  34. Hy Charles,
    thats very great articles.
    but I want to ask you something.
    My teacher give me some homework, and there’s n >200. how if i want to know the value from n = 240?

    thanks before.

    Reply

  35. Hi Charles,

    I have data of 1.176 households over 13 weeks in my dataset, which makes 25.288 lines of data. I have 22 explanatory variables in my model + an intercept. My DW statistic is 1.511.
    How can I test whether autocorrelation is an issue?

    Thanks,
    Mark

    Reply

    • Diva,
      Here are the values for 1300 and 1350. You will need to interpolate to get the value for 1346 (although obviously it will be pretty close to the value for 1350). I assume that alpha is .05 (and not .5) and that 3 variables means in addition to the constant term.
      n = 1300: dl = 1.90420 and du = 1.91345
      n = 1350: dl = 1.90607 and du = 1.91498
      You can also use the Real Statistics functions DLowerCrit and DUpperCrit.
      Charles

      Reply

  37. Charles,

    I have a time sequence of 48 numbers (quarterly crime stats in fact). DW test statistic calculates as 1.632. The alpha=5% lower and upper bounds for k=1 n=48 (interpolated) are 1.492 & 1.577. As d is > than du there is failure to reject the null of no auto-correlation. When checking against the alpha=1% bounds the interpolated lower and upper bounds are 1.310 & 1.392. d is now even farther from the upper critical value. However as the 1% test is a more rigorous test, I would have intuitively thought that the 1% upper bound would move towards the value of 2 (no auto-correlation) rather than away from it. Why is the 1% test less demanding than the 5% one for a DW test of a hypothesis?

    Joe

    Reply

    • Joe,
      When alpha = 1% it should be easier to retain the null hypothesis than when alpha = 5%. This is indeed the case.
      When alpha = 1% it should be harder to reject the null hypothesis than when alpha = 5%. This is indeed the case.
      Charles

      Reply

  38. what is the dl and du for 258 observations with 40 independent variables at 5%, noting that the 32 of these 40 idependent variable are dummy variables used for the fixed effect model.

    Reply

    • Sawsan,
      I have not seen any tables of critical values with more than 20 independent variables. I will look into creating an approximation for such critical values.
      Charles

      Reply

  39. can you help me to explain how to interpolate for n=205?
    i have read your link about it, but i still don’t understand

    Reply

    • Merin,

      You won’t be able to interpolate for values of n larger than 200 since the table provided on the website only goes up to n = 200.

      The following are the table values for n = 210 and alpha = .05. You can now interpolate between n = 200 and n = 210. In fact, the linear interpolations are simply the average of the values for n = 200 and n = 210 for any given value of k

      n k dL dU
      210 1 1.76445 1.78358
      210 2 1.75483 1.79326
      210 3 1.74513 1.80305
      210 4 1.73537 1.81295
      210 5 1.72554 1.82294
      210 6 1.71563 1.83305
      210 7 1.70566 1.84325
      210 8 1.69561 1.85355
      210 9 1.6855 1.86394
      210 10 1.67532 1.87445
      210 11 1.66508 1.88505
      210 12 1.65478 1.89574
      210 13 1.64441 1.90653
      210 14 1.63398 1.91742
      210 15 1.62348 1.92839
      210 16 1.61293 1.93947
      210 17 1.60232 1.95063
      210 18 1.59165 1.96188
      210 19 1.58094 1.97323
      210 20 1.57015 1.98467

      Charles

      Reply

    • Zhyan,
      This depends on the alpha value, but if alpha = .05, then the table has values for n=45 and n=50 and you will need to interpolate between these values to get the answer you are looking for. See the following webpage for details abouit interpolation:
      Interpolation
      Charles

      Reply

  43. please i have TTF- TIME TO FAILURES values as follows; 28,52,42,8,14,13,47,38,25,12,50,42. How do i know my n and k so to check on DW table for du and dl.
    Thanks

    Reply

  44. If a (one period) auto-correlation adjustment is made, does the adjustment count as an additional k (independent) variable in evaluating DW limits. Thanks

    Reply

    • Brad,
      What sort of (one period) auto-correlation adjustment are your referring to? Are you referring to differencing?
      Charles

      Reply

    • Aditya,
      You need to interpolate the values in the table between the entries for 40 and the entries for 45. This is explained on the webpage
      Interpolation
      Alternatively, you can use the Real Statistics functions DLowerCrit and DUpperCrit
      Charles

      Reply

  47. Hi Charles,

    thank you for all the info on this website!
    I was wondering where you got those tables from? I noticed that in Durbin & Watson’s paper from 1951 (Testing for serial correlation), they only go up to an N = 100 (and I am particularly interested in higher N’s). Is there another paper that I have been missing?

    Thank you!

    Olga

    Reply

    • Hi Cheng,
      The tables are for the case where there is an intercept, but k does not include the intercept. Thus if k = 2, there are 2 independent variables plus an intercept.
      Charles

      Reply

  50. Dear Dr. Zaiontz. I was wondering, how to interpret bounds for Durbin-Watson test (dU, dL) if dU is greater than 2.0. I know that it is an extreme case, but just want to know…

    For example, for alpha=0.01 if n=13 and k=8 than dU=3.182, dL=0.090. Then 4-dU=0.818, 4-dL=3.91… Does it mean that between 0.090 and 3.190 test is inconlusive? It is quite strange situation, I know that there is plenty of tests better than Durbin-Watson one, but it is nice to know such details.

    Love your website (thank you!) and your nice Slavic surname.
    Greetings from Central Europe.

    Reply

    • Good to hear someone from Central Europe and thanks for your kind words about the website.
      The bounds for the Durbin-Watson test are indeed strange. If the test produces a value between dL and dU, i.e. between .818 and 3.10 in this case, then yes the test is inconclusive.
      Charles

      Reply

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