In the following tables n is the sample size and k is the number of independent variables. See Autocorrelation for details.
Alpha = .01
Alpha = .05
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?
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.
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.
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.
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
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
ok thank you so much .. that helpfull
How can I find DL and DU for n=48 with 4 independent variable
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:
How if I want to know the value for n = 665?
See the following webpage>
You will need to interpolate between the values in the table.
Hy charles, can I know how the table of durbin watson for n=204
reply my coment please 🙂
Please see the following website, which contains values for 200 and 210. You will need to interpolate to get the value at 204.
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.
See the following webpage
Please am still waiting for the answer to my question.
If a (one period) auto-correlation adjustment is made, does the adjustment count as an additional k (independent) variable in evaluating DW limits. Thanks
What sort of (one period) auto-correlation adjustment are your referring to? Are you referring to differencing?
If I want to know for n=41, how can I know value
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
Alternatively, you can use the Real Statistics functions DLowerCrit and DUpperCrit
Thank you, Charles!
I appreciate you spending time to have this important table available.
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?
One source is
thanks for the quick reply! When I click on the link, it required authorization. Do you know if there’s another source I could click on? Thanks again!
Olga, no I don’t.
Thanks for this!
Thank you for your excellent website.
Can I confirm that the k in durbin watson table excludes intercept.
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.
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.
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.
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