What Is the Durbin Watson Test? How to Read and Handle It in SPSS
What Is the Durbin Watson Test?
You run a linear regression in SPSS, open the Model Summary table, and see a column called Durbin-Watson. The number usually falls between 0 and 4, but many guides only say that it should be close to 2 without explaining why. The Durbin Watson test, also called the Durbin Watson statistic or DW test, checks for first-order autocorrelation in the residuals of a regression model.
A residual is the difference between the actual value of the dependent variable and the value predicted by the model. When the residual for one observation is related to the residual for the next observation, the assumption that errors are independent is affected. This issue is more common with time-series data, data arranged in an order, or samples with a sequential structure.
The Durbin Watson value is written as d and is calculated from consecutive residuals:
d = Σ(e_t - e_(t-1))² / Σe_t²
Here, e_t is the residual for observation t. If consecutive residuals are almost unrelated, their differences are not excessively large, and d is usually close to 2. A low value suggests possible positive autocorrelation, while a high value suggests possible negative autocorrelation. This is a diagnostic indicator. It is not a measure that tells you whether a regression model is good or bad in every respect.
You can also review the guide to linear regression to place the Durbin Watson test correctly in your analysis workflow. DW is only one part of assumption checking, after you have identified the independent variables, dependent variable, and suitable regression model.
Why the Durbin Watson Test Matters in Quantitative Research
In linear regression, many inferential tests rely on the assumption that errors are independent of one another. If residuals are autocorrelated, the standard errors of the regression coefficients may be estimated incorrectly. As a result, the t, F, and p-value values may no longer reflect the strength of evidence for your research hypotheses accurately.
The Durbin Watson test helps answer this question: do the model residuals follow a consecutive pattern? For example, if positive residuals often appear next to one another and negative residuals also form clusters, DW may be lower than 2, suggesting positive autocorrelation. If the signs of the residuals change too sharply between observations, DW may be higher than 2.
You still need to read DW in the context of your data. In cross-sectional survey data, each row is usually one respondent, and the row order may only reflect the order in which the data were entered. In that situation, DW may still appear in the output, but the meaning of autocorrelation by row order needs to be interpreted carefully. If your data consist of monthly revenue, quarterly figures, or repeated observations over time, this check is usually more relevant.
DW does not replace the other checks. It does not tell you whether multicollinearity exists, assess whether the residuals are normally distributed, or test whether the error variance is constant. You need to examine those issues separately in the regression model. When you need to examine relationships among independent variables, see what is multicollinearity.
What Durbin Watson Value Is Acceptable?
A common way to read the statistic in a thesis is to check whether the DW value is close to 2. Some practical guides use a range from 1 to 3 as a simple diagnostic rule. This threshold is presented in Field's practical SPSS guide (Field, 2013). State clearly that this is an approximate interpretation rule, not an official DW table that applies in exactly the same way to every sample size and number of variables.
For a stricter conclusion, the Durbin Watson table must be based on the sample size n, the number of explanatory variables k, and the selected significance level. The table produces two bounds, usually written as dL and dU. When the observed value falls between the two bounds, the conclusion may be inconclusive. You should therefore avoid taking one fixed number and declaring every model acceptable.
| Value or checking range | Practical interpretation | Source or note |
|---|---|---|
| Close to 2 | The residuals tend not to show clear first-order autocorrelation | Practical interpretation rule according to (Field, 2013) |
| From 1 to 3 | Often treated as an acceptable range in many regression reports | (Field, 2013) |
| Less than 1 | Check for possible positive autocorrelation and review the data order | Diagnostic interpretation, requiring comparison with a DW table |
| Greater than 3 | Check for possible negative autocorrelation and review the data | Diagnostic interpretation, requiring comparison with a DW table |
Between dL and dU | The table gives an inconclusive result, so do not force it into an acceptable or unacceptable category | The DW table depends on n, k, and the significance level |
The phrase “Durbin Watson DW table” is often searched because readers want to compare the dL and dU bounds. Use the table that matches the number of observations and independent variables in your model. If the table you have does not match your research design, report the limitation instead of selecting an approximate table to make the result look better.
How to Read the Durbin Watson Test in SPSS Output
In SPSS, run Analyze > Regression > Linear. Move the dependent variable into Dependent and the independent variables into Independent(s), then select the Statistics button. Select Estimates, Model fit, Confidence intervals, and Durbin-Watson, then select Continue and OK.
SPSS places the DW value in the Model Summary table. You will not find this statistic in the Coefficients table, and you should not read it from the Sig. column for each independent variable. The Coefficients table answers questions about individual coefficients, while Durbin-Watson assesses the residuals of the regression model as a whole.
Illustrative output
The table below is illustrative output, not the result of a real study. Assume that the model has dependent variable Y and three independent variables, X1, X2, and X3.
| Model | R | R Square | Adjusted R Square | Std. Error of the Estimate | Durbin-Watson |
|---|---|---|---|---|---|
| 1 | 0.684 | 0.468 | 0.452 | 0.517 | 1.842 |
With Durbin-Watson = 1.842, the result falls between 1 and 3 under the practical rule from (Field, 2013). You can report that there is no clear sign of first-order autocorrelation in the residuals under the selected criterion. This statement does not mean that the model has met every assumption, because you still need to check multicollinearity, residual variance, and unusual observations.
When reading the output, check the correct Model row. If you run several models, each model may have a different DW value. Do not copy the value from an earlier run into a new results table. You should also save the output file for each version, especially after removing a variable or changing the order of the data.
A common mistake is to confuse the DW value with R Square, Adjusted R Square, or Sig. F Change. These three statistics concern explanatory power or model significance, while DW focuses on the independence of the residuals.
What to Do When the Durbin Watson Test Does Not Meet the Criterion
Before changing the model, verify that the issue comes from the data structure rather than a data-entry error. Follow the sequence below so that you do not remove variables arbitrarily.
Check the order and continuity of the data
Check whether the data are arranged by time, geographic area, respondent group, or questionnaire code. If you are analyzing cross-sectional data and the row order only reflects data entry, a low or high DW value should not be interpreted mechanically as a time relationship. Check for duplicate rows, repeated observation codes, and data that have been rearranged.
Check residuals and unusual observations
In the Linear Regression dialog box, select Plots and place *ZPRED on the X-axis and *ZRESID on the Y-axis. You can also choose to save Standardized Residual and Cook's Distance through the Save button. The residual plot can show clusters of points, trends, or observations that differ substantially from the others.
An unusual observation is not automatically incorrect data. Return to the questionnaire or data source, identify the reason, and record your decision. Deleting a row only because it makes the DW value look better gives you a weak explanation before the committee.
Consider omitted variables or model form
Autocorrelation can sometimes reflect an important explanatory variable that is missing from the model or a relationship between variables that has not been specified correctly. Return to the theoretical model and hypotheses instead of adding a variable only to move DW closer to 2. If the original model does not fit time-series data, basic linear regression may not be sufficient to handle that structure.
Use a method suitable for the data
With time-series data, you may need a more specialized procedure, such as a model with lagged components or an estimator with suitable standard errors. SPSS includes many procedures, but the procedure must be selected according to the data design and research objective. If your study is a cross-sectional questionnaire survey, discuss the issue with your supervisor before switching to a time-series model simply because DW is outside your preferred range.
Report the result honestly if it still does not meet the criterion
If the issue remains after checking the data, report the DW value, the criterion used, the limitation of the test, and the way you handled the issue. The committee is usually more interested in the logic behind the decision than in a number that has been made to look better. You can also review the linear regression model to check the related assumptions before writing the results chapter.
Distinguishing the Durbin Watson Test from Other Autocorrelation Tests
The Durbin Watson test focuses on first-order autocorrelation in the residuals and is usually read from the Model Summary table in linear regression. It is not a multicollinearity test. Multicollinearity occurs when independent variables are too strongly related to one another and is commonly assessed using VIF and Tolerance in the Coefficients table.
DW is also different from a heteroscedasticity test. Heteroscedasticity concerns changes in the spread of residuals across predicted values or explanatory variables. You can inspect the ZPRED and ZRESID plot, but you should not use DW to conclude that the residual variance is constant.
DW also differs from the Ljung-Box test and other autocorrelation tests used in different contexts. Each test has its own assumptions and interpretation. When your study uses time-series data, state clearly which test you used, because the sentence “autocorrelation was tested” does not tell the reader how it was tested.
If you are working through an exercise and want to compare the complete procedure, see the solved linear regression exercise. Reference material should help you understand how to read the tables. It should not become a reason to copy illustrative values into your own thesis.
Common Errors When Reading the Durbin Watson Test
The first error is claiming that “DW must equal 2.” A value of 2 is a reference point, not a mandatory condition. Real data rarely produce exactly 2, and a value different from 2 is not enough to conclude that the model is wrong.
The second error is using the range from 1 to 3 as an absolute rule. This range can be used for screening and practical reporting according to (Field, 2013), but the official table also depends on n, the number of independent variables, and the significance level. If the value falls in the inconclusive region, say so clearly.
The third error is reporting DW without saying which model it belongs to. When you have several models, place the DW value in a summary table, state the model number, and identify the variables included. This presentation helps the reader connect the result with the corresponding hypothesis and model.
The fourth error is removing an observation or variable only because the DW value does not look good. Every data-removal decision needs a verifiable reason, such as an entry error, an invalid questionnaire, or an influential observation that has been checked. Record the number of rows before and after processing so that the analysis trail remains clear.
The final error is writing an overly broad conclusion. An acceptable DW value does not mean that the model establishes causal relationships, has no multicollinearity, or supports every hypothesis. Separate each conclusion according to the statistic on which it is based.
Frequently asked questions
What is the Durbin Watson test and what is it used for?
The Durbin Watson test checks whether the residuals in a regression model show signs of first-order autocorrelation. A value close to 2 usually indicates no clear sign of autocorrelation, while a much lower or higher value requires further checking.
What Durbin Watson value is acceptable?
In many practical reports, the range from 1 to 3 is used as an acceptable range according to (Field, 2013). However, if you need to use a DW table, compare dL and dU based on the sample size, number of independent variables, and significance level. Do not use one fixed threshold for every study.
Is a Durbin Watson value of 1.2 acceptable?
A value of 1.2 falls between 1 and 3, but it is fairly close to the lower bound. You can report it under the practical rule if that is the criterion you selected, while also checking the DW table and reviewing the residual plot. The final conclusion depends on the data design, especially on whether the data have a time order.
Which SPSS table shows Durbin Watson?
SPSS displays this statistic in the Model Summary table, in the Durbin-Watson column. Run Analyze > Regression > Linear, open Statistics, select Durbin-Watson, and run the model. Do not read this statistic from the Coefficients table.
What should I do when Durbin Watson does not meet the criterion?
First, check the data order, duplicate rows, entry errors, standardized residuals, and highly influential observations. Then review omitted variables and the model form. Do not delete data or add variables only to move DW into the preferred range, because that decision needs a clear methodological reason.
Open your .sav file, record the Durbin-Watson value from the Model Summary table, compare it with your selected criterion, and save the output from that run separately. If you need to rerun the regression on your own data, DoThesis M4 analysis supports this step with SPSS and SmartPLS using your real data.