Which test? The Test Atlas

Every test in this module, 29 of them, with what it looks for. Filter by the kind of problem, or search by a name or a symptom, and open a card for the null hypothesis, the statistic and its distribution, how to decide, and what to do next. The last line of each card links to the lesson that teaches it.

Four questions sort any test: what is the null? (usually that nothing is wrong, but KPSS and Farrar-Glauber differ in what the null states), what does rejecting mean?, what distribution gives the cutoff? (t, F, chi-square, or a special table such as Dickey-Fuller’s), and what do I do next?

The same material turned round: what you see, and the test that looks into it. The last column is the lesson that teaches it.

Ten symptoms, one at a time. The reason under each is the rule to keep.

Do two groups, or two periods, follow the same regression line? Fit the regression once to everyone (the restricted model: one set of coefficients) and once to each group separately (the unrestricted model: two sets). If the separate fits reduce the residual sum of squares by more than chance would, the groups differ. That is an F test of the kind lesson 3 taught, with k restrictions, one for each coefficient (the intercept included) being forced equal:

The exam’s version lists the steps: run the pooled regression and keep its residual sum of squares; run the two sub-sample regressions and keep both; compute F; look up the critical F; do not reject the null if the calculated F is below it. That order, with the decision rule last, is the answer to UGC NET December 2023 Q81, and it is the order in which the lab below displays its table.

In the survey the lab splits the households three ways and fits three equations. Try each combination before reading on.

For earnings on schooling, splitting by town and village gives F = 16.61 on 2 and 596 degrees of freedom (p < 0.0001), and splitting the file into halves gives F = 1.47 (p = 0.23). The first reflects the survey’s real design (the town’s earnings sit higher at the same schooling, with the same true slope). The second is the control: the file is in no particular order, so there is no break to find.

The same test with dummies. Add a dummy for the second group and its interaction with every regressor to one pooled regression, then test that all of them are zero with the F test for restrictions. The statistic is identical to the Chow F, as the two last cells of the lab show. The dummy version is the one to use when you want to know which coefficient moved (lesson 5), or want robust standard errors.

Lesson 2 said the classical assumptions need no normality for OLS to be the best linear unbiased estimator, and that normal errors are needed for exact t and F distributions in small samples. How do we check? Two common tests, both with the null hypothesis that the errors are normal:

• Jarque-Bera measures the residuals’ skewness S (zero for a normal) and kurtosis K (three for a normal) and adds up the departures. It is chi-square with two degrees of freedom under the null, so the 5% cutoff is 5.99.
• Shapiro-Wilk compares the ordered data with the order statistics a normal sample would give. It is a better choice in small samples, and is the other correct answer in GATE 2023 Q41.

Try the lab with the survey’s residuals (normal by construction, so they should pass), then with the three simulated shapes, and watch how the verdict and the rejection rate depend on the sample size.

The table gives the share of 1,000 samples in which a 5% Jarque-Bera test rejects normality, by the true shape and the sample size.

Read down the first row: with truly normal errors the test should reject 5% of the time, and it does so only in large samples, because the chi-square cutoff is a large-sample approximation. Read down the others: it finds a skew very quickly, heavy tails more slowly, and light tails (the uniform) slowly indeed. A pass is therefore weak evidence of normality in a small sample, and normality matters most exactly there.

The questions on methodology ask for the order of the steps from theory to policy. The standard list, in the order a textbook such as Gujarati’s Basic Econometrics gives it:

An exam item may list only some of these, as UGC NET June 2026 Q73 does (theory, mathematical model, econometric model, data, hypothesis testing). The order is what counts: theory first, then the mathematical form, then the statistical form with its error term, then data, then estimation and testing.

Matching lists are a regular format in UGC NET, and they appear in CUET and JNU too. They are quick when you have the atlas in your head, and hard to guess. Two habits help. Anchor on the pair you are sure of (Durbin-Watson with autocorrelation, say) and strike the options that disagree. Watch for the near-synonym trap: Breusch-Godfrey and Durbin-Watson both test autocorrelation, but one is “general”; White is the general test of heteroscedasticity and Goldfeld-Quandt is not.

One item, UGC NET June 2026 Q38, prints “Cornbetch alpha” for what is plainly Cronbach’s alpha, a measure of the internal consistency of a survey scale, and pairs it with “rationality of data”. The other three pairs are certain (Goldfeld-Quandt with heteroscedasticity, the F test with overall significance, Augmented Dickey-Fuller with stationarity), so the first pair is fixed by elimination and the key follows. Questions that pair a cross-tabulation, a contingency table or an F test for several means with a test belong to the statistics modules as well.

The hardest questions of the module, from the Delhi School, are collected in lesson 18.