GATE ST common mistakes
GATE ST · Understand the traps and how to avoid them.
Treating a 'which of the following is NOT' or 'select the incorrect statement' item as a positive question and picking the first true-looking option, then moving on without re-reading the stem.
Under 3-hour pressure candidates pattern-match stems to familiar definitions and skip the negation, especially in multiple-select (MSQ) items where more than one option is true.
What to do instead
Before evaluating options, underline or mentally bold the negation word and restate the stem to yourself as a question ('Which statement is false?'). After choosing, re-read the stem once and confirm your choice answers the negated question. In MSQs, count how many options you believe are true and check that against the stem's wording.
Computing a confidence interval or test statistic but reporting the wrong quantity: giving the half-width instead of the full interval, giving the standard error instead of the standard deviation, or giving the variance instead of the SD.
The arithmetic is done correctly, so the candidate stops checking the target quantity; numerical-answer (NAT) items have no options to catch the mismatch.
What to do instead
Before computing, write the exact requested quantity in symbols (e.g., 'need s, not s^2') and circle units. After computing, do a dimensional/sanity check: an SD and a variance differ by a square root, a CI is symmetric about the estimate with length 2z*SE. Compare magnitude to the estimate to catch unit slips.
Using a z critical value or normal approximation where the sample size is small and the population variance is unknown, instead of the t distribution with n-1 df.
Most practice problems involve large n, and the t and z values are close there, so the distinction is never reinforced; under time pressure the familiar z value is recalled first.
What to do instead
Adopt a decision checklist for every inference problem: known sigma and normal population -> z; unknown sigma, normal population -> t with n-1 df; large n -> z acceptable. Memorize t critical values for df = 5, 10, 20 at 5% and 1% so the difference is visible and you notice when you are using the wrong one.
Applying a formula (Bayes, inclusion-exclusion, variance of a sum, MGF of a sum) without first checking the independence or identical-distribution assumption it requires.
Formulas are memorized as symbols and the conditioning clause ('provided X and Y are independent') is dropped; exam items deliberately test dependent or non-identically-distributed cases.
What to do instead
For every probability/expectation calculation, write the assumption list next to the formula before substituting: independence, identical distribution, disjointness, finite mean. If the assumption fails, switch to the general form (Cov term in Var(X+Y), P(A∩B) = P(A)P(B|A), inclusion-exclusion). Practice by constructing one counterexample per formula where the assumption fails.
Confusing estimator properties: claiming an estimator is unbiased because it is consistent, or consistent because it is unbiased, and mixing MSE with variance.
The three properties are taught together and share the 'good estimator' connotation, so candidates collapse them into one idea; MSE = Var + Bias^2 is often reduced to 'variance'.
What to do instead
Write the three definitions side by side and attach a distinct counterexample to each: unbiased-but-inconsistent (first observation of a sample as estimator of the mean), biased-but-consistent (n/(n+1) times sample mean), and MSE decomposition. When a question asks about a property, state the definition formally before evaluating the estimator.
Losing track of degrees of freedom or of the correct test statistic in ANOVA, chi-square tests, and regression: using k instead of k-1, or n instead of n-p-1.
Each procedure has its own df bookkeeping, and under exam pressure the formulas blur together; the arithmetic then proceeds correctly on the wrong df.
What to do instead
Before computing, write the df formula for that specific procedure in words (one-way ANOVA: groups minus one and total minus groups; chi-square independence: (r-1)(c-1); regression error: n minus number of estimated parameters). Verify df sum correctly (between + within = total) as an arithmetic check.
Reading a regression or ANOVA output table incorrectly: taking the standard error column as a t statistic, ignoring the sign of a coefficient, or misreading p-values as probabilities that the null is true.
Output tables are dense and look familiar, so candidates grab the first plausible number; the p-value misinterpretation is a widely held misconception reinforced by loose everyday language.
What to do instead
Reconstruct the table from first principles for one practice dataset: coefficient / SE = t, t^2 = F for a single predictor, and p-value = P(observing data at least this extreme | H0 true). When reading any table, label each column in your own words before using a number, and check sign and magnitude against the model's meaning.
In hypothesis testing, stating the conclusion as 'we accept H0' or as 'there is no effect', and failing to distinguish significance level from p-value.
Everyday phrasing treats non-rejection as proof of the null, and the numeric proximity of alpha and p encourages conflating them.
What to do instead
Use the fixed sentence template: 'At the alpha level, there is insufficient evidence to reject H0; we do not conclude H0 is true.' Define alpha as the pre-set Type I error rate and p as the tail probability under H0, and state both roles explicitly in any written answer. In MSQs, reject options that say 'accept H0' or 'prove H0'.
In linear algebra and multivariate questions, computing eigenvalues, determinants, or ranks correctly but then misinterpreting them: calling a matrix invertible when an eigenvalue is zero, or confusing rank with dimension of the null space.
The computation consumes the available time and the conceptual step is rushed; the rank-nullity relation is remembered as a formula rather than as a meaning.
What to do instead
Attach a one-line meaning to each quantity before computing: zero eigenvalue -> singular; rank = number of linearly independent columns = dimension of column space; nullity = n - rank. After any eigenvalue computation, immediately check the product equals the determinant and the sum equals the trace.
Spending too long on one difficult NAT item and then rushing the remaining questions, leaving easy marks unattempted or making transcription errors in the final minutes.
GATE ST has no negative marking for NATs in the current pattern but does penalize wrong MCQs, and candidates over-invest in a single hard derivation because partial credit feels within reach.
What to do instead
Adopt a two-pass strategy: first pass solves everything you can in under 90 seconds each and flags the rest; second pass returns to flagged items with a hard time cap, then a final 10 minutes for transcription checks. Practice with timed mock sections to calibrate the 90-second threshold and to rehearse abandoning a problem without regret.