Non-Parametric Methods MCQs 2026

Non-parametric methods are called distribution-free because they

1. Amake fewer assumptions about the population distribution shape✓
2. Balways assume perfect normality✓
3. Crequire known variance only✓
4. Duse only parametric t-tests✓

Non-parametric tests are preferred when

1. Asample size is huge and normality holds✓
2. Bdata are ordinal or normality is doubtful in small samples✓
3. Conly interval data with exact normality✓
4. Donly when means are equal✓

The sign test uses

1. Aonly the direction of differences relative to a hypothesized median✓
2. Bfull magnitude rankings always✓
3. Cnormality of differences✓
4. Dthe F-distribution✓

Wilcoxon signed-rank test is appropriate for

1. Atwo independent samples always✓
2. Bmore than three independent groups as first choice✓
3. Conly categorical frequency tables✓
4. Dpaired observations on a continuous or interval scale✓

Mann–Whitney U test (Wilcoxon rank-sum) compares

1. Apaired differences only✓
2. Btwo independent samples using ranks✓
3. Cthree or more means with F-test✓
4. Donly proportions in a 2×2 table✓

Runs test examines

1. Awhether the sequence of observations is random✓
2. Bonly central tendency of two groups✓
3. Conly regression slopes✓
4. Donly seasonal indices✓

Kolmogorov–Smirnov test compares

1. Aan empirical distribution to a specified distribution or two empirical distributions✓
2. Bonly means of two groups✓
3. Conly variances with F✓
4. Donly correlation coefficients✓

Compared with parametric tests, non-parametric tests are generally

1. Aalways more powerful✓
2. Bless powerful when parametric assumptions are met✓
3. Cidentical in power always✓
4. Dunusable with ordinal data✓

The one-sample sign test can test whether

1. Apopulation variance equals zero only✓
2. BPearson r equals one✓
3. Cblock effects are zero✓
4. Dthe population median equals a specified value✓

Wilcoxon signed-rank test requires

1. Aperfect normality always✓
2. Bindependent groups✓
3. Conly nominal categories✓
4. Dsymmetric distribution of differences for testing the median difference✓

Mann–Whitney U and Wilcoxon rank-sum test are

1. Adifferent tests with unrelated statistics✓
2. Bonly for paired data✓
3. Cequivalent for two independent samples✓
4. Donly parametric alternatives✓

In rank tests, ties are handled by

1. Adropping tied values always✓
2. Bassigning rank 1 to all ties✓
3. Cconverting ties to missing data✓
4. Dassigning average ranks to tied observations✓

Runs test for randomness counts

1. Aonly the median✓
2. Bonly SS_between✓
3. Cthe number of runs of identical symbols in a sequence✓
4. Donly Laspeyres weights✓

Too few runs in a sequence suggests

1. Aperfect randomness✓
2. Bnegative correlation only✓
3. Cpositive serial dependence or clustering✓
4. Dhomoscedasticity✓

The two-sample Kolmogorov–Smirnov test detects

1. Aonly a difference in means✓
2. Bonly equal variances✓
3. Conly linear correlation✓
4. Dany difference between two distribution functions✓

One-sample K–S test compares data to

1. Aonly another sample always✓
2. Ba fully specified theoretical distribution✓
3. Conly regression residuals without a model✓
4. Donly ANOVA tables✓

Empirical distribution function Fₙ(x) is

1. Aalways a normal CDF✓
2. Bthe Pearson r formula✓
3. Cthe step function giving the fraction of sample ≤ x✓
4. Dthe Laspeyres index✓

Parametric two-sample t-test assumes

1. Aapproximately normal populations with equal or handled variances✓
2. Bonly ordinal ranks✓
3. Conly zero sample size✓
4. Dno independent observations✓

Sign test loses information compared with Wilcoxon signed-rank because it

1. Aignores magnitudes of differences✓
2. Buses ranks of absolute differences✓
3. Crequires normality✓
4. Duses two independent samples✓

For large samples, Mann–Whitney U can be approximated by

1. Aonly χ² with one df always✓
2. Ba normal distribution✓
3. Conly the sign distribution✓
4. Donly Fisher index✓

Kruskal–Wallis test extends rank methods to

1. Apaired blocks only✓
2. Bthree or more independent groups✓
3. Conly two categories✓
4. Donly time-series trend✓

Median test is

1. Aidentical to Pearson regression✓
2. Bthe same as two-way ANOVA always✓
3. Ca parametric z-test on means✓
4. Da crude non-parametric comparison using counts above/below a common median✓

Non-parametric methods are robust to

1. Aall design flaws✓
2. Black of any data✓
3. Coutliers relative to mean-based parametric tests✓
4. Dperfect multicollinearity in regression✓

Ordinal measurement suits

1. Arank-based non-parametric analysis✓
2. Bonly ratio-scale physics quantities always✓
3. Conly meaningless labels without order✓
4. Donly geometric index numbers✓

Exact p-values in small samples for sign and Wilcoxon tests come from

1. Aenumerating the null distribution of the test statistic✓
2. Balways normal tables only✓
3. CLaspeyres formula✓
4. DANOVA F tables only✓

Permutation (randomization) tests share with non-parametrics the idea of

1. Aassuming perfect normality✓
2. Busing only index relatives✓
3. Cignoring the data✓
4. Dinference without strict distributional formulas✓

Hodges–Lehmann estimator associated with Wilcoxon signed-rank estimates

1. Aonly the sample mean✓
2. Bthe median of pairwise averages of observations✓
3. Conly the sign count✓
4. Donly block means✓

Zero differences in Wilcoxon signed-rank are typically

1. Aassigned the highest rank always✓
2. Btreated as infinite✓
3. Cdropped from ranking✓
4. Dconverted to missing blocks✓

Mann–Whitney U statistic is based on

1. Aonly signs of paired diffs✓
2. Brank sums of one sample relative to the other✓
3. Conly squared residuals✓
4. Donly seasonal ratios✓

K–S test statistic D equals

1. Athe mean difference only✓
2. Bthe product of variances✓
3. Cthe correlation r✓
4. Dthe maximum absolute difference between two CDFs✓

Choosing sign test over Wilcoxon signed-rank trades

1. Amore power always✓
2. Bfewer assumptions for less power when symmetry holds✓
3. Cparametric normality requirement✓
4. Dpaired independent samples✓

Non-parametric correlation for ranks is

1. APearson r on raw values only✓
2. Bthe F-ratio✓
3. CSpearman ρ✓
4. DLSD critical value✓

χ² test on contingency tables is

1. Aidentical to Mann–Whitney✓
2. Ba regression method✓
3. Can index number✓
4. Dnon-parametric in the sense of not assuming normality of cell counts✓

When normality clearly holds and sample size is adequate, parametric tests are usually

1. Apreferred for higher power✓
2. Bavoided always✓
3. Cless powerful than sign test✓
4. Dunrelated to efficiency✓

Runs test null hypothesis is

1. Ameans are equal across groups✓
2. Bthe sequence is random with given proportion of symbols✓
3. Cslope is zero✓
4. Dindex is 100✓

For skewed income data with outliers, comparing medians via Mann–Whitney may be

1. Aless meaningful always✓
2. Bidentical to comparing means always✓
3. Cmore representative than a t-test on means✓
4. Dinvalid on interval scale✓

Order statistics are central to

1. Aonly CRD blocking✓
2. Bonly Laspeyres weighting✓
3. Conly multiple regression VIF✓
4. Drank-based non-parametric procedures✓

Large-sample z approximation for sign test uses

1. Aonly Student t with n−2 df✓
2. Bonly MS_within✓
3. Cthe binomial count of positive signs✓
4. Donly moving averages✓

K–S is more sensitive than t-test to

1. Aequal means only✓
2. Bonly block effects✓
3. Cdifferences in distribution shape, not only means✓
4. Donly r²✓

Non-parametric does not mean

1. Ano assumptions at all✓
2. Bfewer distributional assumptions✓
3. Cuseful with ordinal data✓
4. Dalternative when normality fails✓