Non-Parametric Methods MCQs 2026

The two-sample Kolmogorov–Smirnov test detects

1. A only a difference in means ✓
2. B only equal variances ✓
3. C only linear correlation ✓
4. D any difference between two distribution functions ✓

Non-parametric methods are called distribution-free because they

1. A make fewer assumptions about the population distribution shape ✓
2. B always assume perfect normality ✓
3. C require known variance only ✓
4. D use only parametric t-tests ✓

Non-parametric tests are preferred when

1. A sample size is huge and normality holds ✓
2. B data are ordinal or normality is doubtful in small samples ✓
3. C only interval data with exact normality ✓
4. D only when means are equal ✓

The sign test uses

1. A only the direction of differences relative to a hypothesized median ✓
2. B full magnitude rankings always ✓
3. C normality of differences ✓
4. D the F-distribution ✓

Wilcoxon signed-rank test is appropriate for

1. A two independent samples always ✓
2. B more than three independent groups as first choice ✓
3. C only categorical frequency tables ✓
4. D paired observations on a continuous or interval scale ✓

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

1. A paired differences only ✓
2. B two independent samples using ranks ✓
3. C three or more means with F-test ✓
4. D only proportions in a 2×2 table ✓

Runs test examines

1. A whether the sequence of observations is random ✓
2. B only central tendency of two groups ✓
3. C only regression slopes ✓
4. D only seasonal indices ✓

Kolmogorov–Smirnov test compares

1. A an empirical distribution to a specified distribution or two empirical distributions ✓
2. B only means of two groups ✓
3. C only variances with F ✓
4. D only correlation coefficients ✓

Compared with parametric tests, non-parametric tests are generally

1. A always more powerful ✓
2. B less powerful when parametric assumptions are met ✓
3. C identical in power always ✓
4. D unusable with ordinal data ✓

The one-sample sign test can test whether

1. A population variance equals zero only ✓
2. B Pearson r equals one ✓
3. C block effects are zero ✓
4. D the population median equals a specified value ✓

Wilcoxon signed-rank test requires

1. A perfect normality always ✓
2. B independent groups ✓
3. C only nominal categories ✓
4. D symmetric distribution of differences for testing the median difference ✓

Mann–Whitney U and Wilcoxon rank-sum test are

1. A different tests with unrelated statistics ✓
2. B only for paired data ✓
3. C equivalent for two independent samples ✓
4. D only parametric alternatives ✓

In rank tests, ties are handled by

1. A dropping tied values always ✓
2. B assigning rank 1 to all ties ✓
3. C converting ties to missing data ✓
4. D assigning average ranks to tied observations ✓

Runs test for randomness counts

1. A only the median ✓
2. B only SS_between ✓
3. C the number of runs of identical symbols in a sequence ✓
4. D only Laspeyres weights ✓

Too few runs in a sequence suggests

1. A perfect randomness ✓
2. B negative correlation only ✓
3. C positive serial dependence or clustering ✓
4. D homoscedasticity ✓

One-sample K–S test compares data to

1. A only another sample always ✓
2. B a fully specified theoretical distribution ✓
3. C only regression residuals without a model ✓
4. D only ANOVA tables ✓

Empirical distribution function Fₙ(x) is

1. A always a normal CDF ✓
2. B the Pearson r formula ✓
3. C the step function giving the fraction of sample ≤ x ✓
4. D the Laspeyres index ✓

Parametric two-sample t-test assumes

1. A approximately normal populations with equal or handled variances ✓
2. B only ordinal ranks ✓
3. C only zero sample size ✓
4. D no independent observations ✓

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

1. A ignores magnitudes of differences ✓
2. B uses ranks of absolute differences ✓
3. C requires normality ✓
4. D uses two independent samples ✓

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

1. A only χ² with one df always ✓
2. B a normal distribution ✓
3. C only the sign distribution ✓
4. D only Fisher index ✓

Kruskal–Wallis test extends rank methods to

1. A paired blocks only ✓
2. B three or more independent groups ✓
3. C only two categories ✓
4. D only time-series trend ✓

Median test is

1. A identical to Pearson regression ✓
2. B the same as two-way ANOVA always ✓
3. C a parametric z-test on means ✓
4. D a crude non-parametric comparison using counts above/below a common median ✓

Non-parametric methods are robust to

1. A all design flaws ✓
2. B lack of any data ✓
3. C outliers relative to mean-based parametric tests ✓
4. D perfect multicollinearity in regression ✓

Ordinal measurement suits

1. A rank-based non-parametric analysis ✓
2. B only ratio-scale physics quantities always ✓
3. C only meaningless labels without order ✓
4. D only geometric index numbers ✓

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

1. A enumerating the null distribution of the test statistic ✓
2. B always normal tables only ✓
3. C Laspeyres formula ✓
4. D ANOVA F tables only ✓

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

1. A assuming perfect normality ✓
2. B using only index relatives ✓
3. C ignoring the data ✓
4. D inference without strict distributional formulas ✓

Hodges–Lehmann estimator associated with Wilcoxon signed-rank estimates

1. A only the sample mean ✓
2. B the median of pairwise averages of observations ✓
3. C only the sign count ✓
4. D only block means ✓

Zero differences in Wilcoxon signed-rank are typically

1. A assigned the highest rank always ✓
2. B treated as infinite ✓
3. C dropped from ranking ✓
4. D converted to missing blocks ✓

Mann–Whitney U statistic is based on

1. A only signs of paired diffs ✓
2. B rank sums of one sample relative to the other ✓
3. C only squared residuals ✓
4. D only seasonal ratios ✓

K–S test statistic D equals

1. A the mean difference only ✓
2. B the product of variances ✓
3. C the correlation r ✓
4. D the maximum absolute difference between two CDFs ✓

Choosing sign test over Wilcoxon signed-rank trades

1. A more power always ✓
2. B fewer assumptions for less power when symmetry holds ✓
3. C parametric normality requirement ✓
4. D paired independent samples ✓

Non-parametric correlation for ranks is

1. A Pearson r on raw values only ✓
2. B the F-ratio ✓
3. C Spearman ρ ✓
4. D LSD critical value ✓

χ² test on contingency tables is

1. A identical to Mann–Whitney ✓
2. B a regression method ✓
3. C an index number ✓
4. D non-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. A preferred for higher power ✓
2. B avoided always ✓
3. C less powerful than sign test ✓
4. D unrelated to efficiency ✓

Runs test null hypothesis is

1. A means are equal across groups ✓
2. B the sequence is random with given proportion of symbols ✓
3. C slope is zero ✓
4. D index is 100 ✓

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

1. A less meaningful always ✓
2. B identical to comparing means always ✓
3. C more representative than a t-test on means ✓
4. D invalid on interval scale ✓

Order statistics are central to

1. A only CRD blocking ✓
2. B only Laspeyres weighting ✓
3. C only multiple regression VIF ✓
4. D rank-based non-parametric procedures ✓

Large-sample z approximation for sign test uses

1. A only Student t with n−2 df ✓
2. B only MS_within ✓
3. C the binomial count of positive signs ✓
4. D only moving averages ✓

K–S is more sensitive than t-test to

1. A equal means only ✓
2. B only block effects ✓
3. C differences in distribution shape, not only means ✓
4. D only r² ✓

Non-parametric does not mean

1. A no assumptions at all ✓
2. B fewer distributional assumptions ✓
3. C useful with ordinal data ✓
4. D alternative when normality fails ✓