Which one of the following is not a non-parametric test ?
2013
Which one of the following is not a non-parametric test ?
Answer: A. t-test — Statistical tests are grouped by what they assume about the population from which the data come. A test is parametric when it assumes a specified population…
- A.
t-test
- B.
Sign test
- C.
Chi-square test
- D.
Run test
Show answer & explanation
Correct answer: A
Statistical tests are grouped by what they assume about the population from which the data come. A test is parametric when it assumes a specified population distribution — usually the normal distribution — and draws its inference about that distribution's parameters, such as the mean and the variance, which requires interval or ratio level measurement. A test is non-parametric, or distribution-free, when it assumes no particular shape for the population and works instead on counts, signs, ranks or the order of the observations, so it can be applied to nominal and ordinal data.
The stem asks for the single entry in the list that is not distribution-free, so each option is checked against that definition.
Test | What the test statistic is built from | What it assumes about the population distribution |
|---|---|---|
t-test | Sample means and their estimated variances, on interval-level scores | Assumes an approximately normal population and infers about its mean, so it is parametric |
Sign test | The count of plus and minus signs among paired differences | Assumes no particular shape for the population, so it is distribution-free |
Chi-square test | Observed versus expected frequencies in nominal categories | Assumes no particular shape for the population, so it is distribution-free |
Run test | The number of runs in a sequence taken in the order the observations occurred | Assumes no particular shape for the population, so it is distribution-free |
A quick cross-check confirms the split. The sign, chi-square and run procedures can each be carried out from nominal or ordinal information alone — directions, frequencies and the order of symbols — and none of them estimates a population mean or variance. The t procedure cannot even be computed without interval-level scores, and its validity rests on the normality assumption.
Therefore the one listed test that is not a non-parametric test is the t-test.