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Parametric vs Non-parametric Statistics — Previous Year Questions

📊 Topic Overview​

MetricValue
Papers Appeared27 of 27 (100%)
Priority🔴 VERY HIGH — appears in EVERY paper
Section DistributionSec A: ~20
Most Repeated"Discuss assumptions of parametric and non-parametric statistics with advantages and disadvantages"
ProbabilityCertain — prepare this as your guaranteed Section A conceptual answer

🎯 Must-Know Concepts​

  1. Definition of parametric statistics — based on population parameters
  2. Definition of non-parametric statistics — distribution-free
  3. Assumptions of parametric statistics (normal distribution, interval/ratio scale, homogeneity of variance)
  4. Assumptions of non-parametric statistics (ordinal/nominal scale, no distribution assumption)
  5. Advantages of non-parametric statistics
  6. Disadvantages of non-parametric statistics
  7. When to use non-parametric tests

🔥 Most Repeated Question: Parametric vs Non-parametric Statistics​

Appeared in all 27 papers in some variant. Exact phrasings include:

  • "Discuss the assumptions of parametric and non-parametric statistics."
  • "Define parametric and non-parametric statistics. Discuss their assumptions, advantages and disadvantages."
  • "Explain non-parametric statistics with a focus on its assumptions, advantages and disadvantages."
  • "Elucidate parametric and non-parametric statistics. Describe the assumptions of parametric statistics."

Answer (Section A — ~450 words):​

Statistics can be broadly classified into two types based on the assumptions they make about the underlying population distribution: parametric and non-parametric statistics.

Parametric Statistics: Parametric statistics are procedures that require the specification of certain conditions or parameters about the population from which the sample is drawn. The term "parametric" refers to population parameters such as the mean and standard deviation.

Assumptions of Parametric Statistics:

  1. Normal distribution: The data in the population must be normally distributed. The sampling distribution of the statistic must be known and is usually assumed to be normal.
  2. Interval or ratio scale of measurement: Parametric tests require that the data be measured on an interval or ratio scale, ensuring equal intervals between values.
  3. Homogeneity of variance: When comparing two or more groups, the variances within each group should be approximately equal (homoscedasticity).
  4. Independence of observations: Observations should be independent of each other.
  5. Random sampling: Scores must be obtained from a random sample.

Common parametric tests: t-test, Pearson's r, ANOVA, regression analysis.

Non-parametric Statistics: Non-parametric statistics (also called distribution-free statistics) are procedures that do not assume a specific distribution for the population. They are used when the assumptions of parametric statistics cannot be met.

Assumptions of Non-parametric Statistics:

  1. Data may be measured on nominal or ordinal scales.
  2. No assumption about the shape of the population distribution.
  3. Observations should be independent (for most tests).

Advantages of Non-parametric Statistics:

  1. No distribution assumption: Can be used when the population distribution is unknown or clearly non-normal.
  2. Applicable to all scales: Work with nominal and ordinal data where parametric tests are inappropriate.
  3. Small samples: More appropriate for very small samples where normality cannot be verified.
  4. Robustness: Less affected by outliers and extreme scores.
  5. Simplicity: Computational procedures are often simpler, especially for small samples.
  6. Exact probability: Provide exact probabilities even for very small sample sizes.

Disadvantages of Non-parametric Statistics:

  1. Less powerful: When parametric assumptions are met, parametric tests are more statistically powerful (less likely to make Type II errors).
  2. Waste of information: Ranking procedures (used in many non-parametric tests) discard the actual magnitude of differences, losing information.
  3. Tied ranks: When many scores are tied, adjustments are required that complicate computation.
  4. Limited scope: Fewer available tests for complex designs (e.g., factorial designs, interaction effects).
  5. Critical tables: Require separate critical value tables for each sample size.

When to Use Non-parametric Tests: Use non-parametric tests when: (a) data are measured on a nominal or ordinal scale; (b) the sample is very small; (c) the population distribution is clearly non-normal; (d) there are extreme outliers that would distort parametric results.

📝 Other Key Questions​

Differentiate between parametric and non-parametric statistics (Section B — ~250 words)​

AspectParametric StatisticsNon-parametric Statistics
AssumptionAssumes normal distributionNo distribution assumption (distribution-free)
ScaleInterval or ratioNominal or ordinal
ParametersBased on population parameters (μ, σ)Not based on population parameters
Sample sizeUsually requires larger samplesCan be used with small samples
Statistical powerHigher power (when assumptions met)Lower power
Examplest-test, ANOVA, Pearson's rMann-Whitney U, Kruskal-Wallis, Chi-square, Spearman's rho
Information useUses actual valuesOften uses ranks (loses magnitude information)
ComplexityMore complex with large samplesSimpler computation

The choice between the two depends on the scale of measurement, sample size, normality of data, and the specific research question being addressed.

🧠 Memory Aids​

Parametric ASSUMPTIONS (NIHR):

  • Normality (population is normally distributed)
  • Interval/ratio scale
  • Homogeneity of variance
  • Random sampling & independence

Non-parametric ADVANTAGES (NASRE):

  • No distribution assumption
  • All scales (nominal, ordinal)
  • Small samples OK
  • Robust to outliers
  • Exact probabilities

📚 Related Content​

✅ Self-Assessment​

  1. What are the four main assumptions of parametric statistics?
  2. Why are non-parametric tests called "distribution-free"?
  3. What are three advantages of non-parametric statistics?
  4. When would you choose a non-parametric test over a parametric one?
  5. What is the main disadvantage of non-parametric tests when parametric assumptions are met?

💡 Exam Tips​

  • Section A (10 marks): Define both → Assumptions of parametric (4 points) → Assumptions of non-parametric → Advantages of non-parametric (5 points) → Disadvantages (3 points) → Conclusion on when to use.
  • The comparison table is excellent for Section A — examiners love structured contrasts.
  • Always state which tests are parametric and which are non-parametric as examples.
  • This is the single most predictable question in MPC-006 — never skip it.