Which one of the following is a non‐parametric statistic?

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UGC NET (Odia) Official Paper-I (Held On: 4th Jan 2022 Shift 2)
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  1. F‐ statistic
  2. t ‐ statistic
  3. Pearson's correlation
  4. Spearman's correlation

Answer (Detailed Solution Below)

Option 4 : Spearman's correlation
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UGC NET Paper 1: Held on 21st August 2024 Shift 1
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The nonparametric approach is a statistical method that makes no assumptions about the sample's characteristics (its parameters) or whether the observed data is quantitative or qualitative.

Key Points

  • Certain descriptive statistics, statistical models, inference, and statistical tests are examples of nonparametric statistics. 
  • The model structure of nonparametric approaches is determined from data rather than being established a priori.
  • The normal distribution model and the linear regression model are examples of nonparametric statistics.
  • Ordinal data is sometimes used in nonparametric statistics which means it does not rely on numbers but rather on a ranking or order of sorts.
  • The Spearman rank-order correlation coefficient is a nonparametric statistics measure of the strength and direction of the relationship between two variables assessed on an ordinal scale.
  • The test is used for ordinal variables or continuous data that fails to meet the assumptions required for the Pearson's product-moment correlation to be conducted.

​Thus, Spearman's correlation is a non‐parametric statistic. 

Additional Information

  • F‐ statistic: An F-test is any statistical test in which the test statistic has an F-distribution under the null hypothesis. The F statistic simply compares the combined effect of all variables. 
  • t ‐ statistic: The t-value expresses the magnitude of the difference in terms of the variation in your sample data. 
  • Pearson's correlation: This correlation coefficient is a single number that measures both the strength and direction of the linear relationship between two continuous variables.
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