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Which one of the following is a non‐parametric statistic?
- a)F ‐ statistic
- b)t ‐ statistic
- c)Pearson's correlation
- d)Spearman's correlation
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
Which one of the following is a nonparametric statistic?a)F statistic...
The non-parametric 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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Which one of the following is a nonparametric statistic?a)F statistic...
Nonparametric Statistics
Nonparametric statistics are statistical methods that do not rely on the assumptions of a specific probability distribution. These methods are often used when the data does not meet the assumptions necessary for traditional parametric tests. Nonparametric statistics offer flexibility and are widely used in various fields, including social sciences, biology, and economics.
Understanding the Options
Let's analyze each option given and determine whether it is a nonparametric statistic or not:
a) F statistic: The F statistic is used in analysis of variance (ANOVA) tests, which are parametric tests. ANOVA assumes that the data is normally distributed and that variances are equal across groups. Therefore, the F statistic is not a nonparametric statistic.
b) t statistic: The t statistic is commonly used for hypothesis testing when the sample size is small and the population standard deviation is unknown. The t statistic assumes that the data is normally distributed and that the sample is drawn from a population with a normal distribution. Thus, the t statistic is also a parametric statistic.
c) Pearson's correlation coefficient: Pearson's correlation coefficient measures the strength and direction of the linear relationship between two continuous variables. It assumes that the data follows a bivariate normal distribution. Therefore, Pearson's correlation coefficient is a parametric statistic.
d) Spearman's correlation coefficient: Spearman's correlation coefficient, also known as Spearman's rank correlation coefficient, is a nonparametric measure of the strength and direction of the monotonic relationship between two variables. It does not assume any specific probability distribution for the data and is based on the ranks of the observations. Thus, Spearman's correlation coefficient is a nonparametric statistic.
Conclusion
Among the given options, only Spearman's correlation coefficient (option D) is a nonparametric statistic. It does not rely on any specific distribution assumptions and can be used with ordinal or non-normally distributed data. The other options (F statistic, t statistic, and Pearson's correlation coefficient) are all parametric statistics that assume specific distributions for the data.
Nonparametric statistics are statistical methods that do not rely on the assumptions of a specific probability distribution. These methods are often used when the data does not meet the assumptions necessary for traditional parametric tests. Nonparametric statistics offer flexibility and are widely used in various fields, including social sciences, biology, and economics.
Understanding the Options
Let's analyze each option given and determine whether it is a nonparametric statistic or not:
a) F statistic: The F statistic is used in analysis of variance (ANOVA) tests, which are parametric tests. ANOVA assumes that the data is normally distributed and that variances are equal across groups. Therefore, the F statistic is not a nonparametric statistic.
b) t statistic: The t statistic is commonly used for hypothesis testing when the sample size is small and the population standard deviation is unknown. The t statistic assumes that the data is normally distributed and that the sample is drawn from a population with a normal distribution. Thus, the t statistic is also a parametric statistic.
c) Pearson's correlation coefficient: Pearson's correlation coefficient measures the strength and direction of the linear relationship between two continuous variables. It assumes that the data follows a bivariate normal distribution. Therefore, Pearson's correlation coefficient is a parametric statistic.
d) Spearman's correlation coefficient: Spearman's correlation coefficient, also known as Spearman's rank correlation coefficient, is a nonparametric measure of the strength and direction of the monotonic relationship between two variables. It does not assume any specific probability distribution for the data and is based on the ranks of the observations. Thus, Spearman's correlation coefficient is a nonparametric statistic.
Conclusion
Among the given options, only Spearman's correlation coefficient (option D) is a nonparametric statistic. It does not rely on any specific distribution assumptions and can be used with ordinal or non-normally distributed data. The other options (F statistic, t statistic, and Pearson's correlation coefficient) are all parametric statistics that assume specific distributions for the data.
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