Describe the application and uses of parametric and non-parametric statistics. Differentiate between parametric and non-parametric statistics.

1. Parametric Statistics: Application and Uses

Parametric statistics are based on specific assumptions about the population distribution, typically assuming that the data follows a normal distribution. These statistics require interval or ratio level data and are used in situations where the underlying population distribution is known or can be reasonably assumed to be normal.

Application and Uses of Parametric Statistics:

• Parametric statistics are commonly used in hypothesis testing and estimation of population parameters, such as means and variances.
• They are applied in various fields, including psychology, biology, economics, and engineering, to analyze experimental data, conduct regression analysis, and compare group means.
• Parametric tests, such as t-tests, analysis of variance (ANOVA), and linear regression, are used to examine relationships between variables, assess treatment effects, and make predictions based on regression models.
• Parametric statistics provide precise estimates and inferential tests with high statistical power when the assumptions are met, making them valuable for making accurate conclusions about populations.

2. Non-parametric Statistics: Application and Uses

Non-parametric statistics do not rely on assumptions about the population distribution and are used when the data do not meet the requirements for parametric tests. Non-parametric methods are often employed with ordinal or nominal level data or when the sample size is small.

Application and Uses of Non-parametric Statistics:

• Non-parametric statistics are applied in situations where the data are skewed, have outliers, or violate assumptions of normality and homogeneity of variances.
• They are commonly used in social sciences, medicine, environmental studies, and market research to analyze survey data, rank observations, and compare medians or proportions.
• Non-parametric tests, such as the Wilcoxon rank-sum test, Kruskal-Wallis test, and Mann-Whitney U test, are used to compare groups, assess relationships between variables, and conduct trend analysis without making distributional assumptions.
• Non-parametric statistics provide robust alternatives to parametric tests, particularly when dealing with non-normally distributed data or small sample sizes, ensuring valid and reliable results even under challenging conditions.

3. Difference Between Parametric and Non-parametric Statistics

Assumptions:

• Parametric statistics require assumptions about the population distribution, such as normality and homogeneity of variances, while non-parametric statistics do not rely on distributional assumptions and are more flexible in their application.

Data Type:

• Parametric statistics are suitable for interval or ratio level data, whereas non-parametric statistics can be applied to nominal, ordinal, interval, or ratio level data.

Sample Size:

• Parametric tests are more robust with larger sample sizes, while non-parametric tests can be used with smaller sample sizes or when the distributional assumptions of parametric tests are violated.

Precision:

• Parametric statistics provide more precise estimates and inferential tests when assumptions are met, whereas non-parametric statistics offer less precise estimates but are more robust in the presence of outliers or skewed distributions.

Conclusion

Parametric and non-parametric statistics serve distinct purposes and are applied in different situations depending on the nature of the data and the underlying assumptions. Parametric statistics rely on assumptions about the population distribution and are used with interval or ratio level data when these assumptions are met. Non-parametric statistics, on the other hand, do not make distributional assumptions and are employed when dealing with non-normally distributed data or small sample sizes. Understanding the differences between parametric and non-parametric statistics is essential for selecting the appropriate statistical methods and ensuring valid and reliable results in research and data analysis.