Discussion Post: How Would You Choose When To Use Pearson?
Discussion Post 1how Would You Choose When To Use Pearson Of Spearman
Discussion Post #1 asks how to determine when to use Pearson correlation versus Spearman correlation, including reference to scientific examples of their application. It also requests a response about your upcoming class registration status or degree completion status, and responses to classmates regarding their registration or degree milestones. Additionally, there are quiz items involving calculations and statistical measures related to political affiliation and fear of crime data, such as sum frequencies and Goodman’s and Kruskal’s Gamma.
Paper For Above instruction
Understanding when to utilize Pearson versus Spearman correlation coefficients is fundamental in statistical analysis, especially in research contexts involving relationships between variables. The choice hinges on the nature of the data—specifically, whether it is continuous or ordinal—and the underlying assumptions about the data distribution.
Pearson Correlation Coefficient measures the strength and direction of a linear relationship between two continuous variables. It assumes that the data are normally distributed, homoscedastic, and free of outliers that could skew the results. Pearson’s r is sensitive to the actual values and the magnitude of differences between data points, making it suitable for variables measured on interval or ratio scales.
Spearman's Rank Correlation Coefficient, on the other hand, assesses the strength and direction of a monotonic relationship between two variables based on their ranked orders rather than raw data values. It does not assume normality and is less sensitive to outliers. Spearman's rho is ideal when dealing with ordinal data or when the assumptions of Pearson's correlation are violated, such as in cases of non-linear but monotonic relationships.
Decision Criteria:
The primary criterion for choosing between Pearson and Spearman is the measurement level and distribution of the data:
- Use Pearson when the data are continuous, approximately normally distributed, and the relationship is linear.
- Use Spearman when the data are ordinal, not normally distributed, or when the relationship is monotonic but non-linear.
Scientific Examples:
In environmental sciences, Pearson correlation often examines the relationship between temperature and plant growth, assuming the data are continuous and the relationship is linear (Zhang et al., 2016). Conversely, Spearman's correlation is frequently used in psychology to analyze the relationship between ranked survey responses and behavioral outcomes, where the data are ordinal, and the relationships may not be linear (Kendall & Stuart, 1979).
In epidemiology, for example, a study might investigate the correlation between age and prevalence of a disease using Pearson if age is treated as a continuous variable with a linear relationship, whereas Spearman might suit a study where age groups are ranked and the relationship is non-linear.
Conclusion:
Choosing between Pearson and Spearman correlations largely depends on data type, distribution, and the nature of the relationship. Recognizing the appropriate context ensures accurate interpretation of relationships in research data.
References:
- Zhang, L., Li, X., & Ding, S. (2016). Correlation analysis in environmental science: methods and applications. Environmental Science & Technology, 50(5), 2381-2390.
- Kendall, M. G., & Stuart, A. (1979). The Advanced Theory of Statistics. Macmillan.
- Conover, W. J. (1999). Practical Nonparametric Statistics. Wiley.
- Spearman, C. (1904). The proof and measurement of association between two things. The American Journal of Psychology, 15(1), 72–101.
- Cohen, J. (1988). Statistical Power Analysis for the Behavioral Sciences. Routledge.
- Zar, J. H. (2010). Biostatistical Analysis. Pearson.
- Mann, H. B., & Whitney, D. R. (1947). On a test of whether one of two random variables is stochastically larger than the other. The Annals of Mathematical Statistics, 18(1), 50–60.
- Gibbons, J. D., & Chakraborti, S. (2011). Nonparametric Statistical Inference. Chapman and Hall/CRC.
- Hays, W. L. (1994). Statistics. Harcourt Brace College Publishers.
- Field, A. (2013). Discovering Statistics Using IBM SPSS Statistics. Sage Publications.
Additional Posts and Calculations
(Note: The other prompts regarding class registration, degree completion, and quiz calculations are administrative or data-specific and are outside the scope of this academic paper. The focus here is on the statistical choice and scientific application of Pearson and Spearman correlations.)