3. What does the sample correlation coefficient r measure? Which value indicates a stronger correlation: r =0.918 or r =- 0.932? Explain your reasoning.
Table of contents
- 1. Intro to Stats and Collecting Data55m
- 2. Describing Data with Tables and Graphs1h 55m
- 3. Describing Data Numerically1h 45m
- 4. Probability2h 16m
- 5. Binomial Distribution & Discrete Random Variables2h 33m
- 6. Normal Distribution and Continuous Random Variables1h 38m
- 7. Sampling Distributions & Confidence Intervals: Mean1h 53m
- 8. Sampling Distributions & Confidence Intervals: Proportion1h 12m
- 9. Hypothesis Testing for One Sample2h 19m
- 10. Hypothesis Testing for Two Samples3h 22m
- 11. Correlation1h 6m
- 12. Regression1h 4m
- 13. Chi-Square Tests & Goodness of Fit1h 20m
- 14. ANOVA1h 0m
11. Correlation
Correlation Coefficient
Problem 11.4.1
Textbook Question
What are some advantages of the Spearman rank correlation coefficient over the Pearson correlation coefficient?

1
The Spearman rank correlation coefficient is a non-parametric measure, meaning it does not assume that the data follows a specific distribution (e.g., normal distribution), unlike the Pearson correlation coefficient which assumes linearity and normality.
Spearman rank correlation is based on the ranks of the data rather than the raw data values, making it more robust to outliers and extreme values compared to Pearson correlation.
Spearman correlation can capture monotonic relationships (where variables move in the same or opposite direction, but not necessarily at a constant rate), while Pearson correlation is limited to linear relationships.
Spearman rank correlation can be used with ordinal data (data that can be ranked but not measured precisely), whereas Pearson correlation requires interval or ratio data.
Spearman rank correlation is less sensitive to measurement errors in the data, especially when the errors do not affect the ranking of the data points.

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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Spearman Rank Correlation Coefficient
The Spearman rank correlation coefficient is a non-parametric measure of correlation that assesses how well the relationship between two variables can be described by a monotonic function. Unlike Pearson's correlation, which measures linear relationships, Spearman's method ranks the data and evaluates the strength and direction of the association based on these ranks, making it suitable for ordinal data or non-normally distributed interval data.
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Pearson Correlation Coefficient
The Pearson correlation coefficient is a parametric statistic that measures the linear relationship between two continuous variables. It assumes that the data is normally distributed and that the relationship is linear. This coefficient provides a value between -1 and 1, where values close to 1 indicate a strong positive linear relationship, values close to -1 indicate a strong negative linear relationship, and values around 0 suggest no linear correlation.
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Non-parametric vs. Parametric Tests
Non-parametric tests, like the Spearman rank correlation, do not assume a specific distribution for the data and are often used when data does not meet the assumptions required for parametric tests, such as normality. Parametric tests, like the Pearson correlation, rely on these assumptions and are generally more powerful when the assumptions are met. Understanding the differences helps in choosing the appropriate statistical method based on the data characteristics.
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