Question

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Discuss the difference between chi square test, Pearson's product Moment Correlation and Spearman's rho test.

Answer 1

The Chi Square statistic is commonly used for testing relationships between categorical variables. The null hypothesis of the Chi-Square test is that no relationship exists on the categorical variables in the population; they are independent.

Pearson Product-Moment Correlation

Correlation coefficients measure the strength of association between two variables. The most common correlation coefficient, called the Pearson product-moment correlation coefficient, measures the strength of the linear association between variables.

The sign and the absolute value of a Pearson correlation coefficient describe the direction and the magnitude of the relationship between two variables.

• The value of a correlation coefficient ranges between -1 and 1.
• The greater the absolute value of a correlation coefficient, the stronger the linear relationship.
• The strongest linear relationship is indicated by a correlation coefficient of -1 or 1.
• The weakest linear relationship is indicated by a correlation coefficient equal to 0.
• A positive correlation means that if one variable gets bigger, the other variable tends to get bigger.
• A negative correlation means that if one variable gets bigger, the other variable tends to get smaller.

Keep in mind that the Pearson correlation coefficient only measures linear relationships. Therefore, a correlation of 0 does not mean zero relationship between two variables; rather, it means zero linear relationship. (It is possible for two variables to have zero linear relationship and a strong curvilinear relationship at the same time.

Spearman's Rho is a non-parametric test used to measure the strength of association between two variables, where the value r = 1 means a perfect positive correlation and the value r = -1 means a perfect negataive correlation. So, for example, you could use this test to find out whether people's height and shoe size are correlated (they will be - the taller people are, the bigger their feet are likely to be).