Pearson’s coefficient of correlation and Chi square test

Pearson’s coefficient of correlation and Chi square test

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Pearson coefficient shows how variables are related and is a measure of correlation between two given variables. The correlation coefficient is a measure of degree of dependence given a result that is between +1 and -1 where +1 is a positive correlation and -1 is a negative correlation. Example is the Correlation between purchasing in a mall and median income in the region.

Pearson’s correlation, measures how two variables change together, and depends on sample size. Some factors take precedence in such situation, such as season, sample size, type of cloths, and income earned. Let’s take purchasing power to be x and income in the region as y i.e. if r is positive, x will increase and y will also increase and when x decreases ,y will tend to decrease the same way. Positive correlation .When r is negative when y increases x decreases and when y decreases x increases this is negative correlation

Chi square is a test of independency is best used to examine if two variables are associated with each other. This test can be used to test the behavioral situation and get the null hypothesis. Example if a company wants to test if changing product mix would affect profit. Let’s test the correlation of brand preference in shoes and income earned .The best way to test for this statistic is using goodness of fit. (C., 2002)

In such scenarios we can either reject the Null hypothesis or accept the alternative of accept the Null hypothesis and reject the alternative .This is usually indicated if e.g. Z calc>Z critical reject the null hypothesis and accept the alternative (Greenwood, 1996).

Reference

Greenwood, P. E. (1996). A guide to chi-squared testing (Vol. 280, pp 2-75) New York: John Wiley & Sons.

C. , H. (2002). Goodness-of-fit tests and model validity (pp 56-85) Paris: Springer.