{"id":4332,"date":"2024-08-08T08:50:47","date_gmt":"2024-08-08T06:50:47","guid":{"rendered":"https:\/\/www.psyctc.org\/psyctc\/?post_type=docs&p=4332"},"modified":"2024-08-12T15:10:40","modified_gmt":"2024-08-12T13:10:40","password":"","slug":"pearson-correlation-coefficient","status":"publish","type":"docs","link":"https:\/\/www.psyctc.org\/psyctc\/glossary2\/pearson-correlation-coefficient\/","title":{"rendered":"Pearson correlation coefficient"},"content":{"rendered":"\n

A correlation coefficient indexes whether increases and decreases in values for one variable are associated with increases and decreases in values on another variable. So this is a bivariate measure, i.e. about relationships between two variables and observations must be paired. Examples might be whether clients’ ages are related to how many sessions of therapy they attend for in a service offering fairly open lengths of therapy, another might be whether assessment scores on a measure are systematically related to scores on a different measure (this is an index of “convergent validity” if the two measures are expected to show a positive relationship. The Pearson coefficient is one of a number of correlation coefficients, see details.<\/p>\n\n\n\n

Details<\/h4>\n\n\n\n

The Pearson is pretty much the paradigmatic correlation coefficient. It is an index of the arithmetic, i.e. linear, relationship between the pairs of scores. The first step to compute is to replace the scores on the first variable by how much each value differs from the mean for that variable, then to do the same for the other variable. Here’s an illustration for this very small dataset.<\/p>\n\n\n

Raw data for Pearson correlation<\/h2>\n
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1<\/td>\n chris<\/td>\n 05\/08\/2024 06:15 PM<\/td>\n chris<\/td>\n 05\/08\/2024 06:15 PM<\/td>\n 1<\/td>\n -0.45<\/td>\n -0.15<\/td>\n <\/tr>\n
2<\/td>\n chris<\/td>\n 05\/08\/2024 06:15 PM<\/td>\n chris<\/td>\n 05\/08\/2024 06:15 PM<\/td>\n 2<\/td>\n -0.11<\/td>\n -1.02<\/td>\n <\/tr>\n
3<\/td>\n chris<\/td>\n 05\/08\/2024 06:15 PM<\/td>\n chris<\/td>\n 05\/08\/2024 06:15 PM<\/td>\n 3<\/td>\n 0.59<\/td>\n 0.90<\/td>\n <\/tr>\n
4<\/td>\n chris<\/td>\n 05\/08\/2024 06:15 PM<\/td>\n chris<\/td>\n 05\/08\/2024 06:15 PM<\/td>\n 4<\/td>\n 0.71<\/td>\n 0.57<\/td>\n <\/tr>\n <\/tbody> \n\n \n \n \n <\/table>\n\n<\/div>