Week 5_PTA_CorrelationAndRegression.pdf

CORRELATION AND REGRESSION CORRELATION In correlational analysis, we ask whether two variables covary. In other words, does Y get larger as X gets larger? For example, does the patient feel dizzier when the doctor increases the dose of a drug? Do people get more diseases when they are under more...

CORRELATION AND REGRESSION CORRELATION In correlational analysis, we ask whether two variables covary. In other words, does Y get larger as X gets larger? For example, does the patient feel dizzier when the doctor increases the dose of a drug? Do people get more diseases when they are under more stress? CORRELATION Correlational analysis is designed primarily to examine linear relationships between variables. 4 A correlation coefficient is a mathematical index that describes the direction and magnitude of a relationship. POSITIVE CORRELATION high scores on Y are associated with high scores on X, and low scores on Y correspond to low scores on X. NEGATIVE CORRELATION higher scores on Y are associated with lower scores on X, and lower scores on Y are associated with higher scores on X. NO CORRELATION REGRESSION REGRESSION Simple regression is used to examine the relationship between one dependent and one independent variable. After performing an analysis, the regression statistics can be used to predict the dependent variable when the independent variable is known. 9  MEASURING CORRELATION COEFFICIENTS 1) PEARSON PRODUCT CORRELATION It is the most commonly used because most often we want to find the correlation between two continuous variables. Continuous variables such as height, weight, and intelligence can take on any values over a range of values. 11 2) SPEARMAN RHO Spearman’s rho is a method of correlation for finding the association between two sets of ranks. The rho coefficient (r) is easy to calculate and is often used when the individuals in a sample can be ranked on two variables but their actual scores are not known or have a normal distribution. 12 3) BISERIAL COEFFICIENT biserial correlation expresses the relationship between a continuous variable and an artificial dichotomous variable 13 4) POINT BISERIAL COEFFICIENT biserial correlation expresses the relationship between a continuous variable and a true dichotomous variable 14 5) PHI COEFFICIENT When both variables are dichotomous and at least one of the dichotomies is “true,” then the association between them can be estimated using the phi coefficient. 15 6) TETRACHORIC CORRELATION If both dichotomous variables are artificial, we might use a special correlation coefficient known as the tetrachoric correlation. 16  THE CORRELATION- CAUSATION PROBLEMS Just because two variables are correlated does not necessarily imply that one has caused the other. For example, a correlation between aggressive behavior and the number of hours spent viewing television does not mean that excessive viewing of television causes aggression. This relationship could mean that an aggressive child might prefer to watch a lot of television. A correlation alone does not prove causality, although it might lead to other research that is designed to establish the causal relationships between variables.