![]() The closer the value of r is to |1.00|, the stronger the relationship. A value of zero (0.00) indicates that there is no relationship between the two variables. A perfect negative correlation is indicated by a value of -1.00. The highest possible value of r is 1.00, which represents a perfect correlation. (We will discuss correlation techniques that consider the relationship between more than two variables in the later section on Multiple Correlations). The term bivariate means that two variables are represented by the correlation. Note that Pearson’s r is a bivariate correlation technique. The most widely used correlation coefficient is the Pearson r. By direction we mean whether both variables go up or down together (a positive or direct relationship) or whether one goes up when the other goes down (a negative or inverse relationship). Correlations also tell us the direction of the relationship. Finally, a correlation of 0.Correlation coefficients are a numerical indicator of the strength of a relationship between two variables. Likewise, a correlation of 1.00 indicates a perfect positive relation as \(X\) goes up by some amount, \(Y\) also goes up by the same amount. A correlation of -1.00 is a perfect negative relation as \(X\) goes up by some amount, \(Y\) goes down by the same amount, consistently. Our correlation coefficients will take on any value between -1.00 and 1.00, with 0.00 in the middle, which again represents no relation. Higher numbers mean greater magnitude, which means a stronger relation. The magnitude is how strong or how consistent the relation between the variables is. ![]() The number we calculate for our correlation coefficient, which we will describe in detail below, corresponds to the magnitude of the relation between the two variables. If the line it flat, that means it has no slope, and there is no relation, which will in turn yield a zero for our correlation coefficient. If the line has a positive slope that moves from bottom left to top right, it is positive, and vice versa for negative. The direction of the relation corresponds directly to the slope of the hypothetical line we draw through scatterplots when assessing the form of the relation. If it is zero, then there is no relation. If the number is positive, it is a positive relation, and if it is negative, it is a negative relation. That number will be either positive, negative, or zero, and we interpret the sign of the number as our direction. A negative relation is just the opposite: \(X\) and \(Y\) change together in opposite directions: as \(X\) goes up, \(Y\) goes down, and vice versa.Īs we will see soon, when we calculate a correlation coefficient, we are quantifying the relation demonstrated in a scatterplot. A positive relation is one in which \(X\) and \(Y\) change in the same direction: as \(X\) goes up, \(Y\) goes up, and as \(X\) goes down, \(Y\) also goes down. We saw this concept earlier when first discussing scatterplots, and we used the terms positive and negative. The direction of the relation between two variables tells us whether the variables change in the same way at the same time or in opposite ways at the same time.
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