To find relationships between naturally occuring events, researchers use correlational studies measure one variable (X)
measure a second variable (Y)
determine a statistical relationship between the variables.
Correlational studies MEASURE variables, they do not manipulate variables.
The correlation coefficient is statistical value that indicates the strength of the relationship between two variables. The mathematical representation for the correlation coefficient is r. Correlation(r) = ( NΣXY - (ΣX)(ΣY) ) / Sqrt([NΣX2 - (ΣX)2][NΣY2 - (ΣY)2])
Correlation Coefficient: -1 < (or equal to) r < (or equal to) 1
- If x and y have a strong positive linear correlation, r i close to +1. - An r value of exact +1 indicates a perfect positive fit.
- Positive values indicate a relationship between x and y variables such as values for x increases, values for y also increase. Negative
- If x and y have a strong negative linear correlation, r is close to -1. - An r value of exactly -1 indicates a perfect negative fit. - Negative values indicate a relationship between x and y such that as values for x increases, values for y decrease. Correlation Coefficient: -1 < (or equal to) r < (or equal to) No correlation:
- not a linear relationship, but a curve
- if there is no line correlation or a weak linear correlation, r is close to 0. - a value near zero means that there is a random, nonlinear relationship between the two variables.
Coefficient of Determination: r^2
The coefficient of determination r^2 is useful because it gives the proportion of the variance (fluctuation) of one variable that is predictable from the other variable. It is a measure that allows to determine how certain one can be in making predictions from a certain model/graph. The ratio of the explained variation to the total variation. 0 < r2 < 1, and denoted the strength of the linear association between x an dy....