Multivariate Analysis Trying to establish a mathematical relationship between multiple data sets. (e.g. smoking/cancer, salary/productivity, pressure/volume, etc.) (We will limit our examples to two variables)

Multivariate Analysis Correlation: Mathematical tool used to establish a dependency between two data sets. X and Y represent the two sets of data Covariance (shown below) Product of Standard deviations Deviations from average value

Multivariate Analysis R: Value ranges between -1 and +1. Applies only to linear systems Interpretation is subjective but in general the closer to -1 or +1 the more highly correlated is the data.

Correlation Continued Magnitude of association Correlation coefficient with a value between -1 and 1. Weak Moderate Strong Discipline dependent

Correlation Continued Direction Sign of the correlation coefficient Positive correlation (+) - an increase in one variable is accompanied by an increase in the other Negative correlation (-) - an increase in one variable is accompanied by an decrease in the other

Multivariate Analysis R close to zero X Y

Multivariate Analysis R close to +0.5

Multivariate Analysis R close to +1

Multivariate Analysis Excel Functions –COVAR(array1, array2) –CORREL(array1, array2)

Correlation Continued Correlation or association between two variable does not give causation More experimentation must be done to determine causation.

Causation Consistency - measurements of the same two properties yield nearly the same results Responsiveness - Change in one variable elicits corresponding change in the other variable Mechanism - finding a valid and reasonable explanation for the cause and effect between the pair of variables

Establishing Causation Continued A valid and reasonable explanation establishes the sequential ordering of events and, thus, provides the rationale for the existence of such a relationship. Cause must precede effect, otherwise there is no causality