Determining and Interpreting Associations between Variables Cross-Tabs Chi-Square Correlation

Types of Relationships between Variables Non-monotonic - there is no direction to the relationship. Monotonic - there is a general direction of the relationship. Increasing - +ve relation. Decreasing - -ve relation. Linear - y=a+bx Curvilinear - exponential, log, s shape, etc.

Characteristics of Relationships Presence - is it significance. Direction - monotonic or non-monotonic; -ve or +ve sign. Strength of association

Cross-Tabulations Cross-tabulations (cross-tabs) consist of rows and columns defined by the categories classifying each variable. u Frequencies Table u Raw Percentages Table u Column Percentages Table u Row Percentages Table

Cross-Tabs and Chi-Square n Cross-Tabs and Chi-square (x 2 ) are used to assess whether or not a relationship exists between two nominally scaled variables. n Null hypotheses is that the two variables under investigation are NOT associated. n Chi-square statistics is calculated based on the difference between observed and expected frequencies

Chi-Square n Chi-square distribution is determined by its degrees of freedom n Degrees of freedom = (r-1)(c-1) u r = number of rows u c = number of columns Chi-sq =  (observed-expected)Sq/Expected

Correlation Coefficient n An index number constrained to fall between -1.0 and 1.0 that communicates both the strength and direction of association between two variables. n The greater the absolute size of the correlation coefficient, the greater the covariation between the two variables or the stronger is their association.

Is the correlation statistically significant? n If the correlation is not statistically significant, then it has very little meaning. n Null hypotheses states that the population correlation is zero; therefore, the null hypotheses needs to be rejected. n A correlation indicates the strength of association between variables by its size. The sign indicates the direction of the association.

Correlation Coefficient Ranges

Pearson Product Moment Correlation n The Pearson Product Moment Correlation ( r) measure the degree of linear association between two variables. n Not only indicates degree of association but direction as well. n Measures the “tightness” of measured points on a straight line (linear) n Interval scaling required

Pearson Product Moment Correlation n Only considers the two variables - all other factors are considered to not have any relationship on the two variables n Does not demonstrate cause and effect n Only expresses linear relationships (no curvilinear patterns)

Spearman Rank Order Correlation n Indicates strength and direction of a relationship between two rank (ordinal) variables. n Other forms of correlation that are specifically designed for ordinal and nominal data.