Characterizing Relationships Between Variables • 1. Presence: whether any systematic relationship exists between two variables of interest • 2. Direction: whether the relationship is positive or negative • 3. Strength of Association: how strong/consistent the relationship is (strong, moderate, weak) o Relationships should be assessed in this order
How to Analyze Relationships 1. Choose variables to analyze 2. Determine if the variables are interval/ratio or nominal/ordinal 3. Use the correct relationship analysis a. For two interval/ratio variables – use correlation b. For two nominal/ordinal variables – use cross-tabs 4. Does a relationship exist? 5. If relationship exists, determine the direction a. Monotonic will be increasing/decreasing b. Nonmonotonic will be looking for a pattern 6. Assess the strength of relationship a. With correlation – size of coefficient denotes the strength b. With cross-tabs – the pattern is assessed
Cross-Tabulations and Chi Square • Cross-tabulations o Consists of rows and columns defined by the categories classifying each variable. Used for nonmonotonic relationships o Sometimes referred to as an “r x c” table (rows x columns) ▪ Crosstabulation cell – intersection of a row and a column o Interested in inner cells to determine relationship before statistically testing ▪ Use the chi-square for statistical tests o Tables consist of four types of numbers in each cell: ▪ Frequency ▪ Raw percentage ▪ Column percentage ▪ Row percentage o When we have two nominal-scaled variables and we want to know if they are associated, we use cross-tabulations
