In a Boolean analysis of data, all variables, both independent and dependent, must be converted to nominal-scale measures. Researchers should note that variables can be measured on different levels using categorical coding. In Boolean algebra, such data tables are called truth tables. All possible combinations of the values 1 and 0 on the independent variable are represented as rows on the truth table. The rows contain both possibilities that exist in the actual data and those that are possible but don't exist in the data set.
Truth tables have as many rows as there are logically possible combinations of variables.
Since countries with either large or small population bases have lower than the median number of medals, the population variable does not seem important and can be considered for logically elimination. It would be tedious and difficult to sort manually through all combinations of variables that are logically associated with the outcome, especially in studies where the number of cases are much larger. The QCA computer program will minimize a truth table to produce an expression that identifies the necessary and sufficient conditions that are true and false for a specified outcome. Accordingly, the above expression shows there are two basic combinations of variables that produce more than the median number of medals. The truth table also can be minimized to discover the conditions that are true or false when the outcome is opposite, i.e., conditions associated with low medal production.