A two-way table is one way to display frequencies for two different categories collected from a single group of people. One category is represented by the rows and the other is represented by the columns. This table can be used to determine the probabilities associated with various possible outcomes involving those two categories.
Two-Way Table Terminology
- Joint Frequency – each entry in the table
- Joint Relative Frequency – the ratio of a joint frequency to the total number of observations.
- Marginal Frequency – sums of the rows and columns
- Marginal Relative Frequency – the sum of the joint relative frequencies in a row or column.
- Relative Frequency – the ratio of one frequency to another frequency
- Conditional Relative Frequency – the ratio of a joint relative frequency to the marginal relative frequency.
Basic Probability Notation
- P(A) = probability of event A
- Marginal Frequency of event A/Total Frequency
- Example: P(Female) = 52/100
- P(AՈB) = probability of event A and event B (happening at the same time)
- Joint Frequency of events A and B/Total Frequency
- Example: P(FemaleՈBaseball) = 23/100
- P(AՍB) = probability of event A or B (but not both)
- Marginal Relative Frequency of event A + Marginal Relative Frequency of event B – Joint Relative Frequency of A and B
- Example: P(FemaleՍBaseball) = (52/100)+(36/100)-(23/100) = 65/100
- P(A|B) = probability of event A given that event B has already occurred
- Joint Frequency of event A/Marginal Frequency of event B
- Example: P(Female|Baseball) = 23/36
