A two-way frequency table, also known as a contingency table, is a table that displays frequencies of data that belong to two different categories. It helps organize data and identify sample spaces to approximate probabilities. For example, consider the two-way table that shows whether the men or women in a classroom play a sport.
Plays a Sport
Does Not Play a Sport
Total
Men
20
6
26
Women
12
8
20
Total
32
14
46
These tables allows us to easily calculate probabilities. Suppose A is the event that a randomly chosen student is a women who does not play a sport. To find the probability, we just need to calculate the relative frequency. This is the ratio of the women who do not play a sport to the total number of students.
P(A)=8/46 ⇒ P(A)≈ 0.17
Moreover, these tables also help us to calculate conditional probabilities. For example, suppose we want to find the probability that a randomly selected student is a women, given that the student does not play a sport. The conditional relative frequency —the ratio of a joint frequency to a corresponding marginal frequency— give us this probability.
P(Woman|Does not play a sport)&=8/14
&⇓
P(Women|Does not play a sport)&≈0.57
Therefore, a two-way table is a table that displays data that belongs to two different categories and can help us calculate from easy to more difficult probabilities. Please note that examples may vary, and that two-way tables are not limited to probability calculations.
