Research 2 - Conditional Frequency

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Before giving the notion of conditional frequency first is important to define what is a contingency table, sometimes called two-way frequency table. A contingency table is a table which displays the (multivariate) frequency distribution of the variables of interest. For instance, consider the following dataset which contains information regarding a basket experiment made on a sample of 33 students.


Boys Girls Totals
Made 7 (21.2%) 6 (18.2%) 13 (39,4%)
Missed 11 (33,3%) 9 (27.3%) 20 (60.6%)
Totals 18 (54.5%) 15 (45.5%) 100%


Every cell contains a joint relative frequency, which is the ratio of the frequency in a particular category and the total number of data values. As an example, 21.2% is obtained dividing 7 (the number of boys that made a basket) by the total of students, which is 33. Thus 7/33 = 21.2% is the joint relative frequency of boys that made a basket.
The numbers in the column on the very right and on the row on the very bottom are the marginal frequency numbers. When analysing data in a two-way frequency table, you'll be looking for marginal relative frequency, which is the ratio of the sum of the joint relative frequency in a row (or column) and the total number of data values (i.e. 54.5% = 18/33 * 100).

Conditional relative frequency numbers are the ratio of a joint relative frequency and related marginal relative frequency. They express the frequency of a particular event restricted (or, equivalently, conditioned) to a fixed characteristic on some other (different) statistical variable.
Sometimes, one might be interested about the frequency of an event given the occurrence of another, such as "given a girl, what's the conditional relative frequency she missed a basket?".
Well, given the definition, this is equals to 9/15 = 0.6 = 60% which briefly means 9 out of 15 girls made a basket. As the reader may have noticed, this is very similar to what's done in probability theory. However, this subtle difference will be clarified soon in the next insight blog post.

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