Research 2 - Conditional Frequency
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.
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.
| 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.
Commenti
Posta un commento