![]() ![]() For example, given that a customer is female, what is the probability she’ll purchase a Mac? Related post: Using Permutations to Calculate Probabilities and Using Combinations to Calculate Probabilities How to Calculate Conditional Probabilities in Contingency TablesĬonditional probabilities are the probability that an event occurs given that another event has occurred. Similarly, the row marginal probabilities (Male and Female) also sum to 1. The column marginal probabilities (PC and Mac) sum to 1. In the table below, the values in parentheses are marginal probabilities for each condition. The numerator equals the row or column total for the individual event in which you’re interested.The process for calculating marginal probabilities using a contingency table is the following: The equations for calculating marginal probabilities in a contingency table for row i and column j are the following: P(A) denotes the probability of event A occurring. Related post: Marginal Distributions: Definition & Example Marginal Probability Notation and Calculations Or, if you want to determine the probability of a female purchasing a computer and not consider the type of computer, take the row total for Female (117) and divide by the grand total (223). Then, use the grand total for the denominator.įor example, if you want to determine the probability for a Mac purchase and disregard gender, you simply take the column total for Mac (127) and divide it by the grand total (223). Statisticians refer to them as marginal probabilities because you find them in the margins of contingency tables!Ĭhoose the individual event you’re interested in and use the corresponding row or column total in the numerator. In contingency tables, you can locate the marginal probabilities in the row and column totals. ![]() In our table, the single events are gender (male or female) and computer type (PC or Mac). This lack of dependency differs from joint probabilities (above) and conditional probabilities (below). These probabilities do not depend on the condition of another outcome. Marginal probabilities are the probabilities that a single event occurs with no regard to other events in the table. Related post: Using the Multiplication Rule to Calculate Probabilities How to Calculate Marginal Probabilities in Contingency Tables Joint probabilities for an entire table always sum to 1. In the table below, the values in parentheses are the joint probabilities for the cells. The denominator equals the grand total number of observations.The numerator equals the count of occurrences for the specific combination of events in which you’re interested.The process for calculating joint probabilities using a contingency table is the following: The equation for calculating joint probabilities in a contingency table for a cell in row i, column j is the following: P(A ⋂ B) is the notation for the joint probability of event “A” and “B” occurring together. Joint Probability Notation and Calculations ![]()
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