# How to Calculate if Two Events Are Statistically Independent

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Statistically independent events occur without any effect on the odds of other independent events occurring. This is in contrast to dependent events, in which the occurrence of one event affects the odds of another's occurring. You can determine whether two events are statistically independent with a review of the data and simple analysis.

## Calculation

Review the data set. Select one event to be “event A” and the other to be called “event B.” This requires a unique definition of the two events to be analyzed so that one occurrence is not accidentally misclassified.

Count the number of observations that were taken.

Count how many times event A occurred. Determine the rate at which the first event A occurs by dividing the number of times A occurred by the total number of observations.

Count how many times event B occurred. Determine the rate at which the second event B occurs by dividing the number of times B occurred by the total number of observations.

Determine how often both the first event A and the second event B occurred at the same time. Determine the rate at which the both events occur by dividing the number of times A and B occurred by the total number of observations.

Review the number of times A occurred when B occurred. If the first event A occurs just as often when B occurs as when not, it may be independent.

Review the number of times B occurred when A occurred. If the second event B occurs just as often when A occurs as when not, it may be independent.

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Multiply the probability of A and B occurring. If the odds of A and B occurring at the same time are equal to the odds of A multiplied by the odds of B, the events are statistically independent.

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