Table A Two way classification of employee responses In favor Against Male 15

# Table a two way classification of employee responses

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Table-A: Two-way classification of employee responses In favor Against Male 15 45 Female 4 36 Table shows the distribution of 100 employees based on two variables or characteristics: gender (male or female) and opinion (in favor or against). Such table is called a contingency table. Each box that contains a number is called a cell. Notice that there are four cells. Each cell gives the frequency for two characteristics. For example, 15 employees in this group possess two characteristics: "male" and "in favor of paying high salaries to CEOs." We can interpret the numbers in other cells the same way. By adding the row totals and the column totals then we have: Table-B: Two-way classification of employee responses with totals In favor Against Total Male 15 45 60 Female 4 36 40 Total 19 81 100 Suppose one employee is selected at random from these 100 employees. This employee may be classified either on the basis of gender alone or on the basis of opinion. If only one characteristics is considered at a time, the employee selected can be a male, a female, in favor, or against. The probability of each of these four characteristics or events is called marginal probability or simple probability. 8

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These probabilities are called marginal probabilities because they are calculated by dividing the corresponding row margins (totals for the rows) or column margins (totals for the columns) by the grand total. Marginal Probability: Marginal probability is the probability of a single event without consideration of any other event. Marginal probability is also called simple probability. As we can observe, the probability that a male will be selected is obtained by diving the total of the row labeled "Male" (60) by the grand total (100), Similarly, Table-C: Listing the marginal probabilities (MP) In favor Against Total MP Male 15 45 60 0.60 Female 4 36 40 0.40 Total 19 81 100 MP 0.19 0.81 Conditional Probability: Now suppose that one employee is selected at random from these 100 employees. Furthermore, assume it is know that this (selected) employee is male. In other words, the event that the employee selected is a male has already occurred. What is the probability that the employee selected is in 9
favor of paying high salaries to CEOs? This probability is written as follows: The event whose probability This event has already occurred is to be determined Read as "given" This probability, , is called the conditional probability of "in favor" given that the event "male" has already happened. It is read as "the probability that the employee selected is in favor given that this employee is a male." Definition: Conditional probability: Conditional probability is the probability that an event will occur given that another event has already occurred. If A and B are two events, then the conditional probability of A given B is written as: and read as "the probability of A given that B has already occurred.

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