# Event probability

## What is event probability?

Event probability is the chance that a specific outcome or event occurs. The opposite of an event is a nonevent. Event probability is also called predicted probability. The event probability estimates the likelihood of an event occurring, such as drawing an ace from a deck of cards or manufacturing a non-conforming part. The probability of an event ranges from 0 (impossible) to 1 (certain).

Each performance in an experiment is called a trial. For example, if you flip a coin 10 times and record the number of heads, you perform 10 trials of the experiment. If the trials are independent and equally likely, you can estimate the event probability by dividing the number of events by the total number of trials. For example, if you flip 6 heads out of 10 coin tosses, the estimated probability of the event (flipping heads) is:

Number of events ÷ Number of trials = 6 ÷ 10 = 0.6

A cumulative event probability estimates the likelihood of a set of events occurring (for example, the probability of rolling 4 or less on a die, which is the summation of the probability of rolling a 1, 2, 3, and 4).

## Calculate event probabilities for binary logistic regression

In binary logistic regression, a response variable has only two possible values, such as the presence or absence of a specific disease. You can enter binary response data in Minitab by indicating columns for the number of events and the number of trials. The event probability is the likelihood that the response for a specific factor or covariate pattern is 1 or an event (for example, the likelihood that a woman older than 50 will develop type-2 diabetes).

• Calculate values that exist in the sample data
1. Choose Stat > Regression > Binary Logistic Regression > Fit Binary Logistic Model.
2. In Response, enter the response. In Continuous predictors, enter the terms. In Categorical predictors, enter the factors.
3. Click Storage, and check Fits (event probabilities). Click OK in each dialog box.
• Calculate values for new observations
1. Choose Stat > Regression > Binary Logistic Regression > Fit Binary Logistic Model.
2. In Response, enter the response. In Continuous predictors, enter the terms. In Categorical predictors, enter the factors. Click OK.
3. Choose Stat > Regression > Binary Logistic Regression > Predict.
4. Enter either individual values, or a column in which the values are stored, for each predictor in the model.
5. Click OK.

## Calculate event probabilities for ordinal and nominal logistic regression

In ordinal and nominal logistic regression, a response variable can have three or more categories. The event probability is the likelihood that a specific factor or covariate pattern has a specific response category. Cumulative event probability is the likelihood that the response for a specific factor or covariate pattern falls into category k or below, for each possible k, where k equals the response categories, 1…k.

• Calculate values that exist in the sample data
1. Choose Stat > Regression > Ordinal Logistic Regression or Stat > Regression > Nominal Logistic Regression. The following steps are the same for both analyses.
2. In Response, enter the response. In Model, enter the predictors. In Categorical predictors (optional), enter the factors.
3. Click Storage.
4. In Enter the number of events, enter the number of distinct values of the response variable. Then check Event probabilities.
5. Click OK in each dialog box.
Minitab stores the event probabilities in the next available columns in the worksheet. The default column names starts with EPROB, followed by a number.
• Calculate values for new observations
1. Choose Stat > Regression > Ordinal Logistic Regression or Stat > Regression > Nominal Logistic Regression. The following steps are the same for both analyses.
2. In Response, enter the response. In Model, enter the predictors. In Categorical predictors (optional), enter the factors.
3. Click Storage and check Coefficients. Click OK in each dialog box.
4. In the worksheet, type the values for which you want to calculate event probabilities in the corresponding predictor columns directly below the existing data. You must type a value in the response column for each additional row of data you enter, but the value of the response will not affect the results.
5. Choose Stat > Regression > Ordinal Logistic Regression or Stat > Regression > Nominal Logistic Regression.
6. Click Options.
7. Choose Estimates for validation model, and enter COEF1. Click OK.
8. Click Storage.
9. In Enter the number of events, enter the number of distinct values of the response variable.
10. Check Event probabilities. Deselect Coefficients. Click OK in each dialog box.
Minitab stores the event probabilities in the next available columns in the worksheet. The default column names starts with EPROB, followed by a number.
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