# Binomial Distribution Probability Calculator - Quick Tab

Power Analysis

The Quick tab of the Binomial Distribution Probability Calculator dialog contains options to compute the cumulative probability and percentage points of X, the binomial random variable. Besides these functions, you can also calculate a value of p, the probability of success, that corresponds to a particular value at a particular percentage point.

In a "binomial process," there are N independent trials, on which two possible events (arbitrarily designated "success" and "failure") can occur with probabilities p and 1 - p, respectively. The binomial random variable X is the number of successes in the N binomial trials.

1 - Cumulative p. Select the 1 - Cumulative p box to show calculations in terms of 1 - Cumulative p, i.e., the probability of obtaining a value greater than the observed X. This can be useful when using the probability calculator to obtain upper rejection points for a hypothesis test, or in computing power.

Parameters. The options in this group box represent four quantities related to the distribution of X. Three of these quantities (Observed X, Pi, Cum. p) may each be calculated as a function of the remaining three quantities, depending on the currently selected alternative in the Compute group box (see below). For example, if p is selected in the Compute group box, then STATISTICA computes Cum. p for the current values of Observed X, N,  and Pi.

Sample Size (N). Enter N, the sample size, in the Sample Size (N) box.

(Pop. Prop.) Pi. Enter the binomial parameter p, population proportion of successes, in the (Pop. Prop.) Pi box.

Observed X.  Enter the number of successes X in the Observed X box if X is one of the input variables in the calculation. If the result of the calculation is a value of X, it is displayed in this box.

Cum. p. The options under Cum. p. change, depending on which option is selected in the Compute group box.

X selected in Compute group box. If the X option button is selected under Compute, there are two boxes here, because X is an integer quantity, and in general it is not possible to find an X that has exactly the requested cumulative probability. Enter the value of Cum. p in the Requested Value box. The Actual box is the actual cumulative probability of the computed X. In general, X is selected to be the smallest value with a cumulative probability greater than or equal to the requested value.

p selected in Compute group box. If the p option button is selected as the computed quantity under Compute, the cdf is evaluated at the X, N, and Pi currently displayed. Cum. p can also be used as the input variable for a calculation. If the 1 - Cumulative p box is checked, then the label on this field will switch to 1 - Cum. p, and calculations will be altered accordingly.

Compute. The option buttons under Compute represent the quantity that is to be the result of the calculation. When the Compute button is clicked, this quantity is computed as a function of the other four quantities under Parameters, and the result is displayed in the appropriate box.

X. Select the X option button to compute a value of X as a function of Pi, N, and Cum. p. (or 1 - Cum. p.) . Note, as mentioned above, that the actual p will be greater than or equal to the requested p.

p (or 1 - p) . Select the p (or 1 - p) option to compute a value of Cum. p (or 1 - Cum. p) as a function of X, Pi, and N.

Pi. Select the Pi option button to compute a value of Pi as a function of X, N, and Cum. p (or 1 - Cum. p).