# Noncentral Chi-square Probability Calculator - Quick Tab

Power Analysis

The Quick tab of the Noncentral Chi-square Probability Calculator contains options to compute the cumulative probability and percentage points of the noncentral Chi-square distribution. Additionally, you can calculate a noncentrality parameter that corresponds to a particular value at a particular percentage point.

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 chi-square. 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 the Parameters group box represent four quantities related to the noncentral Chi-Square distribution. Three of these quantities (Chi-Square, Delta, Cum. p) can 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 Chi-Square, Df, and Delta when the Compute button is clicked.

Chi-square. Enter the value of the Chi-Square-statistic in the Chi-square field if Chi-Square is one of the input variables in the calculation. If the result of the calculation is a Chi-Square value, it appears in this field.

Df. Enter the degrees of freedom of the Chi-Square statistic in the Df field.

Delta. Enter the value of the noncentrality parameter (delta) in the Delta field if δ is one of the input variables in the calculation. If the result of the calculation is a Delta value, it appears in this field after the Compute button is clicked.

Cum. p. Enter the value of p in the Cum. p field if p is one of the input variables in the calculation. If the p option button is selected in the Compute group box, then the cumulative probability function (cdf) is evaluated at the Chi-square, Df, and Delta 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 switches to 1 - Cum. p, and calculations are altered accordingly.

Compute. Use the option buttons in the Compute group box to specify which quantity is to be the result of the calculation. When the Compute button is clicked, this quantity is computed as a function of the other three quantities in the Parameters group box, and the result is displayed in the appropriate field.

Chi-square. Select the Chi-square option button to compute a value of Chi-square as a function of Delta, Df, and Cum. p. (or 1 - Cum. p.)

p (or 1 - p) . Select the p (or 1 - p) option button to compute a value of Cum. p (or 1 - Cum. p) as a function of Chi-square, Df, and Delta.

Delta. Select the Delta option button to compute a value of Delta as a function of Chi-Square, Df, and Cum. p (or 1 - Cum. p).