Multiple R² Probability Calculator - Quick Tab

Power Analysis

The Quick tab of the Multiple R² Probability Calculator contains options to compute the cumulative probability and percentage points of R², the sample squared multiple correlation, assuming a multivariate normal population distribution. Additionally, you can calculate a value of P², the population squared multiple correlation, 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 R². 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 represent five quantities related to the distribution of R².  Three of these quantities (Observed R², 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 Observed R², N, k, and P².

Observed R². Enter the value of the R²-statistic in the Observed R² field if R² is one of the input variables in the calculation. If the result of the calculation is an R²  value, it appears in this field when the Compute button is clicked.

P² (Rho²). Enter the population squared multiple correlation in the P² (Rho²) field.

Ind. Vars. (k).

(k). Enter the number of independent variables (i.e., predictors) in the Ind. Vars. (k) field.

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

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 Observed R², N, P² and Ind. Vars (k) 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.

Computing Algorithm

The Power Analysis and Interval Estimation module allows you to choose from two algorithms:

Faster

Select the Faster option button to employ Lee's (1971, p. 123) non-central F approximation. This approximation is accurate to about four decimal places, and is satisfactory for most applications.

More Accurate

Select the More Accurate option button to perform a slower, but more accurate calculation, based on theory described in Lee (1972), typically exact to at least five decimal places.

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 four quantities in the Parameters group box, and the result is displayed in the appropriate field.

R². Select the R² option button to compute a value of R² as a function of P², N, k, 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 R², P², N, and k.

P² (Rho²). Select the P² (Rho²) option button to compute a value of  P² as a function of R², N, k, and Cum. p (or 1 - Cum. p).