Multiple R²: Sample Size Parameters - Quick Tab

Select the Quick tab of the Multiple R²: Sample Size Parameters dialog box to access options to establish the basic parameters for analyzing sample size for the squared multiple correlation.

Fixed Parameters

The entries in the boxes under Fixed Parameters establish the fixed, or baseline, parameters for subsequent sample size calculations and graphs. Parameters that are not varied explicitly as the independent (X-axis) variables in a graphical analysis will be set equal to these values. Throughout what follows, we will use R² to stand for the sample squared multiple correlation, and P² to stand for its population equivalent.

P²

In the P² box, enter the population squared multiple correlation.

C² (Null P²)

In the C² (Null P²) box, enter a constant between zero and one. This constant is the null hypothesized value of P². Using the Multiple R²: Probability Calculator and the Multiple R²: Interval Estimation dialog boxes that are included in this module, you can perform a variety of procedures on the multiple R² that are not available in standard statistics packages.  Not only can you compare the multiple R² to a value of zero, but you can also perform a variety of other hypothesis tests to compare it to some value other than zero.

Ind. Vars. (k).

(k). In the Ind. Vars. (k) box, enter the number of independent variables in the multiple regression prediction equation.

Alpha

In the Alpha box, enter the type I error rate for the overall significance test.

Power Goal

In the Power Goal box, enter the minimum acceptable power, for which a minimum sample size is calculated. If the search for an acceptable sample size is successful, the actual power of the statistical test will be greater than or equal to this value.

Type of Hypothesis

The choice of option buttons under Type of Hypothesis determines the type of null hypothesis tested.

2-tailed (P2 = C2)

Select the 2-tailed (P2 = C2) option button to test null and alternative hypotheses of the form

H₀: P²  = C² H₁: P² ¹ C²

1-tailed (P2 <= C2)

Select the 1-tailed (P2 <= C2) option button to test null and alternative hypotheses of the form

H₀: P²  ≤ C² H₁: P² > C²

1-tailed (P2 >= C2)

Select the 1-tailed (P2 >= C2) option button to test null and alternative hypotheses of the form

H₀: P²  ³ C² H₁: P² < C²

1-tailed (P2 = 0)

Select the 1-tailed (P2 = 0) option button to test null and alternative hypotheses of the form

H₀: P² = 0 H₁: P² > 0

(This is the hypothesis tested by the standard F-statistic for zero multiple correlation.)