Noncentrality Interval Estimation and the Evaluation of Statistical Models

Select the Quick tab of the 2-Way ANOVA: Interval Estimation dialog box to access options to implement the procedure (Fleishman, 1980; Steiger & Fouladi, 1997) for computing a confidence interval for RMSSE, the root mean square standardized effect size.

Observed F. In the Observed F box, enter the observed value of the F-statistic.

No. of Rows. In the No.of Rows box, enter the number of rows in the two-way ANOVA design.

No. of Columns. In the No. of Columns box, enter the number of columns in the two-way ANOVA design.

Sample Size (N). In the Sample Size (N) box, enter the number of observations in each cell of the two-way ANOVA design.

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

Conf. Level. In the Conf. Level box, enter the confidence level for the confidence interval calculation. Note that confidence limits are given for the following quantities for the selected effect:

Delta. These confidence limits are for the noncentrality parameter of the noncentral F-distribution.

RMSSE. These confidence limits are for the RMSSE

Power. These confidence limits
are post hoc statistical bounds on power. Because the F-statistic
provides information that allows one to set confidence limits on delta, and because power for any particular
ANOVA design is a function of delta,
it is therefore possible to set confidence limits on power, given the
observed data. This technique is a relatively recent idea, and, as such,
is not discussed in the classic textbooks on ANOVA. It is also not discussed
in Cohen's (1983) power analysis text. For an example of this calculation
and its interpretation, see Steiger and Fouladi (1997, page 252).

Power Goal. In the Power Goal box, enter the power goal used as a target in calculating post hoc confidence intervals on sample size.

Effect to Test. Choose the option button corresponding to the effect (Row, Column, or Interaction) for which you want to compute the confidence interval.