Confidence Intervals for Correlation Ratios

It is suggested that for fixed effects experiments, the traditional statistical question is inappropriate. It is suggested that variance ratios—the signal to noise ratio (σ 2 a /σ 2 e ) and the correlation ratio (σ 2 a /σ 2 t )—are more desirable. Criticisms of these values are explored. Finally confidence intervals and percentiles for the random and fixed effects model's signal to noise and correlation ratio are given. The latter being dependent on the evaluation of a family of non-central F distributions. The latter will also give the confidence interval and percentiles of the multiple correlation coefficient in the regression model. The lower limit of the confidence interval can test the traditional null hypothesis. The upper limit of this interval is suggested to be a test which would allow the investigator to accept the null hypothesis.