Some Distributions and Their Implications for an Internal Pilot Study With a Univariate Linear Model

Area of Science:

• Statistics
• Biostatistics
• Quantitative Research Methods

Background:

• Sample size determination often relies on preliminary variance estimates, which can be inaccurate.
• Internal pilot designs allow for sample size adjustment based on early data but may introduce bias.

Purpose of the Study:

• To investigate the statistical properties of internal pilot designs in general linear univariate models.
• To quantify the bias introduced by using fixed sample size methods after sample size re-estimation.

Main Methods:

• Derivation and evaluation of the likelihood ratio test statistic components for general linear univariate models.
• Analysis of the bias in variance estimates and its impact on test size and confidence intervals.

Main Results:

• The uncorrected fixed sample F-statistic is the likelihood ratio test statistic but does not follow an F distribution.
• Fixed sample size variance estimates are biased downward, potentially inflating test size.
• Biased confidence intervals can arise for secondary parameters and the variance estimate.

Conclusions:

• Internal pilot designs, while useful for sample size adjustment, can introduce significant statistical biases.
• Researchers must be aware of and account for potential biases in variance estimation and hypothesis testing when using these designs.