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Carter
Carter
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The sample size formula for a one-sample t-test is often given as:

$$ n = \frac{(z_{1-\alpha/2} + z_\beta)^2 \sigma^2} {\Delta^2} $$$$ n = \frac{(z_{1-\alpha/2} + z_{1-\beta})^2 \sigma^2} {\Delta^2} $$

Meanwhile, G*Power appears to use the t-distribution, which gives larger $n$'s because of the heavier-tailed t-distribution. This strikes me as more accurate since we'll be using the t-distribution for testing. Is using the normal quantiles to calculate sample size then underestimating the necessary sample size for a given power and type-I error?

The sample size formula for a one-sample t-test is often given as:

$$ n = \frac{(z_{1-\alpha/2} + z_\beta)^2 \sigma^2} {\Delta^2} $$

Meanwhile, G*Power appears to use the t-distribution, which gives larger $n$'s because of the heavier-tailed t-distribution. This strikes me as more accurate since we'll be using the t-distribution for testing. Is using the normal quantiles to calculate sample size then underestimating the necessary sample size for a given power and type-I error?

The sample size formula for a one-sample t-test is often given as:

$$ n = \frac{(z_{1-\alpha/2} + z_{1-\beta})^2 \sigma^2} {\Delta^2} $$

Meanwhile, G*Power appears to use the t-distribution, which gives larger $n$'s because of the heavier-tailed t-distribution. This strikes me as more accurate since we'll be using the t-distribution for testing. Is using the normal quantiles to calculate sample size then underestimating the necessary sample size for a given power and type-I error?

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Carter
Carter
  • 124
  • 4

Why are normal quantiles used for sample size calculations instead of the t-distribution?

The sample size formula for a one-sample t-test is often given as:

$$ n = \frac{(z_{1-\alpha/2} + z_\beta)^2 \sigma^2} {\Delta^2} $$

Meanwhile, G*Power appears to use the t-distribution, which gives larger $n$'s because of the heavier-tailed t-distribution. This strikes me as more accurate since we'll be using the t-distribution for testing. Is using the normal quantiles to calculate sample size then underestimating the necessary sample size for a given power and type-I error?