CHAPTER 16 Getting Straight Talk on Straight-Line Regression 231

regression coefficient. Imagine you enroll 20 participants and measure them, then

create a regression model. If you’re really lucky, the SE may be as small as you

wanted, or even smaller, so you know if you conduct a larger study, you will have

enough sample.

But the SE from a pilot study usually isn’t small enough (unless you’re a lot luck-

ier that we’ve ever been). That’s when you can reach for the square-root law as a

remedy! Follow these steps to calculate the total sample size you need to get the

precision you want:

1.

Divide the SE that you got from your pilot study by the SE you want your

full study to achieve.

2.

Take the square of this ratio.

3.

Multiply the square of the ratio by the sample size of your pilot study.

Imagine that you want to estimate the slope to a precision or SE of ±5. If a pilot

study of 20 participants gives you a SE of ±8.4 units, then the ratio is 8 4 5

. / , which

is 1.68. Squaring this ratio gives you 2.82, which tells you that to get an SE of 5,

you need 2 82

20

.

, or about 56 participants. And because we assume you took our

advice, we’ll assume you’ve already recruited the first 20 participants for your

pilot study. Now, you only have to recruit only another 36 participants to have a

total of 56.

Admittedly, this estimation is only approximate. But it does give you at least a

ballpark idea of how big your sample size needs to be to achieve the desired

precision.