Effects can be ignorable

- oh, real, yes, but fine -

So say, worst case scenario,

μ's right there on the line.

The power is the modest chance

Effects as small as μ's

Will have to be significant 

In the C.I. I choose.

I pick a null hypothesis

and set out to reject.

But can I shrink my sample size

and find that small effect?

I am a stingy scientist

   --- Blame NIH, not me!

I pick n = 25

What will that let me see?

I set up an alternative

but have to search a bit

for standard deviations next

by trawling prior lit

I must start by considering

how many tails make sense.

Then, μ and σ both in hand,

It's time for confidence!

Selecting my significance,

Say 95%

I find the corresponding z

For where the tails went

The sample average x̄ vs.

z times standard err'

Shows when the test rejects H-naught

Though α warns, "beware!"

A simple calculation, now

Of x̄ - μ

divided by the standard error

brings power into view

I end up with a last z score

And turn it to percent

The chance effects as small as μ

Turn out significant