2
$\begingroup$

If I have a normally distributed population of 3.5 million elements, and I want to sample enough of them to make a statement with 99.6% confidence on a 1-tailed test, what should my sample size be? Is 100 enough, or would it need to be significantly larger?

$\endgroup$
  • $\begingroup$ Do you have an achieved amount of power that you want? $\endgroup$ – user25658 Sep 12 '13 at 17:04
  • 3
    $\begingroup$ (1) One-tailed test of what parameter? The mean? Standard deviation? Variance? etc. (2) The answer for the mean is a sample size of one. With this you can construct a 99.6% confidence interval. It will be very wide, though :-). $\endgroup$ – whuber Sep 12 '13 at 17:18
5
$\begingroup$

You can use the following R script to generate your required sample:

library(pwr)

pwr.t.test(n = SAMPLE_SIZE , d = EXPECTED_EFFECT_SIZE, sig.level = 0.004 , power = DESIRED_POWER, type = c("one.sample"), alternative = "greater"/"less")

You need to provide 3 of the 4 values (n,*d*,sig.level, and power), while making the 4th value = NULL. For example, if you wanted to see if 100 subjects is enough, you could fill in information for n, d (if you have an expected effect size, for this example d will be equal to 0.4), your significance level of 0.004 (or 99.6% CI), while leaving power as Null. Lastly, you will need to choose the direction for the one-tailed test by choosing "greater" or "less", which for this example, I chose to use "greater". The below R script will perform this calculation:

library(pwr)

pwr.t.test(n = 100 , d = 0.4, sig.level = 0.004 , power = NULL, type = c("one.sample"), alternative = greater)

Below is the generated output:

 One-sample t test power calculation 

          n = 100
          d = 0.4
  sig.level = 0.004
      power = 0.8991141
alternative = greater

As you can see in the above output, we have 89.9% power to test our null hypothesis with an expected difference in effect size of 0.4 with 99.6% confidence ($a$ = 0.004).

| cite | improve this answer | |
$\endgroup$
  • 2
    $\begingroup$ Thanks -- really like this one because you're "teaching a man to fish", while at the same time not being a jerk because he doesn't know how! Very cool. $\endgroup$ – Walrus the Cat Sep 12 '13 at 18:02
  • $\begingroup$ No problem! I try to keep things as simple as possible because everything involving stats can be overwhelming (to say the least!). Let me know if there is anything else that I can help you with in regards to this calculation! Best of luck! $\endgroup$ – Matt Reichenbach Sep 12 '13 at 19:42
  • 1
    $\begingroup$ @MattR - The word greater requires quotes in pwr.t.test(). $\endgroup$ – bill_080 Sep 12 '13 at 21:23

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.