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Newbie, so please bear with me.. I'm trying to get my head around how I can use the awesome tool I found and what it does not give me any info about.

The case: Using this site: http://hedwig.mgh.harvard.edu/sample_size/js/js_parallel_quant.html I have made a pilot study with 7 measurements and stated that I want a power of 80%.

It gives me this output:

The provided parameters were: significance level (adjusted for sidedness) = 0.025, standard deviation = undefined, number of patients = 7, power = 0.8, difference in means = undefined, location of mean in one group as a percentile of the other group = undefined.

The variable calculated was the minimum detectable difference.

A total of 7 patients will enter this two-treatment parallel-design study. The probability is 80 percent that the study will detect a treatment difference at a two-sided 0.05 significance level, if the true difference between treatments is 2.661 times the standard deviation.

My questions:

  • is 2.661 the z-score; _________?

  • I consider 2.661 as a min. resolution that I'm able to differentiate between two different means. Is that a wrong assumption; ___________?

Would plotting the mean with top and bottom error bars with length of 2.661 x STD be the 95% confidence interval; ___________?

A concrete example were I wish to use this knowledge: I wish to know something about the packing of spheres in a cylinder by dividing the total volume of spheres with the cylinder volume.

I have filled up a die with sphere particles and weighted the content afterwards (n=7). Counting the particles and comparing it to the mass, gives me the knowledge that a similar experiment must have had an average of 188,7 particles with std = 2.2 particles.

85% of the particles, or above, have a diameter in the range of 1000-1400 µm.

Plotting the average diameter of the particles against the packing gives me this: Plot

Would it be fair to say that another sample with average in region 1 and 4, and a qual or smaller STD, would be detected by my experiment____?

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  • $\begingroup$ undefined means empty input. So it seems as they are not needed.. $\endgroup$
    – Norfeldt
    Jun 27, 2012 at 15:37
  • $\begingroup$ that is surprising to me. I have no clue how one could calculate power without specifying the true effect size (which is identified by the mean & standard deviation of the differences) $\endgroup$
    – Macro
    Jun 27, 2012 at 15:39
  • $\begingroup$ @Macro The answer really tells what is assumed. "A total of 7 patients will enter this two-treatment parallel-design study. The probability is 80 percent that the study will detect a treatment difference at a two-sided 0.05 significance level, if the true difference between treatments is 2.661 times the standard deviation." The effect size is assumed to be 2.661. The mean difference divided by its standard deviation for a two-sided alpha =0.05 level test and a sample size of 7. The computed power for that effect size is 0.80. $\endgroup$
    – Michael R. Chernick
    Jun 27, 2012 at 16:03
  • $\begingroup$ You're right @Michael, I didn't read carefully enough. $\endgroup$
    – Macro
    Jun 27, 2012 at 16:23

1 Answer 1

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1) 2.661 is the effect size not the z score. You don't know the value of the test statistic when doing a power/sample size calculation. This is done prior to collecting the data to tell you what you can reasonably expect for the given sample size. 2) 2.661 multiplied by the standard deviation is the true difference in means that will be large enough to that you can expect the null hypothesis will be rejected 80% of the time that you apply such a test with that big a true mean difference. 3) You can invert the hypothesis test to get a confidence interval. The construction will depend on the observed value of the mean difference and its known or estimated standard deviation but cannot be inferred from this power calculation at a specified alternative.

I am not attempting to answer the last part of your question regarding the concrete example.

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  • $\begingroup$ I thank you for your time and answer. The reason for asking such 'silly' questions is because I really want to learn apply statistics.. It's a pilot study and I really want to know if I can extract some conclusions from it or if it can tell me to proceed or not. $\endgroup$
    – Norfeldt
    Jun 27, 2012 at 18:24
  • $\begingroup$ These are not silly questions. $\endgroup$
    – Michael R. Chernick
    Jun 27, 2012 at 18:26
  • $\begingroup$ Thank you. (I'm still reading your answer to see if I understand it totally right) $\endgroup$
    – Norfeldt
    Jun 27, 2012 at 18:29
  • $\begingroup$ I'm a bit confused... 1) I would expect that when doing a sample size calculation that I would use the power to set the value of the test statistic? 2) Is 80 % a good rule of thumb? 3) Can you help me a bit more with this answer? Sorry for all these questions, but I'm really struggling here.. $\endgroup$
    – Norfeldt
    Jun 27, 2012 at 18:56
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    $\begingroup$ In sample size determination for clinical trials in the medical device and pharmaceutical industries the FDA requires 80% power. This is not a very high standard but failing to show significance is the manufacturer's risk and the FDA is mainly concerned with controlling the type I error because it represents the consumers risk of having an ineffective product approved. The critical value for a test statistic depends on the sample size and the significance level not the power. Given the sample size and the significance level you know the criticl value for the test statistic. $\endgroup$
    – Michael R. Chernick
    Jun 27, 2012 at 19:07

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