# Interpreting online sample size stat tool in order to (gain) confidence intervals

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:

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____?

• undefined means empty input. So it seems as they are not needed.. Commented Jun 27, 2012 at 15:37
• 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) Commented Jun 27, 2012 at 15:39
• @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. Commented Jun 27, 2012 at 16:03
• You're right @Michael, I didn't read carefully enough. Commented Jun 27, 2012 at 16:23