[editing original post to clarify my question]

I have looked at some of the other posts on this but still can't grasp if these 2 are different approaches to determining somethings stat sig, or if one/both are just plain wrong.

Approach 1: Control group ={mean: 10, CI (90%)=[5,15]} Test Group = {mean: 20, CI(90%)=[17,22]}. This is stat sig because 90 % of control group is below 15, and 90+ % of test group is above 15. Thus the distribution of average test - control > 0 with 90% CI so we have a stat sig result.

Approach 2 : Control group ={mean: 10, CI (90%)=[5,15]}, Test group ={mean: 20}. Because the mean of test group is > +2 SE of the control the effect is stat sig. Are either of these approaches right/wrong?

  • 1
    $\begingroup$ Neither is correct, because neither correctly evaluates the variability of the test statistic (which implicitly is the difference of the means). You can learn more about this at stats.stackexchange.com/questions/18215 and stats.stackexchange.com/questions/31657. $\endgroup$
    – whuber
    Apr 5, 2015 at 12:46
  • $\begingroup$ "because 90 % of control group is below 15". Wrong. The confidence interval of the mean does not directly tell you about the distribution of the values. It is closer to correct to say that there is a 90% chance that the true group mean is less than 15 (though the real definition of a CI is more subtle). $\endgroup$ Apr 5, 2015 at 13:21


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