Cohen's D, Standard Normal Equivalient, Non-Inferiority


Not a robit
Let us see if writing this out helps me wrap my mind around it, that or maybe you all will come to the rescue.

I have two samples (represented by X1 equaling either 0 or 1 in the data frame) with a lognormal outcome (Y) variable. I then natural log transformed the outcome into a normal variable. I now run a non-inferiority test (pretty much a one-sided ttest that can't exceed a margin, where test is difference of mean X1 = 1 minus X1=0, and it can't be larger than margin, well actually the difference's upper confident limit can't be larger than margin). Pretty straightforward, right?

Now I am transforming this into Cohen's D for the difference and the difference's upper confidence interval. How do I transform the margin cut off value as a reference point. The cut-off value doesn't get used in the Cohen D transformation of the parameters. It is a value that I also log transformed that I wouldn't want the difference to super exceed, and if it did, I would say I couldn't rule out Group 1 is not inferior than group 0.

So if I am looking at differences, I am wanting them not to exceed standard normal "1.64" for the one-sided test? Though my brain is being sluggish on what I don't think is a difficult question. So, that would mean the difference could be beyond 1.64 standard deviations, so Cohen's D -0.25 is around 0.40 < 0.95 and the Cohen's D for the differences UCI is 0.16, which is 0.58 < 0.95, but I feel like I am ignoring the margin used in the null hypothesis for the inferiority test.

Let me know what you all think and if this makes sense or if I am botching things up.

If it helps my Cohen's D for the difference is -0.25 and its upper CI is 0.1682391.