Johnson Transformation…..help

1.  Good basic approach you use, that normality is checked before generating non-meaningful statistics.
2.  I do not consider myself adequate t respond to the Johnson transformation aspect of tour query, but I can respond this way:  It is likely that you can find some sort of standard transformation that makes the data look normal … but the burning question is what is inherit in the process that would cause the data to fit the transformation selected?  In other words, if data is not normal, but the log transformation makes it normal but there is no process fundamental why the log should be present, then beware that the transformation is likely not valid.    Just a self-imposed rule I use, and it forces me to think about the process and the measurements.
3.  You mention outliers … have you considered recording errors and special causes?   Perhaps there is another independent variable manifesting itself.
4.  I presume you have weighed the costs/time in getting a larger data set.

Most of the time data would not follow Normal Distribution. You can do Johnson transformation on the data; but the transformation is complex. After doing the transformation; interpreting it is very difficult. My suggestion would be to go to Minitab, find out the distribution which it belongs to and then do corrosponding analysis using that distribution.
Also do root cause for the data which is outlier. If you find a very special cause (not to be repeated again) for that; remove that and do analysis. If not; then you cannot remove the data for analysis. Also collect few more data points to see if you get more outliers. It you get those; it means that your process is not stable.

They kind of make Forrest look like a whining baby, don’t they?Kind of reminds me of the old Taguchi / Classical DOE battles. Those
who engaged in debate did nothing. Those that followed either
method, went and did work learned. I wonder if there is a message
there somewhere?

MM,
I find few applications where I MUST transform data to do the proper analysis with the data.  Stratification and understanding the data usually solves the problem.  If not, then nonparametrics often do the trick.  Box Cox works a lot of times if I really need to transform.  So, here is an example whereby I would need to use a transformation, especially a Johnson.
I am evaluating the purchase of a new machine.  I have collected data on the cycle time it takes to produce quality parts.  Since it is time, the data will be skewed.  I look for outliers and explore the data and it still remains significantly skewed.  The manufacturer has provided specs on the expected average cycle time I can expect.  They fail to provide a median cycle time.  Since the data is so skewed, the concept of comparing my skewed data against the expected average makes no sense.  Therefore, the use of a non parametric one sample sign test is excluded.  Assuming the mean and median to be the same won’t fly. I try transforming the data using Box Cox so that I can do a one sample t test to see if the machine is performing as promised.  Unfortunately, Box Cox doesn’t work.  If your Box Cox doesn’t work then you must use your Johnson.  Assuming that transforms the data, I can now carry out my hypothesis test.  Remember to also transform the spec using the same transformation formula.  I could likewise do some process capability analysis on the transformed data if I didn’t want to try and identify the distribution and then do a non normal process capability.  I would likely not share any of the above outputs with anyone since the units of measurement are strange values.  I would only describe my conclusions.  At the end, if I had to, I could backtransform things back into their original units.  Hope this helps.