

13th April 2012, 01:20 PM

Involved in Discussions
Registration Date: Jun 2011


Posts: 36
Thanks Given to Others: 11
Thanked 1 Time in 1 Post
Karma Power: 16 Karma: 15


Test of Means or Medians for Non Normal Populations?
HI All, I have a number of paired data sets of various characteristics that per my Anderson Darling test one or both of the sets are not normally distributed at a 95% confidence level. I would like to see at that same confidence level if the means are different. I don't think I can use a two sided t test in this case. Is there a test for the means on non normally distributed data? Should I use the MannWhitney U test or Mood's Median test?
Thanks for the advise
Brad

13th April 2012, 01:33 PM

Involved in Discussions
Registration Date: Jul 2011


Posts: 176
Thanks Given to Others: 24
Thanked 144 Times in 87 Posts
Karma Power: 33


Re: Test of means or medians for non normal populations?
Hi Brad
The best thing to do is post your data.
NC

13th April 2012, 01:39 PM


Statistician
Registration Date: May 2005
Location: New Jersey
Age: 49


Posts: 974
Thanks Given to Others: 240
Thanked 362 Times in 252 Posts
Karma Power: 143


Re: Test of means or medians for non normal populations?
Quote:
In Reply to Parent Post by Brad Gover
HI All, I have a number of paired data sets of various characteristics that per my Anderson Darling test one or both of the sets are not normally distributed at a 95% confidence level. I would like to see at that same confidence level if the means are different. I don't think I can use a two sided t test in this case. Is there a test for the means on non normally distributed data? Should I use the MannWhitney U test or Mood's Median test?
Thanks for the advise
Brad

If you have PAIRED data, then the differences of the pairs should be approxminately normal if the two set of data came from the same distribtion. If so, you can use the paired ttest.
__________________
Steven Walfish
When in doubt, ask your company statistician!

Thank You to Statistical Steven for your informative Post and/or Attachment!


13th April 2012, 01:52 PM

Involved in Discussions
Registration Date: Jun 2011


Posts: 36
Thanks Given to Others: 11
Thanked 1 Time in 1 Post
Karma Power: 16 Karma: 15


Re: Test of means or medians for non normal populations?
I believe the data is paired in so far that one instrument measured the exact same point as the other. Unfortunately I only have one set of measured data from both instruments. One company measured each characteristic once as did the other company. Each point corresponds to the exact same area so ideally they should be identical. I will try to post an excel file of the two data sets.
Thanks,
Brad

13th April 2012, 01:57 PM

Involved in Discussions
Registration Date: Jun 2011


Posts: 36
Thanks Given to Others: 11
Thanked 1 Time in 1 Post
Karma Power: 16 Karma: 15


Re: Test of means or medians for non normal populations?
Quote:
In Reply to Parent Post by NumberCruncher
Hi Brad
The best thing to do is post your data.
NC

Hopefully my attachment will get posted
Thanks!
Brad

13th April 2012, 03:24 PM

Involved in Discussions
Registration Date: Jul 2011


Posts: 176
Thanks Given to Others: 24
Thanked 144 Times in 87 Posts
Karma Power: 33


Re: Test of means or medians for non normal populations?
Hi Brad
I've looked at your data. Most of the differences are approximately normally distributed, but there are a few serious outliers in both data sets.
A simple t test suggests that data set 1 is not significantly different to zero, but data set 2 is significantly different to zero. My concern is that, when I take out just 2 outliers, from data set 1, the t test tells me that this is also significantly different to zero.
I am not happy with the t test because of these outliers.
I would suggest using the MannWhitney test on the data and see if this confirms the above conclusions.
NC

16th April 2012, 08:45 AM


Heretical Statistician
Registration Date: Jan 2003
Location: New England


Posts: 2,949
Thanks Given to Others: 1,236
Thanked 2,093 Times in 1,243 Posts
Karma Power: 375


Re: Test of Means or Medians for Non Normal Populations?
Brad: your data is still matched pairs. The fact that you have only one reading from each supplier means that the suppliers individual repeatability is confounded with the between supplier reproducibility. If the total measurement error is acceptable in relation to the specifications then all is well. If it isn't then you need to determine if one or both suppliers has substantial repeatability problems. (what is the specification limit?)
I have attached a spreadsheet with the Youden analysis, Matched pair analysis (and I also threw in a gratuitous distribution analysis).
You have a small bias between the two measuremetns in data set 2 but it is very small compared to the total error.
There is no bias between the two measurements in data set 1.
As an aside, the lack of fit to a Normal distribution is very minor. t tests and ANOVAs are relatively unnaffected by this lack of fit. And in any case a simple plot of the data tells you what you need to know. No need for fretting about mathematical precision.
I think that we have collectively forgotten how to plot and think about our data now that sophisticated statistics can be done in milliseconds with JMP or Minitab...
__________________
Statistics without physics is gambling; Physics without statistics is psychics

Lower Navigation Bar


Do you find this discussion thread helpful and informational?
Visitors Currently Viewing this Thread: 1 (0 Registered Visitors (Members) and 1 Unregistered Guest Visitors)


Thread Tools 
Search this Thread 


Display Modes 
Rate Thread Content 
Linear Mode


Forum Posting Settings

You may not post new threads
You may not post replies
You may not post attachments
You may not edit your posts
HTML code is Off




