Analyzing skewed data, how to determine % spread and variation? Testing method error

#1
Hello everyone,

I'm trying to determine the overall error of a measurement method by comparing it to the true value.

I have a set of data which I'm trying to analyze. I determined the numbers by taking an absolute difference between the true and the measured values and computed the mean and the standard deviation of those differences.

I was trying to show a normal distribution graph with 3 sigma covering 99.7% of data to say that the error for the method that I'm testing is between x and y. For example my mean and stdv is 0.6 +/- 0.5, so my 99.7% data distribution would be -0.9 to 2.1.

Unfortunately, my data turned out to be non-normal. (I also tried to analyze it using true values instead of absolute, which turned our normal and gave me a result of 0 mean +/- 0.8 STDV, but I don't think that this is correct, since I don't care if my errors are positive or negative, I'm just trying to compute an overall error)

I've tried transforming the data, but none of the transformations seem to be working.

My data is right skewed. How do I compute the results so that they are easily understood and can be extrapolated to the use of this method?

My main goal is to say "when measuring something using this method, your error is +/- whatever it is"

I attached the histogram and Q-Q plot.





I really hope that somebody could help me with this.

Thanks
 

hlsmith

Omega Contributor
#2
Re: Analyzing skewed data, how to determine % spread and variation? Testing method er

Please post that same histogram and Q-Q plot for the non-absolute difference values.
 
#3
Re: Analyzing skewed data, how to determine % spread and variation? Testing method er

Problem solved:
I also tried to analyze it using true values instead of absolute, which turned our normal and gave me a result of 0 mean +/- 0.8 STDV,
So the interval is +/- 0.8*z, så for a 95% interval 0.8*1.96 and for a 3 sigma covering 99.7% it is +/- 0.8*3.
 

rogojel

TS Contributor
#4
Re: Analyzing skewed data, how to determine % spread and variation? Testing method er

hi,
just to clarify some points:
1. The measurement errors will scatter left and right of the true value, so, we generally take the deviations from the true value and NOT the absolute deviations. So, your analysis that gave you the normal distribution is the correct one
2. Hovewer, if you look at the distribution of the deviations from the true value, you would expect a mean of zero. The fact that your mean is different shows that your measurement method is biased, which may or may not be a problem, depending on how big the bias is. Fact is you tend to overestimate the measured value by an amount of 0.6

regards
 
#5
Re: Analyzing skewed data, how to determine % spread and variation? Testing method er

Why would I expect a mean of zero in my absolute value calculations? This makes no sense, since I have a mean of zero using positive and negative numbers.

The problem with using both the positive and negative numbers for my analysis, is that I don't really care which way my error goes, whether it's positive or negative.

So, would I still report the mean of 0 (-0.007) and SD of 0.81 for this?

Also, is this normal enough?

Thanks


 
#6
Re: Analyzing skewed data, how to determine % spread and variation? Testing method er

Also, I wanted to point something out. I'm measuring individual components (x and y) of ANGLES, so positive and negative values are arbitrary, exactly why I thought that the absolute values should be used...
 

rogojel

TS Contributor
#7
Re: Analyzing skewed data, how to determine % spread and variation? Testing method er

Also, I wanted to point something out. I'm measuring individual components (x and y) of ANGLES, so positive and negative values are arbitrary, exactly why I thought that the absolute values should be used...
You said that you are looking at the deviations from the true value. Looking at the mean gives you an idea of the bias - if you have a positive mean it means you overestimate the value etc. If you look at the absolute values you miss the bias bit.
 

rogojel

TS Contributor
#8
Re: Analyzing skewed data, how to determine % spread and variation? Testing method er

So, would I still report the mean of 0 (-0.007) and SD of 0.81 for this?
Well, this information is easy to interpret - I would read it as follows: Your measurement method is accurate (no bias to speak of) and roughly 70% of the measured values are less then 0.8 close to the true value (or 95% of all measurements are within +/- 1.6 of the true value). I do not get a similar interpretation for the absolute values of the deviations from the true value.

regards
 
#9
Re: Analyzing skewed data, how to determine % spread and variation? Testing method er

Thanks for your reply, I will be using the pos and neg values in my analysis.

As for the normality of data... Is the q-q plot normal enough? I could never tell...
 

rogojel

TS Contributor
#10
Re: Analyzing skewed data, how to determine % spread and variation? Testing method er

You have sone deviation from normality, but it only impacts a bit the interpretation if the limits , you might have a bit more then 95% in rhe range if +/- 1.6 but I would say that this is not really important.

regards