# Area of overlapping for 2 normal distribution curves

Six Sigma – iSixSigma Forums Old Forums General Area of overlapping for 2 normal distribution curves

Viewing 12 posts - 1 through 12 (of 12 total)
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• #52139

CK
Participant

Hi,
Could anyone advise me on how to calculate the overlapping area under the 2 normal distribution curves?
Eg.

Group A
Group B

Sample Size, n
30
30

Mean, ì
12.
15

Std Dev, ó
0.5
1

regards

0
#183000

Remi
Participant

Hi ck,
wherever would you need that for? Are you sure that this is what you need to be calculated?
Also the 2 values of N are non-informative because they have no influence on the outcome of the question like you stated it.
here is a way to calculate:0] draw a picture of how it looks like 1] calculate at which location X the 2 graphs meet (not 9 but the 13 is the correct outcome (see 0])). 2] Calculate for N(12,0.25) the area to the right of X: P(x>X) and 3] calculate for N(15,1) the area to the left of X: P(x<X)4] Sum up 2] and 3] for the outcome.
Steps 3 and 4 are easy to do in Minitab (Calc -> Prob distr-> Normal->….).
Good luck, Remi

0
#183001

Bower Chiel
Participant

Hi ckCan you put your query in a context? The probability distribution curves for normal distributions with the stated means and standard deviations intersect at ordinate 13.11 but it’s not clear to me exactly what you wish to do with that information.
Best Wishes
Bower Chiel

0
#183002

Sloan
Participant

This looks suspiciously like a homework question. I would not expect to see a lot of background explanation.

0
#183012

sgbb
Member

BowerCan you explain how you arrived at 13.11 ?

0
#183022

Bower Chiel
Participant

Hi sgbbI used the Excel function for the ordinate on a normal distribution curve and the Excel Solver tool. If you post an e-mail address I’ll send you the spreadsheet I used.Best Wishes Bower Chiel

0
#183032

sgbb
Member

Pl send it to me at : [email protected] you for the assistance

0
#183034

CK
Participant

Hi, Remi,

Great thx for the explanation. The purpose of doing this is to differentiate how far apart between both data distribution curves based on area of overlapping, instead of P-value. P-value doesn’t give a good idea how both data sets being separated, instead giving the differences significance. I personally felt that this an another alternative to look at the differences. What is your thought?
Regards

0
#183038

Remi
Participant

Hai Bower Chiel,
13.11 is close but not correct.
Assumption: data is perfect N(Mu, Var).
Then N(Mu1,Var1)=N(Mu2,Var2) collapses into
(X-Mu1)/Stdev1 = +/- (X-Mu2)/St Dev2.
In this case (x-12)/0.5 = +/- (x-15)/1 gives X= 9 and X= 13.
I just realized that you have to use both values because only between 9 and 13 N(12,.25) > N(15,1)  (one can almost ignore the area left of X=9 because it has value < 0.00001)
If data is not perfect ofcourse all these calculations are just an approximation to a value that will never be known.
Remi

0
#183039

Remi
Participant

Hai ck,
sounds ok to me.
Be careful that you don’t give too much value to the mathematically calculated outcomes in the case of real products. You will seldom have perfect normal distributions. And if you base the calculations on only 30 products of each then a simpler method is to calculate the number of “overlapping” (or differing) products. That has as extra advantage that it is distribution independent but as a disadvantage predictions are difficult.
An advantage of p-value-reasoning is that you not only look at the difference as such (abolute comparison) but on how much compared the found difference is to a difference caused by Chance (relative comparison, H0 principle).
Remi

0
#183046

Vallee
Participant

Not used by many but it may give you a different perspective. Look up Signal Detection theory and D prime. Also there are optimal fit programs that may be what you are looking for if you actually describe why and in what context you to expect to use this for… your description is still pretty muddy.

0
#183070

CK
Participant

Hi, Remi,
Agree with your thoughts. and great thx for the input. Good day.
regards
To all,