of Comparison two measurements with known uncertainty This data comparison tool can help evaluate whether measured results agree with each other within their uncertainty limits. Enter your measured values and uncertainties in the highlighted cells.
Measurements and their uncertainties
X 1.2 1.8 u 0.2 0.2 Relative Uncert. 17% 11% Uncertainty Range X-u X+u 1 1.4 1.6 2
A= B=
Percent difference = Hypothesis testing: Does A = B? Z(A-B) =
40%
0
0.5
1
1.5
2.12
p=
0.034
Normalized Gaussian Distributions
p-value is the statistical probability that the two measurements came from the same parent population (are equivalent), found from a two-tailed t-test with infinite degrees of freedom. Note: p-values are based on the following assumptions: 1) u is standard uncertainty 2) X u is 68% confidence interval 3) Measurements exhibit normal distribution properties 4) Sample size is very large
0
1
2
Gaussian (Normal) Probability Distributions with Known Means and Variances G(x) = (1/(sigma*sqrt(2pi)))*exp(-x^2/2sigma^2) X1 G(X1) 0.4 0.48 0.56 0.64 0.72 0.8 0.88 0.96 1.04 1.12 1.2 1.28 1.36 1.44 1.52 1.6 1.68 1.76 0 0 0 0 0 0 1 1 1 2 2 2 1 1 1 0 0 0 X2 1 1.08 1.16 1.24 1.32 1.4 1.48 1.56 1.64 1.72 1.8 1.88 1.96 2.04 2.12 2.2 2.28 2.36 G(X1) 0 0 0.01 0.04 0.11 0.27 0.55 0.97 1.45 1.84 1.99 1.84 1.45 0.97 0.55 0.27 0.11 0.04
1.84 1.92 2
0 0 0
2.44 0.01 2.52 0 2.6 0
thin their uncertainty limits.
their uncertainties
A B
2
2.5
sian Distributions
A B
3
Y 2 2
Comparison of multiple measurements with known uncertainties This data comparison tool can help evaluate whether measured results agree with each other within their uncertainty limits. Enter your measured values and uncertainties in the highlighted cells. Delete values from highlighted cells not being used.
Measurements and their uncertainties
A= B= C= D=
X 5 13 11 17
u 2 5 4 3
Uncertainty Range X-u X+u 3 7 8 18 7 15 14 20
Hypothesis testing: B = C? Z(B-C) = B = D? Z(B-D) = C = D? Z(C-D) = A = C? Z(A-C) = A = B? Z(A-B) = A = D? =
0
0.31 Z(A-D) 0.69 1.20 1.34 1.49 3.33 p= p= p= p= p= p= 0.755 0.493 0.230 0.180 0.137 0.001
5
10
15
20
Complete overlap (both midpoints within ranges): p = 0.5 to 1.0 One midpoint within other range: p = 0.32Gaussian Distributions Normalized to 0.9 Ranges overlap but do not include midpoint: p =0.16 to 0.37 Ranges meet but no overlap: p = 0.16 to 0.32 Almost overlap: p = 0.1 to 0.2 Clearly no overlap: p < 0.2
Note: p-values are based on the following assumptions: 1) u is standard uncertainty 2) X u is 68% confidence interval 3) Measurements exhibit normal distribution properties 4) Sample size is very large
0
5
10
15
20
Gaussian (Normal) Probability Distributions with Known Means and Variances G(x) = (1/(sigma*sqrt(2pi)))*exp(-x^2/2sigma^2) X1 -3 -2.2 -1.4 -0.6 0.2 1 1.8 2.6 3.4 4.2 5 5.8 6.6 7.4 8.2 9 9.8 10.6 G(X1) 7E-05 0.0003 0.0012 0.004 0.0112 0.027 0.0555 0.0971 0.1448 0.1841 0.1995 0.1841 0.1448 0.0971 0.0555 0.027 0.0112 0.004 X2 -7 -5 -3 -1 1 3 5 7 9 11 13 15 17 19 21 23 25 27 G(X1) 3E-05 0.0001 0.0005 0.0016 0.0045 0.0108 0.0222 0.0388 0.0579 0.0737 0.0798 0.0737 0.0579 0.0388 0.0222 0.0108 0.0045 0.0016 X3 G(X1) -5 -3.4 -1.8 -0.2 1.4 3 4.6 6.2 7.8 9.4 11 12.6 14.2 15.8 17.4 19 20.6 22.2 0 0 0 0 0.01 0.01 0.03 0.05 0.07 0.09 0.1 0.09 0.07 0.05 0.03 0.01 0.01 0 X4 G(X1) 5 6.2 7.4 8.6 9.8 11 12.2 13.4 14.6 15.8 17 18.2 19.4 20.6 21.8 23 24.2 25.4 0 0 0 0 0.01 0.02 0.04 0.06 0.1 0.12 0.13 0.12 0.1 0.06 0.04 0.02 0.01 0
11.4 0.0012 12.2 0.0003 13 7E-05
29 0.0005 31 0.0001 33 3E-05
23.8 25.4 27
0 0 0
26.6 27.8 29
0 0 0
their uncertainty limits.
r uncertainties
A B
C D
25
Distributions
A
B C
D
25
Visual comparison of two sets of experimental results This data comparison tool is useful for small data sets where the uncertainties are not well known. Enter measured values and uncertainties in the highlighted cells. Enter zeros in cells not used. Set A 441 426 432 422 444 Set B 432 444 426 433 440
420 425 430
Two Sets of Data
435
440
445
450
A B
450