Comparison of two measurements with known uncertainty
This data comparison tool can help evaluate whether measured results agree with each other within their unc
Enter your measured values and uncertainties in the highlighted cells.
Relative
Uncertainty Range
X
u
Uncert.
Xu
X+u
A =
1.2
±
0.2
17%
1
1.4
B =
1.8
±
0.2
11%
1.6
2
Percent difference =
40%
Hypothesis testing:
Does
A = B?
Z(AB) =
2.12
p =
0.034
came from the same parent population (are equivalent),
found from a twotailed ttest with infinite degrees of freedom.
Note:
pvalues 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
Gaussian (Normal) Probability Distributions with Known Means and Variances
G(x) = (1/(sigma*sqrt(2pi)))*exp(x^2/2sigma^2)
X1
G(X1)
X2
G(X1)
0.4
0
1
0
0.48
0
1.08
0
0.56###
1.16
0.01
0.64###
1.24
0.04
0.72###
1.32
0.11
0.8###
1.4
0.27
0.88###
1.48
0.55
0.96###
1.56
0.97
1.04###
1.64
1.45
1.12###
1.72
1.84
1.2###
1.8
1.99
1.28###
1.88
1.84
1.36###
1.96
1.45
1.44###
2.04
0.97
1.52###
2.12
0.55
1.6###
2.2
0.27
1.68###
2.28
0.11
1.76###
2.36
0.04
1.84###
2.44
0.01
1.92
0
2.52
0
pvalue
is the statistical probability that the two measurements
0
2
4
6
8
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 Spring '08
 any
 Normal Distribution, Light, data comparison tool, p= p= p=, uncertainty limits, 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 11.4 12.2 G

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