BSA Flow Software Installation and User's Guide - CSI

u 2
4
σ
u − u
u
(7-39)
2 N
2
4 N u
For reliable results the expressions above require that N is ”large” (at least
30-50, preferably more), which is normally not a problem in an LDA
experiment.
It is also required that samples are independent. If they are not N must be
replaced by the ”effective” number of samples irrespective of the number of
samples actually taken:
⎧ Tm
⎪
= ⎨2τ
I
⎪
⎩ N
Tm
if N >
2τ
otherwise
Neff I
(7-40)
2
2
-where Tm is the time between first
and last sample, and τI is the integral
time scale of the flow, which must be
estimated either by hand or based on
the samples themselves.
Please refer to the section ”Estimation of the integral time scale τΙ” for
details.
The above expressions will produce 68% confidence limits, meaning that
based on the sample data provided there is 68% confidence that the true
statistic we are looking for will be within the estimated value plus/minus the
confidence limit value from above.
For other confidence levels the confidence limit value must be multiplied by
a factor, that can be derived from the desired confidence level using the
inverse error function:
( ConfLevel)
2
−1
ConfFact = erf
(7-41)
Examples of commonly used factors:
Desired confidence level: 50% 75% 90% 95% 98% 99%
Confidence limit factor: 0.674 1.150 1.645 1.960 2.326 2.576
In BSA Flow Software, we have chosen 95% confidence level, and we
calculate the confidence limits for the first and second moments. We have
implemented the confidence limit calculations applicable to normal
distributions:
Statistic
Mean
u
1.96
N
2
RMS 1.96
95% confidence limit
assuming normal distribution
7-102 BSA Flow Software: Reference guide
u
2 N
2
(9)
(10)