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A.4 Calculating the default threshold for the mean NLR SD
In statistical analysis, you can improve the confidence in the estimated standard
deviation by using many replicate samples. In addition, you can pool variance
estimates from many replicate groups, assuming that the variance is the same
among all the replicate groups. With these principles, you can calculate the
confidence intervals based on the Z or normal distribution:
Z ( α ) × Mean NLR SD
CI = Mean NLR ± -------------------------------------------------------n
Where—
CI is the confidence interval for the mean NLR for a given gene, based on
n replicates. In the Generation III Microarray System, most genes are spotted in
duplicate (n=2). CI specifies a range of values within which the mean NLR SD
may lie. You can calculate the intervals for different confidence levels. For
example, a CI calculated at 99.5% is the range of values that will contain the
true mean 99.5% of the time.
α is the probability of values falling outside the confidence interval because of
random variation. α complements the confidence level for the mean NLR SD.
For example, a 99.5% confidence interval has an α value of 0.005.
Z is a value that is a function of α. Based on a given α value, you can look
up the corresponding Z value in a Z-test table. The Z value for an α of 0.005
is 2.807.
Note: The confidence interval equation assumes that the control samples are
spotted in duplicate. If one of the duplicates is not available, drop the 2 from
the equation.
A.4 Calculating the default threshold for the mean
NLR SD
A gene is significantly differentially expressed if the confidence interval for the
Mean NLR does not include 0. Using the α value of 0.005 (section A.3), you
can approximate the significance in the difference in NLR by calculating the
half-width for the confidence interval:
CIHalf = Z * (Average NLR SD)/ 2
Raise the CIHalf result to the power of 10 to convert the result from logarithmic
space to n-fold space. Table A-2 lists the results of these calculations for an
α value of 0.005. The calculations assume the controls are spotted in duplicate
on the slide.
Lucidea Microarray ScoreCard User’s Guide
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