Setting Display Units; Changing Precision (Sigma Value); Confidence Intervals - Thermo Scientific XL2 User Manual

Setting Display Units

Changing Precision (Sigma Value)

Confidence Intervals

Thermo Scientific
Select the Display Units radio buttons on the Set Display Units page to choose between ppm
(parts per million) and percentage (hundredths of whole) displays when taking readings, and
to change the Sigma value you want for the reading.
In the Display Units area, you can select between Percent composition and Parts per Million
as the units displayed in a measurement, and you can change this setting independently for
any mode. You can also change the Sigma for each of these modes independently. When you
have changed the display units to the appropriate values, select the Close button to save these
settings for use.
Sigma is the symbol used for Standard Deviation, a measure of how much a set of numbers
deviates from the mean. For example, each of the three data sets {0, 0, 14, and 14}, {0, 6, 8,
and 14} and {6, 6, 8, 8} has a mean of 7. Their standard deviations are 7, 5, and 1,
respectively. The third set has a much smaller standard deviation than the other two because
its values are all close to 7. In a loose sense, the standard deviation tells us how far from the
mean the data points tend to be. The number of standard deviations between the process
mean and the nearest specification limit is given in sigmas. As process standard deviation goes
up, or the mean of the process moves away from the center of the tolerance, the sigma number
goes down, because fewer standard deviations will then fit between the mean and the nearest
specification limit.
Confidence intervals assume that the data are from an approximately normally distributed
population - generally, sums of many independent, identically distributed random variables
tend towards the normal distribution as a limit. Using this assumption, about 68 % of the
values must be within 1 standard deviation of the mean, about 95 % of the values must be
within two standard deviations, about 99.7 % must lie within 3 standard deviations, and
about 99.99% of the values must lie within 4 standard deviations.
The greater the sigma value of the test, the more confident you can be that the sample is as it
appears, but the more difficult and time consuming the testing must be to verify this. That's
why it's important to use the most appropriate sigma value for the test. By adjusting the sigma
value for each type of test, you can optimize the process for your needs.
5
Common Operations
Setting Display Units
Niton XL2 Analyzer User's Guide 71