Reporting Uncertainty
The uncertainty is typically reported with the value using the ± symbol. For example, if a 5 mg uncertainty is known to be associated with a weight measurement of 1.505 g, we report
weight = 1.505 ± .005 g
Student's t
The Student's t is given by
The Student's t is a parameter that describes the probable error in a finite series of measurements that sample a normally distributed parent population. It is the valid parameter to use when the standard deviation is also estimated from the series of measurements.
The first use of Student's t is for reporting values with confidence intervals. In this case, we use the form
A value for t is found in a table for a particular confidence level (% chance of being correct). The values are reported, for example, like
Student's t Test
The second use for Student's t is to test for significance. In this case we have two or more data sets that we wish to compare. We want to know whether or not they came from the same parent population (same object, etc.). To do this we
1) Formulate the null hypothesis, i.e, the two results come from sampling the same parent population.
2) If this is true, then the two results have the same m and s.
3) Using two Student's t formulas, equating the m, we calculate tcalc
where
4) we then compare tcalc to that of the table value for N1+N2-2 degrees of freedom.
5) If tcalc<ttable, then the null hypothesis is not wrong, else if tcalc>ttable, then the null hypothesis is wrong, and the two results are different.
This test may also be used to reject data from a data set.
This page was created by Professor Stephen Bialkowski, Utah State University.
Monday, August 28, 2006