2. Statistics and Statistical Tests

If a confidence interval is specified to be 38.5 +/- 0.9 ppm, what does that say about the “true” value for the measurement? (2.6a)

It means there is a 5% chance that the “true” value for the measurement lies outside the range of 37.6-39.4 ppm.

How would the 99% confidence interval compare to the 95% confidence interval reported in (a.) in terms of magnitude of the interval reported? (2.6b)

The interval would be larger. The +/- value will increase.

How do you perform a “Case 1 t-test”? (2.6c)

Perform replicate measurements of a standard reference material (SRM). Determine the confidence interval for your measurement. If the concentration of the SRM is within your confidence interval then you pass the Case 1 t-test.

For two sets of replicate measurements, what would performing an F-test tell you about the two data sets? (2.6d)

F-tests are to compare the precision between the two sets of measurements. The F-test would tell you if there was a statistically significant difference in the precisions of the two measurements or not.

Describe a case where an F-test would be an appropriate test to use for calculating statistical significance. (3.4c)

To test whether there is statistically significant differences in the precision of the two data sets. 

E.g. comparing the precision of a volume delivered by a volumetric pipette vs a graduated cylinder

What is the difference between an F-test and a t-test? (4.1)

An F-test is used to compare level of uncertainty or precision of two sets of measurements. It is used to determine whether they are statistically difference (heteroscedastic) or not (homoscedastic) at a given confidence level.

A t-test is used to test the statistical similarity of two results, based primarily on their average or mean value, but also considering the variability in the measurements T-tests can also be performed at difference confidence intervals.

A histogram depicting the frequency of a large number of measurements subject to random error will have the shape of a (1). Large systematic error is synonymous with poor (2), whereas large random error is synonymous with poor (3). (4). Error is consistently positive or negative and can be corrected. (5) error is either positive or negative; it cannot be corrected, but can be characterized. (5.3)

(1) Normal distribution

(2) Accuracy

(3) Precision

(4) Systematic 

(5) Random

T/F? A t-test is used to compare the precision between two sets of replicate measurements, to judge whether they are similar or different. (6.2a)

False; this is an F-test

T/F?: High systemic error will lead to poor accuracy. (6.2b)

True