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Chem. 31 – 9/24 Lecture

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Chem. 31 – 9/24 Lecture

- Due today
- Pipet/Buret Calibration Lab Report
- HW Additional Problem 1.2

- Quiz 2 today
- Today’s Lecture
- Error and Uncertainty
- Confidence Intervals (how to decrease them)
- Statistical Tests

- Error and Uncertainty

Decrease standard deviation in measurements (usually requires more skill in analysis or better equipment)

Analyze each sample more times (this increases n and decreases t)

Understand variability better (so that s is known and Z-based uncertainty can be used)

t-Tests: Determine if a systematic error exists in a method or between methods or if a difference exists in sample sets

F-Test: Determine if there is a significant difference in standard deviations in two methods (which method is more precise)

Grubbs Test: Determine if a data point can be excluded on a statistical basis

Outcome #1 – There is a statistically significant result (e.g. a systematic error)

this is at some probability (e.g. 95%)

can occasionally be wrong (5% of time possible if test barely valid at 95% confidence)

Outcome #2 – No significant result can be detected

this doesn’t mean there is no systematic error

it does mean that the systematic error, if it exists, is not detectable (e.g. not observable due to larger random errors)

It is not possible to prove a null hypothesis beyond any doubt

Case 1

used to determine if there is a significant bias by measuring a test standard and determining if there is a significant difference between the known and measured concentration

Case 2

used to determine if there is a significant differences between two methods (or samples) by measuring one sample multiple time by each method (or each sample multiple times)

Case 3

used to determine if there is a significant difference between two methods (or sample sets) by measuring multiple sample once by each method (or each sample in each set once)

Methylmannopyranoside (MMP) example

Added as an internal standard at 5 ppm

Analysis will tell if sample causes a bias compared to standard

A winemaker found a barrel of wine that was labeled as a merlot, but was suspected of being part of a chardonnay wine batch and was obviously mis-labeled. To see if it was part of the chardonnay batch, the mis-labeled barrel wine and the chardonnay batch were analzyed for alcohol content. The results were as follows:

Mislabeled wine: n = 6, mean = 12.61%, S = 0.52%

Chardonnay wine: n = 4, mean = 12.53%, S = 0.48%

Determine if there is a statistically significant difference in the ethanol content.

Case 3 t Test used when multiple samples are analyzed by two different methods (only once each method)

Useful for establishing if there is a constant systematic error

Example: Cl- in Ohio rainwater measured by Dixon and PNL (14 samples)

Calculations

Step 1 – Calculate Difference

Step 2 - Calculate mean and standard deviation in differences

ave d = (7.1 + 8.7 + ...)/14

ave d = 7.49

Sd = 2.44

Step 3 – Calculate t value:

tCalc= 11.5

Step 4 – look up tTable

(t(95%, 13 degrees of freedom) = 2.17)

Step 5 – Compare tCalc with tTable, draw conclusion

tCalc >> tTable so difference is significant

Note: These (case 2 and 3) can be applied to two different senarios:

samples (e.g. sample A and sample B, do they have the same % Ca?)

methods (analysis method A vs. analysis method B)

Similar methodology as t tests but to compare standard deviations between two methods to determine if there is a statistical difference in precision between the two methods (or variability between two sample sets)

As with t tests, if FCalc > FTable, difference is statistically significant

S1 > S2

Purpose: To determine if an “outlier” data point can be removed from a data set

Data points can be removed if observations suggest systematic errors

- Example:
- Cl lab – 4 trials with values of 30.98%, 30.87%, 31.05%, and 31.00%.
- Student would like less variability (to get full points for precision)
- Data point farthest from others is most suspicious (so 30.87%)
- Go to board for calculations

If Grubbs test fails, what can be done to improve precision?

design study to reduce standard deviations (e.g. use more precise tools)

make more measurements (this may make outlier more extreme and should decrease confidence interval)

A chemist has developed a new test to measure gamma hydroxybutyrate that is expected to be faster and more precise than a standard method. What test should be used to test for improved precision? Are multiple samples needed or multiple analyses of a single sample?

The chemist now wants to compare the accuracy for measuring gamma hydroxybutyrate in alcoholic beverages. Describe a test to determine if the method is accurate.

Equations you need to know:

Average calculation

t and Z based confidence intervals

Equations I will provide:

Propagation of uncertainty for +/-, *//, and exponent

Standard deviation

Case 2 and 3 t-test, F-test and Grubbs test (if needed)