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Chem. 31 – 2/16 Lecture

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Page 1: Chem. 31 – 2/16 Lecture. Announcements Turn in Pipet/Buret Calibration Report Wednesday –AP1.2 due + quiz Today’s Lecture –Chapter 4 Material Statistical

Chem. 31 – 2/16 Lecture

Page 2: Chem. 31 – 2/16 Lecture. Announcements Turn in Pipet/Buret Calibration Report Wednesday –AP1.2 due + quiz Today’s Lecture –Chapter 4 Material Statistical

Announcements• Turn in Pipet/Buret Calibration Report• Wednesday

– AP1.2 due + quiz• Today’s Lecture

– Chapter 4 Material• Statistical Tests• Calibration and Least Square’s Analysis

Page 3: Chem. 31 – 2/16 Lecture. Announcements Turn in Pipet/Buret Calibration Report Wednesday –AP1.2 due + quiz Today’s Lecture –Chapter 4 Material Statistical

Chapter 4 – Gaussian Distributions

Now for a “real” limit problem example:A man wants to get life insurance. If his measured

cholesterol level is over 240 mg/dL (2,400 mg/L), his premium will be 25% higher. His level is measured and found to be 249 mg/dL. His uncle, a biochemist who developed the test, tells him that a typical standard deviation on the measurement is 25 mg/dL. What is the chance that a second measurement (with no crash diet or extra exercise) will result in a value under 240 mg/dL (e.g. beat the test)?

Page 4: Chem. 31 – 2/16 Lecture. Announcements Turn in Pipet/Buret Calibration Report Wednesday –AP1.2 due + quiz Today’s Lecture –Chapter 4 Material Statistical

Statistical Testst Tests

• Case 1– used to determine if there is a significant bias by

measuring a test standard (concentration known) 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 two 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)

Page 5: Chem. 31 – 2/16 Lecture. Announcements Turn in Pipet/Buret Calibration Report Wednesday –AP1.2 due + quiz Today’s Lecture –Chapter 4 Material Statistical

Case 1 t test

• Methylmannopyranoside (MMP) example

• Added as an internal standard at 5 ppm

• Analysis will tell if sample causes a bias compared to standard

Page 6: Chem. 31 – 2/16 Lecture. Announcements Turn in Pipet/Buret Calibration Report Wednesday –AP1.2 due + quiz Today’s Lecture –Chapter 4 Material Statistical

Case 2 t test Example

• 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.

Page 7: Chem. 31 – 2/16 Lecture. Announcements Turn in Pipet/Buret Calibration Report Wednesday –AP1.2 due + quiz Today’s Lecture –Chapter 4 Material Statistical

Case 3 t Test Example

• 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)

Page 8: Chem. 31 – 2/16 Lecture. Announcements Turn in Pipet/Buret Calibration Report Wednesday –AP1.2 due + quiz Today’s Lecture –Chapter 4 Material Statistical

Case 3 t Test Example –Data Set and Calculations

Conc. of Cl- in Rainwater

(Units = uM)

Sample # Dixon Cl- PNL Cl-

1 9.9 17.0

2 2.3 11.0

3 23.8 28.0

4 8.0 13.0

5 1.7 7.9

6 2.3 11.0

7 1.9 9.9

8 4.2 11.0

9 3.2 13.0

10 3.9 10.0

11 2.7 9.7

12 3.8 8.2

13 2.4 10.0

14 2.2 11.0

7.1

8.7

4.2

5.0

6.2

8.7

8.0

6.8

9.8

6.1

7.0

4.4

7.6

8.8

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:

nS

dt

d

Calc

tCalc = 11.5

Page 9: Chem. 31 – 2/16 Lecture. Announcements Turn in Pipet/Buret Calibration Report Wednesday –AP1.2 due + quiz Today’s Lecture –Chapter 4 Material Statistical

Case 3 t Test Example –Rest of Calculations

• 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

Page 10: Chem. 31 – 2/16 Lecture. Announcements Turn in Pipet/Buret Calibration Report Wednesday –AP1.2 due + quiz Today’s Lecture –Chapter 4 Material Statistical

t- Tests

• Note: These (case 2 and 3) can be applied to two different senarios:– samples (e.g. do fish caught in a lake near a

power plant and far from the plant have the Hg concentration)

– methods (analysis method A vs. analysis method B)

Page 11: Chem. 31 – 2/16 Lecture. Announcements Turn in Pipet/Buret Calibration Report Wednesday –AP1.2 due + quiz Today’s Lecture –Chapter 4 Material Statistical

F - Test

• 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)

22

21

S

SFCalc

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

S1 > S2

Page 12: Chem. 31 – 2/16 Lecture. Announcements Turn in Pipet/Buret Calibration Report Wednesday –AP1.2 due + quiz Today’s Lecture –Chapter 4 Material Statistical

Grubbs Test Example

• 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%)• Demonstrate calculations

Page 13: Chem. 31 – 2/16 Lecture. Announcements Turn in Pipet/Buret Calibration Report Wednesday –AP1.2 due + quiz Today’s Lecture –Chapter 4 Material Statistical

Dealing with Poor Quality Data

• 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 an outlier more extreme and should decrease confidence interval)

Page 14: Chem. 31 – 2/16 Lecture. Announcements Turn in Pipet/Buret Calibration Report Wednesday –AP1.2 due + quiz Today’s Lecture –Chapter 4 Material Statistical

Statistical TestQuestions

1. 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?

2. 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.

Page 15: Chem. 31 – 2/16 Lecture. Announcements Turn in Pipet/Buret Calibration Report Wednesday –AP1.2 due + quiz Today’s Lecture –Chapter 4 Material Statistical

Calibration• For many classical methods direct

measurements are used (mass or volume delivered)

• Balances and Burets need calibration, but then reading is correct (or corrected)

• For many instruments, signal is only empirically related to concentration

• Example Atomic Absorption Spectroscopy– Measure is light absorbed by “free”

metal atoms in flame– Conc. of atoms depends on flame

conditions, nebulization rate, many parameters

– It is not possible to measure light absorbance and directly determine conc. of metal in solution

– Instead, standards (known conc.) are used and response is measured

Light beam

To light Detector

Page 16: Chem. 31 – 2/16 Lecture. Announcements Turn in Pipet/Buret Calibration Report Wednesday –AP1.2 due + quiz Today’s Lecture –Chapter 4 Material Statistical

Method of Least Squares• Purpose of least squares method:

– determine the best fit curve through the data– for linear model, y = mx + b, least squares determines

best m and b values to fit the x, y data set– note: y = measurement or response, x = concentration,

mass or moles• How method works:

– not required to know math to determine m and b– the principle is to select m and b values that minimize

the sum of the square of the deviations from the line (minimize Σ[yi – (mxi + b)]2)

– in lab we will use Excel to perform linear least squares method

Page 17: Chem. 31 – 2/16 Lecture. Announcements Turn in Pipet/Buret Calibration Report Wednesday –AP1.2 due + quiz Today’s Lecture –Chapter 4 Material Statistical

Example of Calibration Plot

Mannosan Calibration

y = 541.09x + 6.9673

R2 = 0.9799

0

50

100

150

200

250

300

0 0.1 0.2 0.3 0.4 0.5 0.6

Conc. (ppm)

Pe

ak

Are

a

Best Fit Line Equation

Best Fit Line

Deviations from line

Page 18: Chem. 31 – 2/16 Lecture. Announcements Turn in Pipet/Buret Calibration Report Wednesday –AP1.2 due + quiz Today’s Lecture –Chapter 4 Material Statistical

Assumptions for Linear Least Squares Analysis to Work Well

• Actual relationship is linear• All uncertainty is associated with the

y-axis• The uncertainty in the y-axis is

constant