Chem. 31 – 6/13 Lecture

Announcements I Pipet and Buret Calibration Lab Report Due Quiz and Homework Returned in Lab Exam 1 on Thursday –Will cover material in lecture notes for today and Tuesday (some may be covered on Wednesday) –Definitely through Ch. 4, with one or two sections of Ch. 6 –Format similar to past exam (1 st part multiple choice or fill in the blank; 2 nd part problem solving)

Announcements II Today’s Lecture - Chapter 4 –Statistical tests Introduction t tests (starting with Case 2) F test Grubb’s test + other ways to deal with data Introduction to least squares method

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.

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)

Case 3 t Test Example – Data Set and Calculations Conc. of Cl - in Rainwater (Units = uM) Sample #Dixon Cl - PNL Cl Calculations Step 1 – Calculate Difference Step 2 - Calculate mean and standard deviation in differences ave d = ( )/14 ave d = 7.49 S d = 2.44 Step 3 – Calculate t value: t Calc = 11.5

Case 3 t Test Example – Rest of Calculations Step 4 – look up t Table –(t(95%, 13 degrees of freedom) = 2.17) Step 5 – Compare t Calc with t Table, draw conclusion –t Calc >> t Table so difference is significant

t- Tests 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)

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) As with t tests, if F Calc > F Table, difference is statistically significant S 1 > S 2

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

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)

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

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: –the principle is to select m and b values that minimize the sum of the square of the deviations from the line (minimize Σ[y i – (mx i + b)] 2 ) –in lab we will use Excel to perform linear least squares method

Example of Calibration Plot Best Fit Line Equation Best Fit Line Deviations from line

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

Calibration and Least Squares - number of calibration standards (N) NConditions 1Must assume 0 response for 0 conc.; standard must be perfect; linearity must be perfect 2Gives m and b but no information on uncertainty from calibration Methods 1 and 2 result in lower accuracy, undefined precision 3Minimum number of standards to get information on validity of line fit 4Good number of standards for linear equation (if standards made o.k.) More standards may be needed for non-linear curves, or samples with large ranges of concentrations

Use of Calibration Curve Mg Example: An unknown solution gives an absorbance of Use equation to predict unknown conc. y = mx + b x = (y – b)/m x = ( )/2.03 x = ppm Can check value graphically Calibration “Curve”