Study Guides (248,683)
Chemistry (67)
ENCH 213 (1)
Quiz

# 6statisticaltests.pdf

5 Pages
56 Views

Department
Chemistry
Course Code
ENCH 213
Professor
Diane Beauchemin

This preview shows pages 1 and half of page 2. Sign up to view the full 5 pages of the document.
Description
Statistical tests • give probabilities only ◦ you still have to interpret the results, decide on accepting/rejecting a value, especially for small data sets (i.e. apply good judgement) • may be helpful for questions: ◦ should an outlying value be rejected or retained in calculation of the mean? ◦ are 2 samples, analysed by the same method, significantly different in composition? ◦ does a difference in precision exist between 2 data sets from different workers/methods? Rejection/retention of outliers: Grubbs test 1. Compute the average, x , and standard deviation, s. 2. G exp= ‌ q – x ‌ /s (mean includes questionable value) → x =qquestionable result 3. Get G critrom Table 4-5 4. Apply test: reject if Gexp> G crit Example: Fe in large mocked soil sample %Pb =1.1, 3.4, 6.9, 3.9, 2.7, 2.8, 1.2, 2.3 • should the 6.9 value be rejected? • x = 3.0; s =1.9 • G exp 6.9 – 3.0 ‌ /1.9= 2.05 • G critor n=8 is 2.032 • Reject because G > exp crit • BLINDAPPLICATION OF TESTS IS DANGEROUS. USE GOOD COMMON SENSE. In case of outliers: • re-examine all data relating to the outlying value: properly kept lab notebok • if possible, estimate the precision expected from the procedure, to check if the outlying value is actually questionable. • repeat the analysis if sufficient sample and time are available. • otherwise, apply Grubbs test. • if retention is indicated, consider reporting the median rather than the mean Example Police have a hit-and-run case and need to identify the brand of red auto paint. The percentage of iron oxide, which gives paint its red color, found during analysis is as follows: 43.15, 43.81, 45.71, 43.23, 42.99, and 43.56%. What is the average percentage of the iron oxide in the paint sample? a. 43.3 b. 43.7 c. 43.6 Example answer: Grubbs test G calc G crit reject 45.71 42.99, 43.15, 43.23, 43.56, 43.81, 45.71 % Mean= 43.74 s=1.0 Recalculate mean= 43.3 (s=0.3) G calc (45.71-43.74)/(1.0) = 1.97 → decrease ins indicationofoutlier G crit822 Hypothesis testing • "null hypothesis" assumes that quantities compared are the same unless proven otherwise by testing at a given probability level: ◦ comparison of mean from analysis with µ certified value of SRM...) ◦ comparison of the means of 2 different sets ◦ comparison of standard deviations from 2 sets of data ◦ comparison of individual differences between two data sets Comparison of mean with an accepted value: Student’s t test • mean - μ = ± ts /√(n) • if |mean-μ| > ts/ √(n) ◦ null hypothesis wrong ◦ determinate error at this confidence level • another way is to calculate t calcnd compare it to t critrom Table 4-2 ◦ t calc= √n x |mean-μ|/s ◦ if t calc tcrit ▪ Null hypothesis wrong at this confidence level Example: New method for the determination of sulfur in kerosenes • data: % S = 0.112, 0.118, 0.115, 0.119 • true = µ = 0.123% S • is there a determinate error? • mean= 0.116% S, s=0.003% • tcalc √4 x |0.116-0.123|/0.003 = 4.7 • tcritor 3 degrees of freedom = 3.182 at 95% confidence level • tcalc tcrit systematic error indicated • At 99% level, t = 5.84: null hypothesis holds crit Q: A systematic error a) can be discovered and corrected. b) arises from the limitations on the ability to make a physical measurement. c) is also known as an indeterminate error. Example 2: Hg in mocked soil sample (small sample) • data: % Hg= 7.5 ± 6.6 • True = µ = 5.86% Hg • Is there a determinate error? • t = √8 |7.5-5.86|/6.6 = 0.548 calc • tcritor 7 degrees of freedom = 2.365 at 95% • confidence level • t < t : no systematic error indicated calc crit Choice of confidence level • if too severe (99.9%) ◦ significant effect may be missed • if too relaxed (50%) ◦ insignificant effect may be judged important • In general ◦ result at 95% confidence level: SIGNIFICANT ◦ result at 99% confidence level: HIGHLY SIGNIFICANT Comparison of the precision of two sets: F test • Fcalc= s1/s 22 2 ◦ s =1ariance of set 1 ◦ s =2ariance of set 2
More Less

Only pages 1 and half of page 2 are available for preview. Some parts have been intentionally blurred.

Unlock Document

Unlock to view full version

Unlock Document
Me

OR

Join OneClass

Access over 10 million pages of study
documents for 1.3 million courses.

Join to view

OR

By registering, I agree to the Terms and Privacy Policies
Just a few more details

So we can recommend you notes for your school.