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Lecture 4

# CHEM 212 Lecture Notes - Lecture 4: Observational Error, F-TestPremium

2 pages42 viewsFall 2016

Department
Chemistry
Course Code
CHEM 212
Professor
Hamilton M.Coreen
Lecture
4

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Chem 212!
Lecture 4!
Sept. 14/2016!
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How to use stats controls on calculator:!
stats mode!
2nd function mode!
RCL then xbar and sx!
clear= 2nd function CA!
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Describing the variation in large data sets:!
-make the same measurement many time... aka replicates!
-Plot the data from measurements you will get normal Gaussian distribution!
-+/- 1SD 68% within 1 std. dev of the mean!
-16% on either side, tails !
-+/- 2 std.dev area is 95.4% within mean!
"-problem resulting 2 std. dev reports larger range thus less value in number!
-95% area is within 2 std.dev!
-99% area is within 3 std.dev!
-If the data set is large then the data set describes the population!
"-the average is mu
"-std. dev is sigma!
-If data set is small then data describes a sample!
"-the average is xbar!
"-std. dev is s
* we use xbar and s to predict mu and sigma!
-Systematic error does not change to shape of the curve it changes the position along the x-axis!
-Eect of change in Precision, Std. dev changes but the mean does not change!
"-conﬁdence interval aected!
-mu and sigma are the true values for the population!
-the larger the n, the better the sample estimates the population!
-We will measure replicates, calculate xbar and s and use known characteristics of Gaussian distributions to make
-We assume that analytical results have random error and apply the concepts from Normal or Gaussian statistics
to interpret our results!
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Stats tools:!
Conﬁdidence Interval:!
Stating results for an unknown sample !1.
Stating accuracy of results for a known sample!2.
Comparison of 2 data sets:!
Comparison of means t test ( news an F test and then a t test)!1.
Comparison of dierences t test- choice of 2 types of t test!2.
Grubbs test!1.
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Conﬁdence Interval: Estimate true value from our experimental data!
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mu=xbar+/- t*S/n^1/2!
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