Chapter 4 Statistics Tools to accept or reject conclusion from experimental measurements Deal with random error only

Is my red blood cell count high today? P82

4-1 The Gaussian Distributions -1 1) Nerve cells muscle cells (1991 Nobel Prize in Medicine & Physiology) Sakmann & Neher absence neurotransmitter present neurotransmitter P83.

4-1 The Gaussian Distributions ion channels response Typical lab measurements: Gaussian distribution P84

4-1 The Gaussian Distributions -3 Gaussian distribution is characterized by 1)Mean: 2)Standard deviation: P84     1n xx S σS xxx n 1 n x x μx i 2 i n21 i i        

4-1 The Gaussian Distributions -5 The smaller the s,  the more precise the results  reproducible P85

4-1 The Gaussian Distributions -4 Other terms Median Range σ & probability Table 4.1 P86

4.2 F test F calculated = (S 2 1 /S 2 2 )

TABLE 4.3

4-3 Student’s t Student’s t is the statistical tool used to express confidence intervals & to compare results from different experiments. confidence interval : allows us to estimate the range within which the true value (  ) might fall, (given probability = confidence level) defined by mean and standard deviation. P86

Calculating confidence intervals (ex) In replicate analyses, the carbohydrate content of a glycoprotein (a protein with sugars attached to it) is found to be 12.6, 11.9, 13.0, 12.7, and 12.5 g of carbohydrate per 100 g of protein. Find the 50 % and 90% confidence intervals for the carbohydrate content. P87

P86

P87

Improving the reliability of your measurements Smaller confidence intervals Better measurement For 90% sure that a quantity lies in the range 62.3  0.5 vs  1.3

Improving the reliability of your measurements

T-test t test : used to compare one set of measurements with another to decide whether or not they are different.

Case A: t test for comparison of means : where P86

Case B significantly different comparing replicate measurements Nobel Prize by Lord Rayleigh. for discovering Inert gas argon :

F calculated = (S 2 1 /S 2 2 )

t test for comparison of means : where P86

Examples case : comparing a measured result with a “known” value Sample: 3.19 wt% (known value) a new analytical method : 3.29, 3.22, 3.30, 3.23 wt% = S =

Does answer agree with the known answer ? 95% confidence t calculate > t table  result is different from the known value.

Cholesterol content (g/L) SampleMethod AMethod BDifferent (d i ) = Examples case : Comparing individual differences

∴ two techniques are not significant different at the 95% confidence level

4-5 Q test for bad data help decide whether to retain or discard a datum

Q calculate > Q t  discard  any datum from a faulty procedure.

4-5 Grubbs Test for an Outlier Then compute the Grubbs statistic G, defined as (4-6) If G calculated from Equation 4-9 is greater than G in Table 4-6, the questionable point should be discarded. Common sense: any datum based on a faulty procedure should be discard, no matter how well it fits the result of data. help decide whether to retain or discard a datum

TABLE 4.6  G calculate > Gt discard ---) any datum from a faulty procedure.

4-4 Finding the “Best” straight line calibration methods  prepare calibration curve. P93

4-4 Finding the “Best” straight line

4-7 Constructing a Calibration Curve 1) Blank standard soln Table 4-6 Spectrophotometer readings for protein analysis by the Lowry method Sample (μg) Absorbance of three independent samples Range Corrected absorbance ( after subtracting average blank ) Standard soln blank 

4-7 Constructing a Calibration Curve 2) Finding the protein in an unknown