1. Chapter 4 Statistics

2. Is my red blood cell count high today?

3. 4.1 The Gaussian Distributions -1 1) Nerve cells muscle cells (1991 Nobel Prize in Medicine & Physiology) Sakmann & Neher absence neurotransmitter present neurotransmitter

4. 4.1 The Gaussian Distributions -2 922 ion channels response Typical lab measurements: Gaussian distribution

5. 4.1 The Gaussian Distributions -3 Gaussian distribution is characterized by 1) Mean: 2) Standard deviation:

6. 4.1 The Gaussian Distributions -5 The smaller the s,  the more precise the results  reproducible

7. 4.1 The Gaussian Distributions -4 Other terms Median Range σ & probability Table 4.1

8. 4.2 Student’s t -1 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.

9. 4.2 Student’s t -3 (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.

10. 4.2 Student’s t -4

12. 4.2 Student’s t -5 Smaller confidence intervals Better measurement For 90% sure that a quantity lies in the range 62.3  0.5 vs. 62.3  1.3

13. 4.2 Student’s t -6

14. 4.2 Student’s t -7 t test : used to compare one set of measurements with another to decide whether or not they are different. Three ways in which a t test can be used will be described.

15. 4.2 Student’s t -8 Case 1 : 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% = 3.26 0 S = 0.04 1

16. 4.2 Student’s t -9 Does answer agree with the known answer ? 95% confidence t calculate > t table  result is different from the known value.

17. 4.2 Student’s t -10 Case 2 comparing replicate measurements. 1904 Nobel Prize by Lord Rayleigh. for discovering Inert gas argon :

18. 4.2 Student’s t -11

19. 4.2 Student’s t -12 t test for comparison of means : where

20. 4.2 Student’s t -13 Case 3 Comparing individual differences Cholesterol content (g/L) SampleMethod AMethod BDifferent (d i ) 11.461.420.04 22.222.38-0.16 32.842.670.17 41.971.800.17 51.131.090.04 62.352.250.10 = 0.06 0

21. 4.2 Student’s t -14 ∴ two techniques are not significant different at the 95% confidence level

22. 4.3 Q test for bad data -1 help decide whether to retain or discard a datum

23. 4.3 Q test for bad data -2 Q calculate > Q t  discard  any datum from a faulty procedure.

24. 4.4 Finding the “Best” straight line -1 calibration methods  prepare calibration curve.

25. 4.4 Finding the “Best” straight line -2

26. 4.5 Constructing a Calibration Curve -1 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 ) 00.099 0.1000.001-0.000 3 0.000 7 50.1850.1870.1880.0030.085 7 0.087 7 0.088 7 100.2820.272 0.0100.182 7 0.172 7 150.3920.3450.3470.047---0.245 7 0.247 7 200.425 0.4300.0050.325 7 0.352 7 0.330 7 250.4830.4880.4960.0130.383 7 0.388 7 0.396 7 Standard soln blank 

27. 4.5 Constructing a Calibration Curve -2 2) Finding the protein in an unknown