Session 9 - How to Test for Trends Part II.docx

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Cell and Systems Biology
William Navarre

HMB325H © Lis| Page 1013 S E S S I O N 9 : H O W TO T E S T F O R T R E N D S ( PA R T I I ) CONFIDENCE INTERVAL FOR A LINE 1. the regression line will run w/in those boundaries (of the 95% CI) 95% of the time 2. the standard error of the line varies, so the CI for the line must be done on a point-by- point basis: 1 x−X ́)2 s ̂y y∗x + 2 √n (n−1)s x sy: standard of error for y (at that x) sy*xvariability about the line x: x-value we’re interested in calculating the CI 3. ex. what is 95% CI of the regression line when x = 40? 1. calculate y 2. use the equation of the line to calculate the y-value when x = 40 3. determine the ‘multiplier’ from table.058, t , df = n – 2 4. CI = (y-value) ± multiplier y s CONFIDENCE INTERVAL FOR AN OBSERVATION 4. (prediction interval) 5. confidence interval around an indiv observation 6. also done on a point-by-point basis, but must also take into consideration the variable of indiv data values for the x-value: 2 1 (x−X)́ s ynews y∗x1+ n 2 √ (n−1)s x 7. (same as CI for a line) STUDY POWER 1. to calculate the power of a correlation study, we need to specify (or have specified) 1. r to be detected 2. sample size needed 2. calculate: Z = ln 1+r ρ 2 (1−r s = 1 Z √ n−3 sz: SD of the z distribution (z is normally distributed w this SD) 3. distribution of the study results will be cpnZred at Z /s 4. subtract this new centred value from the cut-off value of 1.96 (for α = .05) 5. Table 6-2 to find study power HMB325H © Lis| Page 2013 SAMPLE SIZE 1. to calc
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