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# Session 7 - How to Test for Trends Part I.docx

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University of Toronto St. George

Cell and Systems Biology

CSB345H1

William Navarre

Fall

Description

HMB325H © Lis| Page 1013
S E S S I O N 7 : H O W T O T E S T F O R T R E N D S ( PA R T I )
LEARNING OBJECTIVES
1. discuss regression & correlation
2. calculate & interpret a regression line & its parameters
3. calculate & interpret a correlation & its parameters
4. complete the statistical procedures relevant to regression & correlation
1. assessing the relationship bw 2 data variables (NOT dichotomous or
nominal) that are ordinal (categorical data), but mostly continuous
1. ex. does cardiac output change according to the dose of a drug received
2. allows us to assess whether there is evidence of a ‘dose-response’
relationship
DESCRIPTIVE STATISTICS
2. each variable can be described individually (mean, SD, median,
percentages)
3. can be described graphically – scatter plot
1. can identify what the best fit of the data is – what line best approximates
the observed data
4. most commonly identified best fitting line is a linear relationship (y = a + bx)
1. a: y-intercept
2. b: slope of the line, how the y-values change as the x-values change
5. *assumption: data follow a reasonably linear relationship, ordinal or
continuous data
6. ex. is there evidence that ppl’s weight increases according to their height
NULL HYPOTHESIS
7. if there truly is no relationship bw the dependent & independent variable,
the relationship would look like a flat line
1. distribution of y-values for all x-values are around the same – b = 0
8. H 0 flat line, slope = b = 0
ANALYSIS OF LINES
9. the statistics of lines:
1. calculate the ‘best fit’ slope & intercept of that line – equation of the line that
best fits the observed data
1. is where the data values are closest to the lines – the distances bw
the observed values and the estimated line are the smallest (the
least square method – minimize the square of differences bw the
observed data and the line)
2. variability about the regression line – variability of the data around that best fit
line
3. stanadard errors of the slope & intercept
4. statistically test the slope and intercept – what they differ from the null
hypothesis
2. we want to calculate the slope, the intercept isn’t very imp for testing
the null
5. calculate the confidence intervals for the estimated slope & intercept HMB325H © Lisa Zhao 2| Page 2 HMB325H © Li| Page 32013
‘FITTING’ THE BEST LINE
10.to calculate the best fit line
11.y = a + bx
1. a: the y-intercept of the line
2. b: slope of the line
12.the ‘best fit’ line: smallest squared deviations bw the line & the data
n(ΣXY)−(ΣX)(ΣY )
b= 2 2
n Σ X − ΣX )
2
a= (ΣY Σ X − ΣX (ΣXY)
n Σ X −(ΣX) 2
13.the mean value of x or y will always lie on the best fit line
14.variability about2the line:
Σ Y− a+bX )
S y∗x √ n−2
OR
S y∗x n−1 (sY−b s2X2)
√n−2
(not as ac

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