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# Session 2 - How to Test for Differences Between Groups.docx

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University of Toronto St. George

Cell and Systems Biology

CSB345H1

William Navarre

Fall

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HMB325H © Lisa| Page 113
L E C T U R E 2 : H O W T O T E S T F O R D I F F E R E N C E S B E T W E E N G R O U P S
( C H A P T E R 3 )
LEARNING OBJECTIVES
1. describe the difference & the relationship bw a sample & a population
2. explain how each indiv sample provides a single estimate of the quantity being estimated and
how (& why) the estimates arising from multiple samples are normally distributed around the
‘true’ (population) value
3. state what the standard error of the mean (SEM) measures & which 2 factors affect its size
4. describe & carry out the processes necessary to complete an analysis of variance (ANOVA)
5. describe the rationale for ANOVA
6. describe the assumptions of ANOVA & confirm that each has been met
SAMPLES PROVIDE ESTIMATES
1. ex. an anesthesiology researcher studied how diff anesthetic protocols affect patient
heart rates
1. the initial part of the study required the measurement of baseline resting heart
rates of 64 consenting volunteers
2. research goal – to determine the avg heart rate prior to surgery
3. practical limitation – can’t measure & collect the heart rate of every patient prior to
surgery
4. compromise – a sample (representative subgroup) is selected, w/ its mean being used
as an estimate of the ‘true’ (unobserved, population) mean
5. but what would happen if a diff sample had been studied? how do we know if our
estimate is close to the ‘true’ (population) mean?
6. many possible samples can be selected & even when rigorously measured, these will
vary simply by chance
7. how good are the estimates?
1. if this study was repeated many times, w each selecting & using a diff sample, then
we could measure how these diff study means vary from each other
2. the standard deviation of these different study means is called the standard error
of the mean (SEM) and it provides an estimate of the potential variability bw the
same means
3. interpretation – recognizing that other samples from the same pop will differ from
one another, we won’t be surprised if the true pop mean is as high as 80.5 or as
low as 78.5 bpm
1. for the distribution of the true population mean, use ±x SEM
8. distribution of the study means should follow a normal distribution w: ~68% w/in ±1
SD, ~95% w/in ±2 SD, & ~99.7% w/in ±3 SD
1. which value is the best estimate of the ‘true’ (population) mean?
STANDARD ERROR OF THE MEAN (SEM)
9. we don’t need to conduct multiple studies to estimate the SEM
10. instead, the SEM is estimated by the formula:
sample¿¿
√ ¿
SEM= SDof sample
¿
11. do we have more ‘confidence’ in means arising from large or small studies? why?
12. is it probable that a randomly selected sample would have a mean that is ‘extreme’?
1. ~68% is w/in ±1 SD of the mean 32% chance that data is outside of ±1 SD
2. ~95% w/in ±2 SD 5% chance outside ±2 SD
3. ~99.7% w/in ±3 SD 3/1000 chance outside ±3 SD (possible, but much less
probable) HMB325H © Lisa | Page 33
RESULTS BY CHANCE
13. ex. a clinical trial is conducted to compare a novel drug against the standard drug & a
placebo in the tx of high bp
14. explanations for results of studies:
1. random variation (chance) accounts for the results
2. flawed study design (bias, confounding)
15. if the drugs have no effect (null hypothesis), then each of these means is simply an
independent measure of the same underlying ‘true’ (unobserved, population) value
1. any observed difference is simply due to chance (random and/or biologic variation)
2. if that is true, then the differences among the observed group means should be
consistent w the amount of variability w/in the set of data
VARIABILITY
16. the variability (variance) of the underlying pop can be estimated in 2 ways:
1. by the ‘average’ variability (variance) of the observed groups: within-groups variance
2. by the amount of variability (difference) among the group means (the SD amongst the
diff group means = SEM): between-groups variance
1. if there truly is no effect, then these 2 variances will generally be similar to one
another (their ratio should be ~1.0)
1. average of the gro

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