statistics 2
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36 Terms
random errors
typically sample error (small sample size)
good statistical analysis and large sample size protect from random errors
systematic errors
consistent and repeatable deviation between an observed measurement and the true value
random vs systematic error
false positive
type I error
claim a difference when it is the same
reject a true null hypothesis, incorrectly concluding that a significant effect or relationship exists when it does not
false negative
type II error
claim the same when it is different
accept a false null hypothesis, incorrectly concluding that a significant effect or relationship does not exist when it does
null hypothesis
assumption that things are the same
any observed difference in data is due to random chance
power
chance of correctly rejecting the null hypothesis
power of false positive
p-alpha
power of false negative
p-beta
critical value for p-alpha
threshold on a statistical test that acts as a boundary to decide whether to reject or fail to reject the null hypothesis
set a significance level (ie p<0.01)
higher power means a (?) chance of a type II error
smaller (P = 1-beta)
power of 0.8 means
80% chance to find a real difference
power depends on:
type of test
sample size
critical value (to avoid type I errors
low critical value reduces power
normalised effect size
effect size
difference between variables
normalised effect size
how big the difference is compared to the variability between variables
power is low if
sample size is small
effect size is small
low type I error chances → protection from false positives
power analysis
use to calculate sample size needed
specify the minimum normalised effect size you want to measure
choose a test
establish a type I error chance (p<0.05)
establish type II error chance (normally 1-0.8 = 0.2)
use the above to calculate sample size needed
how to plan an experiment
specify measured variable
the levels of each factor; controlled variables
use control groups
comparisons or correlations you want to make
calculate the expected sample size
controls are used to protect from (?) error
systematic
random sampling
unbiased sampling; subset of individuals or data chosen from a larger population
random sampling method
Select subjects at random
Assign to test or control randomly
Dependent on the experiment (ie normal vs asthmatic patients)
Test in random order
convenience samples increase risk of (?) errors
systematic
cluster samples are (?) independent
not
example experiment
common controls (list 4)
time control
test after control or vice versa?
sensitisation/ desensitisation
i.e. if you are testing a muscle tissue sample
how long will it stay viable for testing with repeated touching
vehicle control
check the solution a drug is in
i.e. capsaicin dissolves in ethanol
does the ethanol cause the effect? or the capsaicin?
sex/age control
does male vs female matter
does age matter?
negative control
control designed to produce no change in the experiment
testing a baseline condition where no reaction or response should happen
positive control
control designed to produce a change in the experiment
testing a treatment or factor already known to work
longitudinal study
collects data from the same subjects over an extended period of time
cross-sectional study
collects data from different subjects (test and control groups) at a single point in time
crossover experiment
combines longitudinal and cross-sectional studies
each group is both test and control in reverse order (over time)
blinding
used to remove bias
single blind
the subject does not know if they are test or control
double blind
neither the subject nor the experimenter knows which subjects are test and which are control
blocking
compares members of the same block (not group)
blocking factor → sex; e.g. comparing COPD to controls in female group vs in male group
like a two way ANOVA but without interaction
summary
lecture outline
