Pop/Hypothesis Flashcards
population
universe of things
parameter
characteristic of population - almost always unobservable
Mean US household income
sample
subset of population - cannot observe pop so collect sample
Population: all with PD
Sample: ____
100 patients with PD who are seen at Banner over 5 year period
parameter
characteristic of populatuon
estimate of pop parameter
computed using data from sample we hope is near true value of parameter
statistic
any computed measure from sample
statistic
sample: 100 patients with PD who are seen at Banner over 5 year period
estimate: _____
32/100 have dementia
law of large numbers
as sample size increases, we expect sample mean to be closer to true mean
central limit theorem
as sample size increase sampling distribution of sample mean looks more and more bell shaped
what does statistical significance of 0.05 mean
an observed result is regarded as statistically significant if it had a 5% or smaller likelihood of occurring simply due to chance
type I error
rejecting null when null is true (FP)
alpha usually set to 0.05
type II error
fail to reject null when null is false (FN)
beta
hypothesis testing procedure
1) specify null and alternative
2) choose alpha, prob of making type I error (0.05)
3) compute some value from data (test statistic)
4) compute p value based on test statistic
5) if p value
P value
probability of observing data as supportive or more supportive of the alternative hypothesis than the actual data
two tailed test vs one tailed test example
two tailed H0: the blood pressure before treatment doesn’t equal blood pressure after treatment
one tailed H0: the blood pressure after treatment will decrease
differnece in medicines, or one medicine better than other
why to use two-sided
conservative: if 2-sided significant then one sided will be too
prevents concerns that you may have chosen direction of alt hypothesis after seeing data
causes of type I error
chance, inappropriate methods or assumptions about data
cause of type 2 error
low statistical power
sample size too small
power calculation
1-Beta (typeIIerror)
avoiding type ii error
increase power by increasing sample size
power depends on
sample size, size of true underlying effect, variability in measurements, chosen significance level and its sidedness, type of analysis
decreasing sample size while maintaining statistical power
reduce number tx groups
find more precise measurement
decrease variability in measurements (make subjects more homogeneous, use stratification, average multiple measurements on each subject)
properties of normal distribution
bell-shaped
mean = median = mode
symmetric
tails are asymptotic (never touch the x)
standard normal distribution
mean 0 and standard deviation 1
why is normal distribution important
lots of bio measurements normal approx
CLT: when add/average lots of independent things, result tends to follow normal distrubtion
68-95-99
- 68% of all observations/measures are between -1 SD and +1 SD
- 95% of all observations/measures are between -2 SD and +2 SD
- 99.7% of all observations/measures are between -3 SD and +3 SD
probability
Probability is the proportion of times that an event would occur in an infinitely long series of identical experiments
CI
‘95% confident that the mean bp is between 135 and 145 mm Hg’, using ‘confident’ as a technical term.
o Give the formal interpretation: ‘In 95% of repeated experiments, the confidence interval would contain the mean bp.
