Statistics are used to gain understanding of
a population by describing characteristics
of the population
We discussed several population
characteristics:
µ
σ
p
ρ
β
mean
standard deviation
proportion
Pearson correlation
slope of linear association
And we discussed how to estimate those using
statistics computed from a small sample from
the population
X̅
s
p̂
r
b
sample mean
sample standard deviation
sample proportion
sample correlation
slope of best linear fit line
We repeatedly applied two general
methods of statistical inference
 Hypothesis tests
 Confidence intervals
Both of which follow the general steps of
1. Assume certain values for the
population characteristics
2. Derive the behavior (distribution) of the
sample statistics if the assumptions in step
1 were true.
3. Use that distribution to estimate the
probability of the observed sample statistic
occurring (p-value).
4. If the probability is low, we rule out the
value of the population statistic assumed in
step 1
Take-home message #1
 The evidence we gain from statistics is from
ruling out things.
o Our evidence is much better when we
disprove things,
o It is much more nebulous if we fail to
disprove.
Take-home message #2
 Statistical significance and clinical significance
are different.
o Statistical significance says that our study
has given us enough evidence to disprove
certain values of a parameter of interest.
o Clinical significance is an indication that
the magnitude of an effect is important in
the clinical setting
o Our goal with statistics should be to find
statistically significant evidence of effects
that are clinical significant.