Define p-value
the probability of an observed statistic or some value more extreme in the direction of the alternative hypothesis assuming the null hypothesis is true
n=
sample size
observational units
objects/people measured, "n what?
what variables did we record?
whether or not...
parameter (categorical variable)
pi is the long run probability of event
population (parameter) is an
infinite random process
what statistic will we use to estimate the parameter?
p-hat
the statistic is the
sample proportion of event
alternative hypothesis is also known as
research conjecture
null hypothesis is also known as
chance model
always assume which hypothesis to be true?
Example of how to write null
H0: pi=0.5
on a single probability distribution, proportion of repetitions is:
p-value
on a single probability distribution, proportion of heads is:
null distribution
when p-value is less than or equal to 0.05, event is considered
unlikely
on a single probability distribution, "as extreme as" is
p-hat
if event is unlikely we have...
strong evidence against null
if event is unlikely is it statistically significant?
yes
if event is likely is it statistically significant?
no
if event is unlikely is it plausible?
no
if event is likely is it plausible?
yes
if event>0.05 it is considered
likely
if event is likely we have
weak evidence against null
Central Limit Theorem states, If n is larger enough then:
p-hat follows a norm distribution, centered at pi & mean=pi, SE of p-hat=sigma p-hat
n is large enough if
# of successes & # of failures are each at least 10
theory-based approach follows a
mathematical model
What is |Z|?
the distance from p-hat to pi in SE, ignoring direction
if Z>0
p-hat is bigger than pi
if Z<0
p-hat is less than pi
If Z=0
p-hat=pi
as n increases
SE decreases, p-value decreases, |Z| increases, strength of evidence increases
a n increases, the statistic values are
less variable
as n increases, bell-shape
compresses
two sided tests p-value is
twice as big as one-sided
as p-hat moves further from pi
p-value decreases, |Z| increases, strength of evidence increases
as p-hat gets closer to pi
p-value increases, |Z| decreases, strength of evidence decreases