Please enable JavaScript.
Coggle requires JavaScript to display documents.
Ch 4: testing a null hypothesis (statistical tests determine if statement…
Ch 4: testing a null hypothesis
two ways to find population values (statistical inferences)
estimation
no previous knowledge needed
not in line with empirical cycle
null hypothesis testing
more in line with empirical cycle
based on theory/previous research
tests with data
accept and reject null hypothesis (based on data)-0 no need to alter
null hypothesis and the sample
research hypothesis
: statement about real world that is tested against data
statistical hypothesis
: version of research hyp that refers to a statistic
a null hyp is the most important statistical hypothesis (specifies
one specific value
for the population statistic)
test null by collecting random sample and comparing avg of data to hypothesized avg (not too far apart--> null hyp is plausible; too far--> null is rejected)
statistical tests determine if statement abt population is plausible or not
statement about population (null hypothesis)
sample from pop with info abt statement (variables from sample)
criterion deciding if statement is plausible (significance level)
rejection region
values in which we reject the null hypothesis
a probability for the statement (showing how plausible it is)
p-valye tells how much the sample (at least differs from the null)
if p value is less than the selected significance level, the null hypothesis is rejected bc it is in the rejection region
significance level
rejection region (avg sample falls here if its too high/too low)
accepted threshold value that the sample is among the 5% most unlikely samples (null is rejected and test is
statistically significant
)
type 1 error
: rejecting a null that is actually true
null could be true but we just picked a bad sample
probability we make this error is the sig level (0.05)
5% of the sample allowed to be so different that we reject the null even if its tru
sampling distribution is only made for 1 value (more= more sampling distribution
p-value
two sided p-value
: double the one sided p-value
probability of a sample with mean at least as diff from the hyp value as the sample mean we already found
one sided p-value
: prob we draw sample at least (hyp mean - sample mean) less than hyp
p-value, rejection region, statistical significance depends on value of population statistic specified in null hypothesis
conditional probability bc its the prob under the assumption that null hypothesis is true
types of hypotheses
alternative
: covers all situations not covered by null hyp
we accept alternative hyp when we reject null
accepting it does not mean its true (type 1 error)
also when value is not specified ("expect diff/changes" but not specific)
research hyp becomes alt hyp when we dont specify
null is when we say there is no diff (0= specificed); also called
nil hypothesis
two-sided test
: null hyp rejected is to high/low
when both sides of spectrum are possible
one sided test
: if statistics is at one side of spectrum (too high/too low)
based on prior knowledge, researcher can cancel out half of the distribution
capitalization on chance
separates calculation and does not take them all together when dealing with multiple predictors
increase probability of making a type 1 error