Inferential Statistics (L11) Flashcards
Statistic
A meaningful number derived from a set of data
Inferential statistics
helps to suggest explanations for a situation or
phenomenon. It allows you to draw conclusions based on extrapolations, and
is in that way fundamentally different from descriptive statistics that
merely summarize the data that has actually been measured.
Descriptive Statistics -solely
to describe and summarize or sample.
Inferential Statistics takes data from a sample and makes inferences about
the population. estimating parameters
ex. regression
As opposed to descriptive statistics, in inferential statistics we don’t know the real
answer, so there are a few considerations.
Model assumptions (we are
only dealing with normal
distributions in this course).
1) Normal and
2) We can use the mean and
SD to describe the data.
There will be some error,
and you should account
for this (That’s why we
like to give a range of
answers, not just one
when we estimate).
what are the 3 important elements for “classical” statistical inference?
- standard error
- confidence intervals
- P values (stat sig)
C O N F I D E N C E I N T E R V A L S :
*Most common: 95% Confidence Interval.
*A confidence interval attempts to find a range
of values for which you have ‘confidence’ that
your population parameter is within.
*Therefore, if you repeated your experiment
many times (many samples), the intervals you
calculate will contain the true population
parameter 95% of the time.
*Can be used to estimate any population
parameter value (mean, SD, pearson R,
regression coefficient etc…).
Alternative Hypothesis
= H1(aka Experimental Hypothesis) Hypothesis
or prediction that comes from your theory, typically states that an
effect/difference will be present (Something is happening!).
Null Hypothesis
= HoHypothesis or prediction that states that an
effect/difference is absent (Nothing happening).
what does NHST stand for
Null
Hypothesis
Significance
Testing
*The most commonly used method of inferential
statistics that tests an observation using the null
hypothesis as the default or starting position.
*“Assume there is no effect or difference until
shown otherwise”.
why do we use NHST
*In NHST, the default position is the null –you need
strong evidence to reject the null hypothesis – it’s not
at 50/50 proposition.
*NHST does not prove or disprove things. It can either
1) support the alternative hypothesis (an effect), or 2)
state that there isn’t enough evidence to reject the
null hypothesis (no effect).
*The key point here is that no question is definitively
answered as true or not true!
H O W D O W E K N O W W H E T H E R T H E N U L L O R
T H E A L T E R N A T I V E H Y P O T H E S I S I S S U P P O R T E D ?
Statistical significance is based on the probability that you would get the same or more extreme results in
your experiment if the null hypothesis were true.
Stated another way: P(Your Results | There is no difference) = how likely is it that you would get the result
of your experiment, if there truly was no difference or effect (if the null was true).
We set this value at less than 5% - Statistical significance occurs when the probability of your result is less
than 5% - when this happens, we can support the alternative hypothesis.
P < 0.05 = probability less than 5%
“I shouldn’t be seeing this result if there
really is no difference”
P > 0.05 = probability greater than 5%
“Yea, this is what I expect my results to be,
given that there is no difference”
Problems with
statistical
significance
- Is zero as a basis of comparison valid? Is this ever
true in the real world? - With enough data and tests, you can always reject
the null. - Statistical significance is not the same as practical
importance. - Not significant is not the same as zero.
- Why p < 0.05? Very arbitrary, and do we really feel
the world is best explained with a binary answer of
significant/not significant? - The difference between significant and non-
significant…isn’t significant!
