2. Clearly State the
Null and Alternative Hypotheses
3. Choose the relevant statistical test
4. Calculate p-value
5. Is p-value<0.05?
No
Do not reject null
Reject null hypothesis
Yes
59
60
The process I just described is called hypothesis testing
•
Definition - the
formal
process to use the
statistical
properties
of the data to evaluate your hypothesis (i.e.,
“answer” your RQ)
•
Why do we test hypotheses?
Current state
understanding
(conjecture
beliefs and prior
knowledge)
Data (your
investigation)
A more
advanced state
of
understanding
(knowledge)
Hypothesis
testing
Framework of Scientific Investigation
Your Null and alt.
Hypotheses
Outcome of the
testing

10/04/2019
21
Some key concepts/terms that are important for you
to understand statistical testing conceptually
•
Average (mean)
•
Sample characteristics
•
Population characteristics
• Variability
61
Average (mean)
Just
re-iterating a point made in an earlier slide
•
Why do we care about the mean value:
for the vast majority
of the variables we work with in this unit, when we refer to
them, we refer to their average values
• Examples
•
Does overall satisfaction with Crown casino differ
between men and women?
•
Who spend more time on the daily commute, Sydney-
siders or Melbournians?
•
Statement you regular encounter in the media: such as
“Men earn more money than women”; or “Smoking
shortens smokers’ lives by about 12 years”
62
Sample characteristics vs. population characteristics
•
Sample characteristics
– what you calculate from the
sample, e.g., average grade expectation among male
respondents is 77.38
•
Population characteristics
•
The “true” values (e.g., “true” grade expectation among male
students)
•
They are what your RQs are really asking!
•
Unfortunately, the values are
unknown
(and often unknowable)
•
All research questions are about
population characteristics
,
but all data collected are
sample characteristics
•
In its essence, the
hypothesis testing process
is to use
observed relationships between sample characteristics
to
make inference about relationships between
the
unobservable population characteristics
63

10/04/2019
22
The challenge in using
sample
characteristics to
make inference about
population
characteristics
•
Sample characteristics
population characteristics
•
Sample characteristics
vary!
64
Variability
•
Sample characteristics are
random variables
, e.g., if you collect
data for a few times—e.g., with different samples, or at different
times—you will get different sample averages
•
This variability is an issue that needs to be accounted for with
statistical analysis (in another word, is the difference in
satisfaction we observe in the sample between male and female
students real, or just noise?)
•
The first step is to quantity the variability in sample
characteristics in your data (e.g., through metrics such as
variance and standard deviation)
•
Because these are random variables, the outcome of the test
involve
probabilities
(i.e., P value)
65
Quick Recap
66
•
the challenge we face - the question we ask about
population
essentially
cannot be answered with
certainty
•
the solution – we use statistics to infer what the answer
probably
is (probability)