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HYPOTHESIS TESTING
Often a set of data is collected, or an experiment carried out, not simply with a view to
summarising the results and estimating suitable parameters but rather in order to test an idea. This
idea or hypothesis may arise by purely theoretical reasoning, or it may be suggested by the results
of earlier experiments.
brief overview:
The way statistics is used to set up our hypothesis to test is a little strange. First we start with
what is called the “Null hypothesis.” This is the assumption that there is
no effect
of e.g.
experimental treatment, difference in conditions etc. We test this against an alternative
hypothesis: that is the hypothesis we are attempting to support with our data. Generally we hope
that our data shows sufficient differences from the expectations of the null hypothesis to reject it
and so accept our alternative hypothesis. E.g. from null hypothesis we expect no effect of drug
upon heart rate. Our data shows an increase. If that increase is sufficiently large then we may
conclude that no, the null hypothesis was wrong, there is an effect of this drug which does cause
an increase in heart rate.
(Not always the case we hope for a difference, one may hope that there is no difference.—we can
show there is no effect. Eg. tobacco company may wish to show that smoking their cigarettes
does not cause an in increase of a certain type of cancer. Rather than hope to reject the null
hypothesis, we may hope to be able to “fail to reject” the null hypothesis.)
We then use a statistical test to calculate the probability of observing a difference as large
as that obtained or larger
given the null hypothesis is true
. If the probability is less than some
specified level then we reject the null hypothesis and accept the alternative.
Null hypothesis
The notation commonly used to represent the null hypothesis is H
o
, and that of the alternative
hypothesis H
a
(or H1). However, you do not often see these explicitly written in scientific papers.
You do sometimes see “the hypothesis we wish to test is….
.” However during your research it is
very useful to state the null hypothesis as you would see it in statistical textbooks
Start by assuming there is no effect. What then would you expect? Would write something like:
H
o
:
µ
d

µ
p
= 0
where “d” and “p” represent drug and placebo
[more often written as above rather than H
o
:
µ
d
=
µ
p
but they are the same]
[note we do not use sample parameters but population parameters.]
may be something like:
H
o
:
ρ
= 0
[no correlation]
may be something like:
H
o
:
µ
= 2
vs.
H
a
:
µ
≠
2
If the null hypothesis is rejected then we need an alternative hypothesis to fall back on. (Your
expectations or hypothesis being tested.) This dichotomy is denoted:
H
o
:
µ
d

µ
p
= 0
vs.
H
a
:
µ
d

µ
p
≠
0
or it might be something like:
H
o
:
µ
d

µ
p
= 0
vs.
H
a
:
µ
d
<
µ
p
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Differences between these depends upon your expectations. For instance, if you were developing
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 Spring '10
 Wong
 Statistics, Null hypothesis, Statistical hypothesis testing, Statistical significance

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