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Hypothesis or Significance Testing
Start with a research
question
1)
Make a drawing of the sampling distribution
for the null hypothesis and shade in the area representing the p-value.
Remember, the mean on the drawing always matches with the
m given
in Ho (see below).
2) State
the null and alternative hypothesis mathematically one
of three ways (note that Ho always has the same form). Always use a parameter
never a statistic when stating the a hypothesis.
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Ho: m
= 12,
Ha: m
< 12
p = the area of the lower
tail |
Ho: m
=
12, Ha: m
≠ 12
p = the area of the both tails
Note: a two tailed test has
a p-value twice as high as a single tailed test with the same data |
Ho:
m =
12,
Ha: m
> 12
p = the area of the upper tail
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3)
Find the area under the curve
using a statistic which corresponds to the p-value.
4)
State the definition of p-value
using the number you have just calculated.
Example for p-value = 3%: The probability of obtaining a test
statistic as extreme or more extreme than the one obtained is 3%, assuming Ho is
true.
5) Write a conclusion
that answers the original research question using the above statistical
analysis.
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If Alpha is Given
5) Decide whether to reject or fail to reject the null
hypothesis based on comparing the p-value with alpha.
- If: p-value ≤ alpha level reject Ho
- If: p-value > alpha level fail to
reject Ho
6) Write an English language sentence summarizing your
findings. For example if the null is rejected you might write:
Example 1) Ho rejected: The
sample is statistically significant at the alpha level (p=?) therefore
we reject the null hypothesis and accept the alternative hypothesis that
Bubba's magic pills caused a weight loss in the subjects
who took them.
Example 2) Ho accepted: The
sample is not statistically significant at
the alpha level (p=?), therefore, we fail to reject the null hypothesis.
There is not sufficient evidence to accept the alternative hypothesis that
Bubba's
magic pills caused a weight loss in the subjects who took them.
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If Alpha is Not Given
5) Skip this step
6) Write an English language sentence summarizing your
findings stating whether there is or is not strong statistical evidence for
rejecting the null hypothesis. This is based on your judgment
Example 1) Ho rejected: The
sample provides strong statistical evidence (p=?) for rejecting the null
hypothesis hence, we accept the alternative hypothesis that
Bubba's magic pills caused a weight loss in the subjects
who took them.
Example 2) Ho accepted: The sample does not
provide strong enough statistical evidence (p=?) for rejecting the null
hypothesis, hence, we cannot accept the alternative hypothesis that
Bubba's
magic pills caused a weight loss in the subjects who took them.
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