Page 239 - Statistics for Dummies

If the results are likely to have occurred under the claim, then you fail to reject
H (like a jury decides not guilty). If the results are unlikely to have occurred
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under the claim, then you reject H (like a jury decides guilty). The cutoff point
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between rejecting H and failing to reject H is another whole can of worms
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that I dissect in the next section (no pun intended).
Making Conclusions
To draw conclusions about H (reject or fail to reject) based on a p-value, you
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need to set a predetermined cutoff point where only those p-values less than
or equal to the cutoff will result in rejecting H . This cutoff point is called the
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alpha level (α), or significance level for the test. While 0.05 is a very popular
cutoff value for rejecting H , cutoff points and resulting decisions can vary —
some people use stricter cutoffs, such as 0.01, requiring more evidence
before rejecting H , and others may have less strict cutoffs, such as 0.10,
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requiring less evidence. o Chapter 14: Claims, Tests, and Conclusions 223
If H is rejected (that is, the p-value is less than or equal to the predetermined
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significance level), the researcher can say she’s found a statistically signifi-
cant result. A result is statistically significant if it’s too rare to have occurred
by chance assuming H is true. If you get a statistically significant result, you
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have enough evidence to reject the claim, H , and conclude that something
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different or new is in effect (that is, H ).
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The significance level can be thought of as the highest possible p-value that
would reject H and declare the results statistically significant. Following are
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the general rules for making a decision about H based on a p-value:
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✓ If the p-value is less than or equal to your significance level, then it meets
your requirements for having enough evidence against H ; you reject H .
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✓ If the p-value is greater than your significance level, your data failed to
show evidence beyond a reasonable doubt; you fail to reject H .
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However, if you plan to make decisions about H by comparing the p-value to
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your significance level, you must decide on your significance level ahead of
time. It wouldn’t be fair to change your cutoff point after you’ve got a sneak
peak at what’s happening in the data.
You may be wondering whether it’s okay to say “Accept H ” instead of “Fail to
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reject H .” The answer is a big no. In a hypothesis test, you are not trying to
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show whether or not H is true (which accept implies) — indeed, if you knew
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whether H was true, you wouldn’t be doing the hypothesis test in the first
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place. You’re trying to show whether you have enough evidence to say H is
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false, based on your data. Either you have enough evidence to say it’s false (in
which case you reject H ) or you don’t have enough evidence to say it’s false
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(in which case you fail to reject H ).
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