Page 240 - Statistics for Dummies

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Part IV: Guesstimating and Hypothesizing with Confidence
Setting boundaries for rejecting H
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These guidelines help you make a decision (reject or fail to reject H ) based
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on a p-value when your significance level is 0.05:
✓ If the p-value is less than 0.01 (very small), the results are considered
highly statistically significant — reject H .
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✓ If the p-value is between 0.05 and 0.01 (but not super-close to 0.05), the
results are considered statistically significant — reject H .
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✓ If the p-value is really close to 0.05 (like 0.051 or 0.049), the results
should be considered marginally significant — the decision could go
either way.
✓ If the p-value is greater than (but not super-close to) 0.05, the results are
considered non-significant — you fail to reject H .
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When you hear a researcher say her results are found to be statistically signifi-
cant, look for the p-value and make your own decision; the researcher’s pre-
determined significance level may be different from yours. If the p-value isn’t
stated, ask for it.
Testing varicose veins
In the varicose veins example in the last section, the p-value was found to be
0.1056. This p-value is fairly large and indicates very weak evidence against
H by almost anyone’s standards because it’s greater than 0.05 and even
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slightly greater than 0.10 (considered to be a very large significance level).
In this case you fail to reject H . You didn’t have enough evidence to say the
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proportion of women with varicose veins is less than 0.25 (your alternative
hypothesis). This isn’t declared to be a statistically significant result.
But say your p-value had been something like 0.026. A reader with a personal
cutoff point of 0.05 would reject H in this case because the p-value (of 0.026)
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is less than 0.05. His conclusion would be that the proportion of women with
varicose veins isn’t equal to 0.25; according to H in this case, you conclude
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it’s less than 0.25, and the results are statistically significant. However, a
reader whose significance level is 0.01 wouldn’t have enough evidence (based
on your sample) to reject H because the p-value of 0.026 is greater than 0.01.
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These results wouldn’t be statistically significant.
Finally, if the p-value turned out to be 0.049 and your significance level is 0.05,
you can go by the book and say because it’s less than 0.05 you reject H , but you
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really should say your results are marginal, and let the reader decide. (Maybe
they can flip a coin or something — “Heads we reject H , tails, we don’t!”)
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