Top 10 Mistakes of Hypothesis Tests
Copyright © 2005–2023 by Stan Brown, BrownMath.com
Copyright © 2005–2023 by Stan Brown, BrownMath.com
Summary: Know your enemy! These are the most common mistakes students make in their hypothesis tests on quizzes. Know the right things to do instead!
See also: This article lists blunders. But there are also problems with the theory of hypothesis tests and how they are used by researchers today, as What’s Wrong with Hypothesis Tests? explains.
And hey! write down all your inputs.
There’s no cool memory trick, because every problem is worded differently. Just make it a habit to read each problem carefully and notice whether it’s asking for a two-tailed test (≠) or a one-tailed test (> or <).
Another common problem is misreading “at least” as ≤ instead of the correct ≥, or misreading “no more than” as ≥ instead of the correct ≤. The Symbol Sheet has some common phrases for the inequalities, but again the best practice is just to read the problem carefully and think about what you’re writing.
Think about it logically! You’re not testing the sample — you know the sample. You’re testing whether something is true about the general population that your sample came from.
A related problem is picking <, ≠, or > for your H1 by looking at the sample data. Again, remember that everything about the hypotheses is based on what you want to know, not on the data you actually find.
Again, no magic bullet here. You need to read the problem carefully.
Some students write the values of p and α above the symbols, or next to them: “p > α (0.0257 > 0.01)”. That’s perfectly acceptable, and it can help you make the comparisons correctly.
And the #1 mistake of hypothesis testing …
We can’t tell, at the ____ level of significance, whether the machine is okay or broken.
When p > α you have to write your conclusion in neutral language, not leaning one way or the other.
Don’t say the machine “might” be anything, or “could” be anything. And especially don’t say “we can’t prove it’s broken” or “we can’t prove it’s okay.” Both of those are true, but they’re only half the truth and they lead the reader to a wrong conclusion. (The most effective way to lie is to tell only part of the truth.)
See also: When p>α, you fail to reject H0
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