Type I and Type II Errors

What does this table mean?

• If Ho is true and I say it is (I accept it), then I am CORRECT. Whatever I saw was genuinely due to chance.
• If Ho is true and I falsely reject it (I say that what I saw was a real effect), then I have made a Type I error with probability alpha. Alpha says how much of the effect could have been due to chance.
• If Ho is false but I say it is true (there really was an effect, but I thought it was just chance variations), then I have made a Type II error with probability beta.
• If Ho is false and I say it is (I reject Ho), then I am CORRECT. I say I saw a real effect; it was genuinely real; and the power of my test was 1 - beta.

How to increase power

• Relax Alpha (and let more chance variation come in)
• Use a Parametric test (one with the assumptions; means you need interval or ratio data)
• Increase the Reliability of the measure (its replicability; maybe you want to use a tried-and true old test that others have checked out)
• Do a One-tailed test (this puts all the critical region at the end you're interested in, sort of like increasing alpha)
• Increase N (get more samples)
• Increase the Sensitivity of the design (break it into more factors)

The eyeball method for estimating power

1. Start with the null hypothesis. Get the sampling distribution of the mean is Ho is true. You need xbar and sem, which means you need s and n, so you can run a one group t-test. Recall: sem = s/sqrt(n)
2. If you know population statistics, you can use mu and sigma and run a one group z test instead. (You still have to calculate sem using sigma.)
3. Draw a picture of this sampling distribution, and mark off the critical values from the z-test or t-test.
4. Next, use the alternate hypothesis and draw another curve with the midpoint at the xbar that you would expect if it were true.
5. Shade in the part of the new curve that is above the critical value on the old curve. That is the power. Anything to the left of the shaded area in the new curve is beta.
6. The actual calculation works like this:
   z = (critical value on old curve - midpoint of new curve)/sem
   Use the z score table to figure the proportion of the curve that lies above this z score. That is the power.
7. For a 2 tail test, don't worry about the tail that's nowhere near the new curve. If you want, use a one tail test to increase power.

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