Chapter 13
^ means to power
1)
Describe the similarities between an Fratio and a t statistic?
You use an Fratio when doing ANOVA.
ANOVA can be used to compare the means of more
than 2 groups.
Since ttests can be used to compare the means of only two groups, you can
consider the Fratio/ANOVA a broader form of the tstatistic/ttest.
If you use an Fratio when you could have also used a tstatistic (comparing two groups, in a
linear regression analysis, etc.), the Fratio will be equal to the tstatistic squared.
2)
Explain why you should use ANOVA (ANALYSI OF Variance) instead of
several t tests to evaluate mean differences when an experiment consists of
three or more treatment conditions.
Because if you do multiple ttests, you will increase the chances of reporting a false positive (i.e.
a Type I error).
If you are using a 0.05 level of significance, you have a 5% chance of getting a
Type I error in each test.
If you do several ttests, each of them has a 5% chance of getting a Type I error, so overall, your
chance of getting a Type I error is much higher than you wanted.
If you do an ANOVA, you are
only doing one test, so you can keep your risk of a Type I error where you want it.
3)
A research study comparing three treatment conditions produced means of
M^1 = 2, M^2 = 4, and M^3 = 6.
a)
Compare the variance for the set of three means. (Treat the means as a
sample of n=3 values and compute the sample variance.)
The variance of the list 2, 4, 6 is equal to 4.
b)
Now we will change the third mean from M^3 = 6 to M^3 = 15. Notice that
we have substantially increased the difference among the three means.
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Compute the variance for the new set of n = 3 means. You should find that
the variance is much larger than the value obtained in part a. Note: the
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 Spring '10
 NAKKIEW,PICHAYA
 Statistics, Normal Distribution, Variance, main effect

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