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Chapter+13

# Chapter+13 - Chapter 13 ^ means to power 1 Describe the...

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Chapter 13 ^ means to power 1) Describe the similarities between an F-ratio and a t statistic? You use an F-ratio when doing ANOVA. ANOVA can be used to compare the means of more than 2 groups. Since t-tests can be used to compare the means of only two groups, you can consider the F-ratio/ANOVA a broader form of the t-statistic/t-test. If you use an F-ratio when you could have also used a t-statistic (comparing two groups, in a linear regression analysis, etc.), the F-ratio will be equal to the t-statistic 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 t-tests, 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 t-tests, 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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Chapter+13 - Chapter 13 ^ means to power 1 Describe the...

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