For an experiment comparing more than two treatment conditions, youshould use an

Question

For an experiment comparing more than two treatment conditions, youshould use analysis of variance rather than separate t testsbecause:
a. you are less likely to make a mistake in the computationsof ANOVA b. a test based on variances is more sensitive than a testbased on means c. ANOVA has less risk of a Type 1 Error d. ANOVA has less risk of a Type II Error.
I think the correct answer is b. PLEASE HELP ... IS THISRIGHT? THANKS
a. you are less likely to make a mistake in the computationsof ANOVA b. a test based on variances is more sensitive than a testbased on means c. ANOVA has less risk of a Type 1 Error d. ANOVA has less risk of a Type II Error.
I think the correct answer is b. PLEASE HELP ... IS THISRIGHT? THANKS

Explanation / Answer

There are two reasons why we should use ANOVA in preference tomultiple t tests. Of course an obvious reason is that multiple ttests would involve great number of test where as ANOVA would givethe result in only one test.
Apart from this when we do the t tests @ 5% significance weexpect that there is 5% probability of Type I error.
Now let's say we have 3 groups to compare then we have to do3C2 = 3 tests to do. Probability of type I error of at least 1 test = 1-P(type Ierror of zero test)
= 1- 0.95*0.95*0.95 = 1- 0.8534 = 0.1426 which issignificantly greater than 0.05 level of type I error that we wantfrom the comparison.
so the right answer is ANOVA has less risk of a Type Ierror.
Of course another second reason is that when we do multiple ttests one assumption is that any comparison of two groups isindependent of all other groups. This is not exactlytrue.
Hope this helps . Feel free to ask for anyclarifications.

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