1. When comparing more than two treatment means, why should you use an analysis
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Question
1. When comparing more than two treatment means, why should you use an analysis of variance instead of using several t tests? What is an experimentwise alpha leve? 2. In general what does the F-ratio consist of for both types of research designs? 3. In a between subjects analysis of variance, differences between participants contribute to which source of variance? 4. MS is the notation for 5. If all three treatments have the same mean, which source of variance would be equal to zero? 6. On average, what value is expected for the F-ratio if the null hypothesis is true? 7. What is the purpose for post hoc tests? 8. A researcher reports an F-ratio with df- 2, 18 from an independent-measures research study. Base on the df values, how many treatments were compared in the study, and what was the total number of subjects participating in the study? a. 2 treatments and 19 subjects b. 2 treatments and 20 subjects c. 3 treatments and 21 subjects d. 3 treatments and 22 subjects 9. How would you describe the shape of the distribution of F-ratios? -10. The following table shows the results of an analysis of variance comparing three treatments. What is the vale of ?2, the percentage of variance accounted for, for these data? a. 30/60-.5 b. 30/90 33 c. 60/90-.67 d. 2/30-067 SourceSs df MS Between 30 2 15 F-7.50 Within 60 30 2 Total90 32 11. If an analysis of variance is used for the following data, what would be the effect of changing the value of SSi to 50? ta a. Increase SSwithin and increase the size of the F-ratio Mi 10 M2 20 b. Increase SSwithin and decrease the size of the F-ratio SS-90 SS2-70 c. Decrease SSwithin and increase the size of the F-ratio d. Decrease SSwithin and decrease the size of the F-ratio 9. In an independent-measures ANOVA, individual differences contrbute to the variance in the numerator and in the denominator of the F-ratio. For a repeated-measures ANOVA, what happens to the individual differences in the numerator of the F-ratio? 10. In a repeated-measures analysis of variance, how does the magnitude of the mean differences from one treatment to another contribute to the F-ratio? a. The mean differences add to the numerator of the F-ratio. b. The mean differences add to the denominator of the F-ratio. c. The mean differences add to both the numerator and the denominator of the F- d. The sample mean differences do not influence the F-ratio.
Explanation / Answer
1) The t test is based on the standard error of the difference between the two means and is only used to test differences between two means.
When we want to copare between more than two means, we have two options :-
1) we could compare each mean with other mean using t tests i.e.,conducting multiple t-tests
2)The other option is that we could perform ANOVA
But conducting several t test can lead to severe inflation pf the type I error rate (false positive)and is NOT RECOMMENDED but analysis of variance allows us to test the null Hypothesis against the alternative hypothesis with a specified value of alpha. hence, ANOVA is preferred to test for differences among several means without increasing the type I error rate.
EXPERIMENT WISE ALPHA LEVEL:-
When an experiment involves several different hypothesis tests, the experimentwise alpha level is the total probability of a type I error that is accumulated from all of the individual tests in the experiment.
Typically, the experiment wise alpha level is substantially greater than the value of alpha used for any one of the individual tests.
2) F ratio is given by:-
F=sb2/sw2
Where,sb2=variance between groups
sw2=within group variance
F=Variability due to treatment effect and variability due to chance/variability due to chance
The F ratio is a statistic. When the null Hypothesis is true, then expected value of denominator and numerator of the F ratio will be equal. As a consequence, the expected value of the F ratio when the null Hypothesis is true is also close to 1.when the null Hypothesis is false and there are group differences between the means, the expected value of the numerator will be larger than the denominator.
3)We know that ANOVA is used to study whether the variation between group means is due to an effect /treatment or it is just a chance variation. It checks BETWEEN GROUP VARIATION and WITHIN GROUP VARIATION.
Difference between participants contribute to variation due to treatments i.e.,if treatments have significant effects then variation between groups is higher than variation within groups.
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