1. When you are comparing more than 3 groups, why can’t you use multiple t- test
ID: 3364432 • Letter: 1
Question
1. When you are comparing more than 3 groups, why can’t you use multiple t-tests?
2. What 2 things cause between-group variance?
3. What 1 thing causes within-group variance?
4. What value of F-ratio would you expect to find if the null hypothesis were true?
5. Would you run an ANOVA or t-test? Answer for each possibility:
a. Ben & Jerry are interested in whether different flavors of ice cream produce worse ice cream headaches. Groups of participants try “The Tonight Dough,” “Triple Caramel Chunk,” or “Peanut Butter Cup” very quickly and report the intensity of their resulting headache.
b. Jen & Berry are interested in whether they can compete with Ben & Jerry in a blind taste test. They have one group eat Jen & Berry while another eats Ben & Jerry. Each sample makes a rating of the taste of their ice cream.
Explanation / Answer
Hello,
Hope you are keeping well.
Now, I'm answering the questions in order:
1. Every time we conduct a t-test there is a chance that we will definitely make a Type I error. This error is usually 5% as in most of our tests we take confidence interval to be 95%. Now, by running two t-tests on the same data we will increase our chance of making a mistake to 10%. That is the biggest reason why we don't use t-test and go for ANOVA for three or more groups.
2. The variation due to the interaction between the samples is regarded as the between-group variance. There are k samples involved with one data value for each sample (the sample mean), so there are k-1 degrees of freedom.
3. The variation due to the differences within individual samples is called within-group variance. In this case, no interaction between sample is involved as each of them is taken independently.
4. We fail to reject the null hypothesis if the critical f value is smaller than the F Value, Now, in case of an ANOVA, the Null hypothesis is that the mean (average value of the dependent variable) is the same for all groups.Therefore the F-Ratio will be the value of the variability as per calculations.
5. a) In this case, there are three groups of participants so Ben and Jerry will run ANOVA test for better results.
b) In this case, there are two groups of participants so Ben and Jerry can easily run T-test for the result as they don't need any complications in the calculations.
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