Chapter13ANOVAOverview3PM11.26.19

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School
Montana State University **We aren't endorsed by this school
Course
EGEN 350
Subject
Statistics
Date
Aug 26, 2023
Pages
18
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1 EGEN350 Chapter 13 Analysis of Variance (Section 13-2 Only) ( ANOVA ) w w w
2 Calcium carbonate crystals were made by three separate processes (A, B, C) and assessed using nanoindentation for modulus. How could we test if there is an effect of process type on nanoindentation modulus? C B A 38 37 36 35 34 Process type Nanoindentation modulus (GPa) Should we just use multiple (3) t-tests: A vs B, A vs C, and B vs C? Comparing 3 (or more) population means
3 C B A 38 37 36 35 34 Process type Nanoindentation modulus (GPa) Should we just use multiple (3) t-tests: A vs B, A vs C, and B vs C? NO. Each time we conduct a t-test, we introduce an opportunity for Type I error. Suppose ࠵? = 0.05 . For 1 test: P(Type I Error) = P(Reject ࠵? 0 | ࠵? 0 is true) = 0.05. So, P(FTR ࠵? 0 | ࠵? 0 is true) = 0.95 For 3 tests (A vs B, B vs C, A vs C): P(all FTRs | all ࠵? 0 's are true) = (0.95) 3 = 0.857 P(at least 1 Reject ࠵? 0 | all ࠵? 0 's are true) = 1 - (0.95) 3 = 0.143 Therefore, even if all 3 ࠵? 0 's are true, we have a 14.3% chance of making at least one Type I Error. If you have 3 (or more) population means, use ANOVA , not t-tests. assuming independence
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