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F-Tests / Analysis of Variance (ANOVA) : T Obtained Difference Between Sample Means

This document discusses analysis of variance (ANOVA) tests, which allow researchers to compare more than two sample means at once. ANOVA controls for increased chances of type 1 errors when multiple t-tests are performed. There are different types of ANOVA depending on the experimental design, and assumptions include independent and normally distributed samples with equal variances. ANOVA calculates an F-ratio of variance between sample means over variance expected by chance.

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saira tahir
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50 views2 pages

F-Tests / Analysis of Variance (ANOVA) : T Obtained Difference Between Sample Means

This document discusses analysis of variance (ANOVA) tests, which allow researchers to compare more than two sample means at once. ANOVA controls for increased chances of type 1 errors when multiple t-tests are performed. There are different types of ANOVA depending on the experimental design, and assumptions include independent and normally distributed samples with equal variances. ANOVA calculates an F-ratio of variance between sample means over variance expected by chance.

Uploaded by

saira tahir
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as DOCX, PDF, TXT or read online on Scribd
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F-tests / Analysis of Variance (ANOVA)

T-tests - inferences about 2 sample means

But what if you have more than 2 conditions?

e.g. placebo, drug 20mg, drug 40mg, drug 60mg

Placebo vs. 20mg 20mg vs. 40mg

Placebo vs 40mg 20mg vs. 60mg

Placebo vs 60mg 40mg vs. 60mg

Chance of making a type 1 error increases as you do more t-tests

ANOVA controls this error by testing all means at once - it can compare k number of means. Drawback =
loss of specificity

Different types of ANOVA depending upon experimental design (independent, repeated, multi-factorial)

Assumptions

observations within each sample were independent

samples must be normally distributed

samples must have equal variances

t = obtained difference between sample means

difference expected by chance (error)

F = variance (differences) between sample means

variance (differences) expected by chance (error)

Difference between sample means is easy for 2 samples:

(e.g. X1=20, X2=30, difference =10)

but if X3=35 the concept of differences between sample means gets tricky

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