Week 6 Flashcards
What is analysis of variance used to do? (2)
Compare variances
To compare her greater than three means simultaneously (ANOVA)
Six points about the F distribution?
Continuous Can't be negative Asymmetric Positive skew Asymptotic Family of curves, each determined by number of DofF in numerator and denominator
To assumptions for comparing 2 population variances?
Population just follow normal distribution
Level of measurement is interval or ratio
Equation for F?
F = S1^2/S2^2
Large number always goes in numerator
Two notes for comparing two variances?
One tailed test
If given σ remember to square it!
What does an ANOVA test test?
It tests the equality of several means
Why do you not use many simple hypothesis test instead of an ANOVA test?
It’s lowers the confidence level:
Eg. 0.95^10 = 60% confidence
Three assumptions for an ANOVA test?
Sampled population follow a normal distribution
Populations have equal standard deviations
Samples are randomly selected and independent
5 steps of ANOVA test?
1) form hypothesis:
H0: μ1=μ2=μ3
H1: not all means are equal
2) select significance level
3) select test statistic (F-dist.)
4) decision rule: F(obt)>F(crit) reject H0
5) compute test statistic and make decision
Formulae for ANOVA test (numerator, denominator, SST, SSE, F and SSTotal?
Numerator = k-1 DofF Denominator = n-k DofF
n = total number of observations
k = number of population sampled
F = (SST/(k-1)) / (SSE/(n-k))
SSE = Σ(Xi-Xbarc)^2 SST = SSTotal - SSE or Σ(Xbarc - Xbarg)^2 SSTotal = Σ(Xi - Xbarg)^2
Xi is each observation
Xbarg is overall mean
Xbarc is mean of relevant observation
What is SST?
Treatment variation of all observations between samples
What is SSE?
Total variation of all observations within samples
What does it mean if SST and SSE are similar, and if they are not similar?
We can conclude that the effect of external factors is no greater than random variation
If not similar, we reject H0 therefore external factors do appear to have an effect
3 uses of an F-test?
Testing for difference in means
Testing for differences between two variances
Testing for joint significance of the variables in a regression
ANOVA test degrees of freedom?
Numerator: k-1
Denominator: n-k
