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S13.1 - Comparing Three or More Means
Comparing Three or More Means, One-Way Analysis of Variance
30
Mathematics
Graduate
11/11/2013

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Term
Analysis of variance (ANOVA)
Definition
An inferential method used to test the equality of three or more population means
Term
2 facts about ANOVA
Definition
1. A comparison of two estimates of the same population variance
2. One-way because there is only one factor that distinguishes the various populations
Term
4 requirements of a one-way ANOVA test
Definition
1. There are k simple random variables; one from each of k populations
2. The k samples are independent of each other
3. The populations are normally distributed
4. The populations have the same variance, sigma^2
Term
The methods of one-way ANOVA (are/are not) robust
Definition
The methods of one-way ANOVA are robust
Term
The one-way ANOVA procedures may used provided that
Definition
The largest sample standard deviation is no more than twice the smallest sample standard deviation
Term
Between-sample variability
Definition
The variability among the sample means
Term
Within-sample variability
Definition
The variability of each sample
Term
ANOVA f-test statistic, F0 =
Definition
Between-sample variability/within-sample variability
Term
Mean square
Definition
A sum of squares divided by the corresponding degrees of freedom
Term
s^2 =
Definition
Summation(xi - xbar)^2/n-1
Term
Sum of squares =
Definition
Summation(xi - xbar)^2
Term
Sum of squares measures
Definition
The variability of the data about the sample mean
Term
Degrees of freedom =
Definition
n - 1
Term
The F-statistic is the ratio of
Definition
The between-sample variability and the within-sample variability
Term
Total sum of squares =
Definition
Summation(x-xbar)^2
Term
Mean square due to error (MSE) =
Definition
SSE/Degrees of freedom
Term
Sum of squares due to error (SSE) =
Definition
Summation(dfk)sk^2
Term
The MSE is an unbiased estimator of
Definition
Sigma^2 regardless of H0 and H1
Term
Mean square due to treatment (MST) is
Definition
The between-sample variability estimate of sigma^2 (numerator of the F-statistic)
Term
Sum of squares due to treatment (SST) =
Definition
Summation[nk(xbark - xbar)^2]
Term
MST =
Definition
SST/Degrees of freedom
Term
MST is an unbiased estimator of
Definition
Sigma^2 only if the null is true
Term
F-test statistic, F0 =
Definition
MST/MSE
Term
If F-test statistic is large, it is evidence
Definition
Against the null
Term
1. Computing the F-test statistic
Definition
Compute sample mean, xbar
Term
2. Computing the F-test statistic
Definition
Find sample mean for each sample, x1bar and x2bar
Term
3. Computing the F-test statistic
Definition
Find sample variance for each sample, s1^2 and s2^2
Term
4. Computing the F-test statistic
Definition
Compute SSE and MSE
Term
5. Computing the F-test statistic
Definition
Compute SST and MST
Term
6. Computing the F-test statistic
Definition
F0 = MST/MSE
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