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### Basic Statistics for Business and Economics ch 12

Analysis of Variance (ANOVA) The simultaneous comparison of several population means.
What are the characteristics of the F distribution? There is a family. It is continuous. It cannot be negative. It is positively skewed. It is asymptotic.
The F distribution is used to test: The hypothesis that the variance of one normal population equals the variance of another normal population.
To use the ANOVA, we assume the following: The populations follow the normal distribution. The populations have equal standard deviation (sigma). The populations are independent.
Total Variation The sum of the squared differences between each observation and the overall mean.
Treatment Variation The sum of the squared differences between each treatment mean and the grand or overall mean.
Random Variation The sum of the squared differences between each observation and its treatment mean.
SS Total (Sum of Squares Total) = SST + SSE
SST Sum of Squares Treatment
SSE Sum of Squares Error
MSE (Mean Square Error) = SSE/(n-k)
MST (Mean Square Treatment) = SST/(k-1)
F = MST/MSE
Degrees of freedom in the numerator = k - 1
Degrees of freedom in the denominator = n - k
k = Number of Treatments
n = Number of Observations
Created by: dengler

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