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Business Stats ch 12
Basic Statistics for Business and Economics ch 12
Question | Answer |
---|---|
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 |