Understanding ANOVA Through an Educational Analogy
Imagine students as data points and deciding whether to employ a tutor as introducing a new variable in ANOVA analysis. Just like managing student-teacher ratios, ANOVA involves analyzing data points and deciding if adding a variable is worth the cost based on how much it contributes to the analysis.
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How does ANOVA work? An educational analogy
Students Inherently a good thing we want lots of them! Each makes a contribution (fees) Each needs support (academic assistance) $1 $1 $1 $1 $1 $1 $1 $1 $1 $1 $1 $1
Students Inherently a good thing Each makes a contribution Each needs support Question: Should we employ a tutor? It will cost some money (salary) It will support some students ... but how many? $1 $1 $1 $1 $4 $1 $1 $1 $1 $1 $1 $1 $1
Students Inherently a good thing Each makes a contribution Each needs support Question: Should we employ a tutor? It will cost some money (salary) It will support some students ... but how many? $1 $1 $1 $1 $4 If the tutor supports more than 4students yes, employ them! $1 $1 $1 $1 $1 $1 $1 $1
Students Inherently a good thing Each makes a contribution Each needs support Question: Should we employ a tutor? It will cost some money (salary) It will support some students ... but how many? $1 $1 $1 $1 $4 If the tutor supports more than 4 students yes, employ them! $1 $1 $1 $1 If fewer than 4 students, no point: better to admit 4 fewer students $1 $1 $1 $1
Students = Data Points Inherently a good thing Each contributes 1 df Each adds scatter 1df 1df 1df 1df 1df 1df 1df 1df 1df 1df 1df 1df
Students = Data Points Inherently a good thing Each contributes 1 df Each adds scatter Question: Should we add a variable? It will cost some df 1df 1df 1df 1df 4 df 1df 1df 1df 1df 1df 1df 1df 1df
Students = Data Points Inherently a good thing Each contributes 1 df Each adds scatter Question: Should we add a variable? It will cost some df It will remove some scatter ... but how much? 1df 1df 1df 1df 4 df If the variable removes more scatter than 4 df worth add it! 1df 1df 1df 1df If less than 4 df worth, no point: better off with 4 fewer data points 1df 1df 1df 1df
