Analysis of variance (ANOVA) attempts to address the question if two or more groups are on average different. We’ve previously addressed the linear model. In the linear model we ask whether the slope is different from zero and whether the y-intercept is different from zero. In ANOVA we have predetermined groups and consider the slope for each group to be zero while we ask teh question of whether these groups all have the same y-intercept.
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The linear model is the foundation for much of statistical hypothesis testing. As such, it should be a foundational part of any scientist’s education and career. Unfortunately, it is frequently misunderstood. Here I attempt to explain the linear model with the hope of bringing clarity to the topic.
The linear model is based on the equation for a line, something we all learned in grade school geometry.
y = mx + b Here y is a vector of our response or dependent variables.
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