Week 7
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What is a statistical model?
one or more explanatory variables (each written as X) and parameters relating them to the response
What is εi?
the unexplained bit (deviation of the observed value of Y from the value predicted by the model)
Why are linear models the go-to in biology?
because they’re robust, flexible, and can in principle analyse any response variable
What is a generalised linear model?
a linear model that assumes a non-normal distribution
What is a plain linear model?
is a linear model that assumes a normal distribution
What are numerical responses assumed to have?
In practice, we mostly use them to analyse numerical responses that are assumed to have a normal distribution
What is µ?
is the overall mean
What is Ai?
Ai is the effect of group i in X(µ - µi)
what are residuals?
errors are often called residuals
What is Yij?
Yij is the value of Y for individual j in group i
What is ANOVA for?
a linear model for comparing the means of more than two groups
How does ANOVA work?
by asking if individuals from different groups differ more (on average) than individuals from the same group
Null hypothesis ANOVA?
• H0: all group means are equal
What is F statistic formula?
F = group mean square/error mean square MSgroups/MSerror
What does large f mean?
the larger the F, the more that group means differ relative to spread within groups, and the more likely we are to reject the null
how do you get F?
• partition the sums of squares to separate sources of variance in the response • calculate the ANOVA table