Lecture 6 – Statistical Models – Summary Page
1) Statistical models
a. Start with a question
b. Find or create a theory that addresses question
c. Generate hypotheses based on the theory
d. Collect data that allows you to assess the research question
e. Fit a statistical model to see whether the data you found matches what
you thought would happen.
i.To tell whether or not your model fits the data well, you have to be
able to assess how much error there is.
ii.You want a model with as little error as possible.
iii.The difference between each data point and our model is called the
Difference between actual score and where the person is predicted to be on your
model. So on a graph with all the dots, the line that is your model and the distance
to a dot is the error. Differences between your model and the actual data.
3) Total Error
The amount of error across all your participants – in class def.
a. subtract the mean from each score for each data point.
Total error = ∑ (x−́x) 2
∑ means “take the sum” or “add up for all cases” – add everything up
x = an individual score on variable x
x = the mean of variable x (“x bar”) – the average of the x variable
(in the brackets beside weird e) – everything you need to add up
Want to add up the errors. Take every individual’s data point and then subtract the
average, then add it all up.
Best fitting model will add up to 0. But that doesn’t always mean it’s a perfect
We need the sum of squared errors.
4) Sum of squared errors
SS = ∑ (x−x)
- even a model that fits very well will have a high degree of error if there
are more cases.
- start by squaring every term.
Politician X x- x (x−x)2
1 1 -2 4
2 2 -1 1
3 3 0 0
4 4 1 1