Statistical Models PDF

BEHL 2005 / BEHL 2019 (UO) Introductory Research Methods Statistical models Professor Hannah Keage What are we going to cover? What is a statistical model? What is model error? Content from this lecture references: What is a statistical model? • A statistical model uses maths to summarises a da...

BEHL 2005 / BEHL 2019 (UO) Introductory Research Methods Statistical models Professor Hannah Keage What are we going to cover? What is a statistical model? What is model error? Content from this lecture references: What is a statistical model? • A statistical model uses maths to summarises a dataset relative to multiple variables. • A simple description of relationships in the dataset. • Where descriptive statistics describe the data, inferential statistics use statistical models. These models enable you to make inferences about the data, e.g. you can decide whether two variables are associated or whether one group is bigger than the other. What is a statistical model? • No statistical model is perfect. • Data = model + error • London = model of London + wrong bits • We can use models to predict values (but these predictions will always have error around them). Data/participants Model Error What is a statistical model? 50 Shoe size EU 48 44 40 36 32 130 140 150 160 170 Height in cm 180 190 200 Data/participants Model Error What is a statistical model? 50 Shoe size EU 48 From the model, we would predict that the participant who was 160cm tall would have a 40.5 EU shoe size, but they measured at 47.0. 44 40 36 32 130 140 150 160 170 Height in cm 180 190 200 Why do we care about error? Data = model + error (note: error sometimes called residuals) It tells us that we don’t fully understand our outcome/dependent variable. It tells us there may be interesting factors at play in the relationship/data under investigation. If we can reduce model error, we may have a better chance of detecting a significant effect. Why do we care about error? Data = model + error Height and shoe size Difference between data and correlation line Correlation line (estimate of the relationship between height and shoe size) The correlation between height and shoe size isn’t perfect. There are likely other factors at play, e.g. sex. If we included covariates such as sex, we may have a better chance of detecting a significant effect. Why do we care about error? Sex: male Data/participants Model Error Sex: female Data/participants Model Error A model with no error…? 50 Shoe size EU 48 44 40 36 32 130 140 150 160 170 Height in cm 180 190 200 Data/participants Model Error A model with little error…? 50 Shoe size EU 48 44 40 36 32 130 140 150 160 170 Height in cm 180 190 200 Data/participants Model Error A model with lots of error…? 50 Shoe size EU 48 44 40 36 32 130 140 150 160 170 Height in cm 180 190 200 What is a good statistical model? • The smaller the error, the better the model “fit”. • There are caveats, but they are beyond the scope of this course. You can include so many variables that you “over fit” the model to the data, which is problematic in terms of generalisation (using the model in different contexts and samples). BEHL 2005 / BEHL 2019 (UO) Introductory Research Methods Statistical models Professor Hannah Keage