Behavioural Research Methods 2
BRM2
Summary of Lectures
BakedToast
EINDHOVEN UNIVERSITY OF TECHNOLOGY
, CONTENTS:
LECTURE 1: ........................................................................................................................................ 4
Kinds of variables:.......................................................................................................................... 4
Roadmap/Learning objectives ....................................................................................................... 5
LECTURE 2 ......................................................................................................................................... 5
Stappenplan Statistics:................................................................................................................... 6
Terminology: ................................................................................................................................. 6
About P-value: ............................................................................................................................... 6
Central limit theorem: ................................................................................................................... 7
Getting an intuition for confidence intervals: ................................................................................. 7
How to calculate confidence interval: ............................................................................................ 7
LECTURE 3 ......................................................................................................................................... 8
Fisher’s exact: The procedure (Example 1.2) ......................................................................... 9
Fisher’s exact in stata: ................................................................................................................... 9
Stata: ............................................................................................................................................. 9
STATA: ......................................................................................................................................... 10
LECTURE 4: ...................................................................................................................................... 11
One continuous and one (binary) categorical variable:................................................................. 11
Test-statistic: ............................................................................................................................... 12
Information about t: .................................................................................................................... 12
Recap procedure for all statistical tests:....................................................................................... 12
On one- and two-sided (or -tailed) tests....................................................................................... 12
Assumption 1: Normality ............................................................................................................. 12
Shapiro-Wilk test for normality (Swilk)......................................................................................... 13
Test for skewness and kurtosis (sktest) ........................................................................................ 13
Testing for normality in Stata: ...................................................................................................... 13
Assumption number 2: Testing for equality of variance ............................................................... 13
Transform your data: workflow step 2 → .................................................................................... 13
Stata: the ladder command (Example 2) ............................................................................ 14
When transformations do not work: ranksum and median test (book 7.11) ................................. 14
Effect size: Cohen’s D................................................................................................................... 15
Interpretation of effect size: ........................................................................................................ 15
Paired t-test: (Example 2.3) ................................................................................................ 15
LECTURE 5 ....................................................................................................................................... 16
Learning objectives: ..................................................................................................................... 16
, Graphs in Stata: ........................................................................................................................... 16
Correlation: How close are data points to the regression line? ..................................................... 17
Correlation r and R2 ..................................................................................................................... 17
Significance of correlation: .......................................................................................................... 18
Calculating Correlation (and its significance) in Stata ................................................................... 18
The target variable and the predictor: ......................................................................................... 18
Changing the Variables: ............................................................................................................... 19
Standardization of variables: ....................................................................................................... 19
Understanding or predicting? ...................................................................................................... 19
LECTURE 6 ....................................................................................................................................... 20
Learning objections: .................................................................................................................... 20
Multiple regression (1Y, more X’s) : ............................................................................................. 20
MODEL FIT: .................................................................................................................................. 21
Model fit notations/definitions: ................................................................................................... 21
Introducing: The adjusted R2 ........................................................................................................ 21
From sample to population:......................................................................................................... 21
Multiple regression:..................................................................................................................... 22
Going through a regression table: ................................................................................................ 22
Technically… ................................................................................................................................ 22
Including a categorical variable with more than 2 categories: ...................................................... 22
The test-command (revisited). ..................................................................................................... 23
Some background information on multiple regression: ................................................................ 23
Notations/definitions: ................................................................................................................. 24
Why is it beautiful: ...................................................................................................................... 24
Regression vs t-test: .................................................................................................................... 25
LECTURE 7: ...................................................................................................................................... 26
Learning objectives: ..................................................................................................................... 26
Multiple regression – refreshing summary of lecture 6 ................................................................ 26
Components of a regression run: ................................................................................................. 26
Ramsey’s ‘omitted variable test’ (a misleading name) .................................................................. 28
Multiple regression is much less a standard recipe: ..................................................................... 31
The multiple regression lectures summary:.................................................................................. 31
LECTURE 8: ...................................................................................................................................... 32
Assumptions in regression analysis: ............................................................................................. 32
Part 1: No multi-collinearity: Your predictor variables should not be too alike ............................. 33
Checking correlations: (Detect 1) ................................................................................................. 33
, Calculating Variance inflation factors (VIF) Statistics (Detect 2) .................................................... 33
Part 2: All relevant predictor variables included ........................................................................... 33
Step 3/4: Homoscedasticity and linearity ..................................................................................... 34
Assumptions in regression analysis: ............................................................................................. 34
Checking plots: ............................................................................................................................ 34
Rvfplot (“residual versus fitted plot”) ........................................................................................... 35
Avplots (“added variable plots”): ................................................................................................. 35
White’s test for heteroscedasticity: ............................................................................................. 35
Stata Heteroscedasticity: ............................................................................................................. 35
When do you get heteroscedasticity? .......................................................................................... 36
Solutions to heteroscedasticity/nonlinearity (continued) ............................................................. 36
Step 5: Independent Errors .......................................................................................................... 36
Step 6: The noise should be distributed normally......................................................................... 37
Not too many non-significant predictor variables ........................................................................ 37
Stepwise regression: NO .............................................................................................................. 38
A standard multiple regression run .............................................................................................. 38
Typical assignment Exam/Statistics: ............................................................................................. 38
LECTURE 9: ...................................................................................................................................... 39
Learning objectives: ..................................................................................................................... 39
General information: ................................................................................................................... 39
Stata commands: ......................................................................................................................... 39
X → Y: An(c)ova ........................................................................................................................... 40
ANOVA Assumptions: .................................................................................................................. 40
ANCOVA: Adding a covariate ....................................................................................................... 41
ANcOVA Assumptions:................................................................................................................. 41
2-Way ANOVA (or Factorial ANOVA) ............................................................................................ 41
Recap: AN(c)OVA: ........................................................................................................................ 41
LECTURE 10: .................................................................................................................................... 42
Sample size determination: ......................................................................................................... 42
How much power is enough?....................................................................................................... 43
Stratified samples: Smarter than random sampling...................................................................... 44
RECAP:......................................................................................................................................... 45
BRM2
Summary of Lectures
BakedToast
EINDHOVEN UNIVERSITY OF TECHNOLOGY
, CONTENTS:
LECTURE 1: ........................................................................................................................................ 4
Kinds of variables:.......................................................................................................................... 4
Roadmap/Learning objectives ....................................................................................................... 5
LECTURE 2 ......................................................................................................................................... 5
Stappenplan Statistics:................................................................................................................... 6
Terminology: ................................................................................................................................. 6
About P-value: ............................................................................................................................... 6
Central limit theorem: ................................................................................................................... 7
Getting an intuition for confidence intervals: ................................................................................. 7
How to calculate confidence interval: ............................................................................................ 7
LECTURE 3 ......................................................................................................................................... 8
Fisher’s exact: The procedure (Example 1.2) ......................................................................... 9
Fisher’s exact in stata: ................................................................................................................... 9
Stata: ............................................................................................................................................. 9
STATA: ......................................................................................................................................... 10
LECTURE 4: ...................................................................................................................................... 11
One continuous and one (binary) categorical variable:................................................................. 11
Test-statistic: ............................................................................................................................... 12
Information about t: .................................................................................................................... 12
Recap procedure for all statistical tests:....................................................................................... 12
On one- and two-sided (or -tailed) tests....................................................................................... 12
Assumption 1: Normality ............................................................................................................. 12
Shapiro-Wilk test for normality (Swilk)......................................................................................... 13
Test for skewness and kurtosis (sktest) ........................................................................................ 13
Testing for normality in Stata: ...................................................................................................... 13
Assumption number 2: Testing for equality of variance ............................................................... 13
Transform your data: workflow step 2 → .................................................................................... 13
Stata: the ladder command (Example 2) ............................................................................ 14
When transformations do not work: ranksum and median test (book 7.11) ................................. 14
Effect size: Cohen’s D................................................................................................................... 15
Interpretation of effect size: ........................................................................................................ 15
Paired t-test: (Example 2.3) ................................................................................................ 15
LECTURE 5 ....................................................................................................................................... 16
Learning objectives: ..................................................................................................................... 16
, Graphs in Stata: ........................................................................................................................... 16
Correlation: How close are data points to the regression line? ..................................................... 17
Correlation r and R2 ..................................................................................................................... 17
Significance of correlation: .......................................................................................................... 18
Calculating Correlation (and its significance) in Stata ................................................................... 18
The target variable and the predictor: ......................................................................................... 18
Changing the Variables: ............................................................................................................... 19
Standardization of variables: ....................................................................................................... 19
Understanding or predicting? ...................................................................................................... 19
LECTURE 6 ....................................................................................................................................... 20
Learning objections: .................................................................................................................... 20
Multiple regression (1Y, more X’s) : ............................................................................................. 20
MODEL FIT: .................................................................................................................................. 21
Model fit notations/definitions: ................................................................................................... 21
Introducing: The adjusted R2 ........................................................................................................ 21
From sample to population:......................................................................................................... 21
Multiple regression:..................................................................................................................... 22
Going through a regression table: ................................................................................................ 22
Technically… ................................................................................................................................ 22
Including a categorical variable with more than 2 categories: ...................................................... 22
The test-command (revisited). ..................................................................................................... 23
Some background information on multiple regression: ................................................................ 23
Notations/definitions: ................................................................................................................. 24
Why is it beautiful: ...................................................................................................................... 24
Regression vs t-test: .................................................................................................................... 25
LECTURE 7: ...................................................................................................................................... 26
Learning objectives: ..................................................................................................................... 26
Multiple regression – refreshing summary of lecture 6 ................................................................ 26
Components of a regression run: ................................................................................................. 26
Ramsey’s ‘omitted variable test’ (a misleading name) .................................................................. 28
Multiple regression is much less a standard recipe: ..................................................................... 31
The multiple regression lectures summary:.................................................................................. 31
LECTURE 8: ...................................................................................................................................... 32
Assumptions in regression analysis: ............................................................................................. 32
Part 1: No multi-collinearity: Your predictor variables should not be too alike ............................. 33
Checking correlations: (Detect 1) ................................................................................................. 33
, Calculating Variance inflation factors (VIF) Statistics (Detect 2) .................................................... 33
Part 2: All relevant predictor variables included ........................................................................... 33
Step 3/4: Homoscedasticity and linearity ..................................................................................... 34
Assumptions in regression analysis: ............................................................................................. 34
Checking plots: ............................................................................................................................ 34
Rvfplot (“residual versus fitted plot”) ........................................................................................... 35
Avplots (“added variable plots”): ................................................................................................. 35
White’s test for heteroscedasticity: ............................................................................................. 35
Stata Heteroscedasticity: ............................................................................................................. 35
When do you get heteroscedasticity? .......................................................................................... 36
Solutions to heteroscedasticity/nonlinearity (continued) ............................................................. 36
Step 5: Independent Errors .......................................................................................................... 36
Step 6: The noise should be distributed normally......................................................................... 37
Not too many non-significant predictor variables ........................................................................ 37
Stepwise regression: NO .............................................................................................................. 38
A standard multiple regression run .............................................................................................. 38
Typical assignment Exam/Statistics: ............................................................................................. 38
LECTURE 9: ...................................................................................................................................... 39
Learning objectives: ..................................................................................................................... 39
General information: ................................................................................................................... 39
Stata commands: ......................................................................................................................... 39
X → Y: An(c)ova ........................................................................................................................... 40
ANOVA Assumptions: .................................................................................................................. 40
ANCOVA: Adding a covariate ....................................................................................................... 41
ANcOVA Assumptions:................................................................................................................. 41
2-Way ANOVA (or Factorial ANOVA) ............................................................................................ 41
Recap: AN(c)OVA: ........................................................................................................................ 41
LECTURE 10: .................................................................................................................................... 42
Sample size determination: ......................................................................................................... 42
How much power is enough?....................................................................................................... 43
Stratified samples: Smarter than random sampling...................................................................... 44
RECAP:......................................................................................................................................... 45
