Correlational research methods
Lecture 0 3
Mean, standard deviation and variance 3
Z-score 3
T-statistic 3
Statistical power 3
Pearson’s R 4
Lecture 1 Basics of statistical research and correlation 5
Descriptive statistics 5
Inferential statistics 5
P-values and statistical power 5
Measurement levels 6
Research designs 6
Relationships between variables 6
Lecture 2 Simple regression 1/2 7
Confidence interval 7
Regression analysis 8
Lecture 3 Simple regression 2/2 10
Interpretation of the estimated regression coefficient b1 10
Standardized regression coefficient (β) 10
Total variance and R2 10
Other forms of inferential statistics 11
Lecture 4 Multiple regression analysis 12
Basics of multiple regression analysis 12
Correlations and regression analysis 12
Lecture 5 Multiple regression analysis 13
How well can we predict the variance in Y using the entire set of predictors? 13
How well does every predictor explain/predict variance in Y, controlled for all other
predictors in the model? 14
Lecture 6 Multiple regression analysis 15
Multiple linear regression analysis 15
Hypothesis testing 15
Lecture 7 multiple regression analysis 16
Partial effects for each predictor 16
Nested models 16
Testing for partial effect of a cluster of variables 16
Hierarchical regression analysis 17
,Lecture 8 Dummy variable 18
Multiple regression with dichotomous categorical predictors 18
Multiple regression with a categorical and quantitative predictor 18
Multiple regression with a categorical predictor with more response categories 19
Lecture 9 Interaction effects 20
Interaction between a continuous and dichotomous variable 20
Interaction between continuous variables and nominal variables with more than 2
categories 20
Lecture 10 multicollinearity 21
Probing 21
Multicollinearity 21
Lecture 11 Logistic regression analysis 22
Dichotomous logistic regression 22
Binary logistic regression 23
Lecture 12 types of logistic regression 24
Multiple logistic regression (continuous predictors) 24
Multiple logistic regression (continuous + binary predictor) 24
Multiple logistic regression (continuous + categorical predictor) 24
Multiple logistic regression with interaction 25
Significance testing 25
, Lecture 0
Mean, standard deviation and variance
When two scores change from the original but have the same outcome (15 becomes 17 and
7 becomes 5).
- Mean: stays the same, same average
- Variance: increases, SS increases because the deviance scores are bigger.
- Standard deviation: increases
When all scores are two units lower than the original scores
- Mean: decreases, lower average
- Variance: stays the same (same difference between scores)
- Standard deviation: stays the same
When all scores are multiplied by 2
- Mean: increases, higher average
- Variance: increases, scores get higher and difference between scores is bigger
- Standard deviation: increases
Z-score
A statistic that gives the location in a comparable sense relative to its distribution: you can
find how close/far a value is from the mean. Used for hypothesis testing by using critical
regions and seeing if the score lies there.
Sampling distribution
Sampling distribution of the mean: disctribution of outcomes that is obtained when
thousands of random samples are taken from the population and the mean is calculated for
each sample. Standard error is the standard deviation of this distribution. This gets smaller
with a larger sample.
T-statistic
Similar to Z-score but used when you don’t know the population standard deviation.
Statistical power
Type 1 error: reject the null hypothesis while the null hypothesis is actually true (false
positive).
Type 2 error: fail to reject the null hypothesis while alternative hypothesis is actually true
(false negative).
Statistical power: the probability of rejecting the null hypothesis when the alternative
hypothesis is true (true positive). Influenced by:
- α level, higher is higher power
- Effect size, larger is higher power
- Sample size, larger is higher power
Lecture 0 3
Mean, standard deviation and variance 3
Z-score 3
T-statistic 3
Statistical power 3
Pearson’s R 4
Lecture 1 Basics of statistical research and correlation 5
Descriptive statistics 5
Inferential statistics 5
P-values and statistical power 5
Measurement levels 6
Research designs 6
Relationships between variables 6
Lecture 2 Simple regression 1/2 7
Confidence interval 7
Regression analysis 8
Lecture 3 Simple regression 2/2 10
Interpretation of the estimated regression coefficient b1 10
Standardized regression coefficient (β) 10
Total variance and R2 10
Other forms of inferential statistics 11
Lecture 4 Multiple regression analysis 12
Basics of multiple regression analysis 12
Correlations and regression analysis 12
Lecture 5 Multiple regression analysis 13
How well can we predict the variance in Y using the entire set of predictors? 13
How well does every predictor explain/predict variance in Y, controlled for all other
predictors in the model? 14
Lecture 6 Multiple regression analysis 15
Multiple linear regression analysis 15
Hypothesis testing 15
Lecture 7 multiple regression analysis 16
Partial effects for each predictor 16
Nested models 16
Testing for partial effect of a cluster of variables 16
Hierarchical regression analysis 17
,Lecture 8 Dummy variable 18
Multiple regression with dichotomous categorical predictors 18
Multiple regression with a categorical and quantitative predictor 18
Multiple regression with a categorical predictor with more response categories 19
Lecture 9 Interaction effects 20
Interaction between a continuous and dichotomous variable 20
Interaction between continuous variables and nominal variables with more than 2
categories 20
Lecture 10 multicollinearity 21
Probing 21
Multicollinearity 21
Lecture 11 Logistic regression analysis 22
Dichotomous logistic regression 22
Binary logistic regression 23
Lecture 12 types of logistic regression 24
Multiple logistic regression (continuous predictors) 24
Multiple logistic regression (continuous + binary predictor) 24
Multiple logistic regression (continuous + categorical predictor) 24
Multiple logistic regression with interaction 25
Significance testing 25
, Lecture 0
Mean, standard deviation and variance
When two scores change from the original but have the same outcome (15 becomes 17 and
7 becomes 5).
- Mean: stays the same, same average
- Variance: increases, SS increases because the deviance scores are bigger.
- Standard deviation: increases
When all scores are two units lower than the original scores
- Mean: decreases, lower average
- Variance: stays the same (same difference between scores)
- Standard deviation: stays the same
When all scores are multiplied by 2
- Mean: increases, higher average
- Variance: increases, scores get higher and difference between scores is bigger
- Standard deviation: increases
Z-score
A statistic that gives the location in a comparable sense relative to its distribution: you can
find how close/far a value is from the mean. Used for hypothesis testing by using critical
regions and seeing if the score lies there.
Sampling distribution
Sampling distribution of the mean: disctribution of outcomes that is obtained when
thousands of random samples are taken from the population and the mean is calculated for
each sample. Standard error is the standard deviation of this distribution. This gets smaller
with a larger sample.
T-statistic
Similar to Z-score but used when you don’t know the population standard deviation.
Statistical power
Type 1 error: reject the null hypothesis while the null hypothesis is actually true (false
positive).
Type 2 error: fail to reject the null hypothesis while alternative hypothesis is actually true
(false negative).
Statistical power: the probability of rejecting the null hypothesis when the alternative
hypothesis is true (true positive). Influenced by:
- α level, higher is higher power
- Effect size, larger is higher power
- Sample size, larger is higher power
