Refresh lessons:
Correlation coefficent A standardized number to assess the strength of a linear
relationship.
Pearson:
- Scale between -1 and 1, 0 = no linear
relationship, 1 = maximum
- No causal relation!
Linear regression Used to make predictions about linear relations
B1 = slope, how much Y increases if X increases by 1
B0/constant/intercept = the point where the regression
line crosses the y-axis
Residual / error The difference between the true value Y and the
predicted value Y^
Least squares method Look for the line that will result in the smallest possible
sum of squared errors.
R-squared Determines the proportion of the variance of the
response variable that is ‘explained’ by the predictor
variable(s).
- Determines the ‘fit’
- Proportion between 0 and 1
Bayes factor Tells us how much more one hypothesis is supported in
comparison to another. Null-hypothesis versus an
alternative hypothesis
Construct validity The extent to which the measurement instruments
(operational definition) succeed in measuring the
concepts/constructs and thus fit the conceptual
definition. In experimental research, this is also about
the extent to which the intended manipulation
succeeded.
- About the correspondence between
operationalization and theoretical concept
Internal validity The extent to which the research method can eliminate
alternative explanations for an effect.
- About the ability to determine whether there is a
causal relationship
In principle: higher internal validity with experimental research than with qualitative or correlational
External validity The extent to which the research results can be
generalized to other groups, times and situations.
Statistical validity The extent to which the results of a statistical analysis
are accurate and well-founded
ANOVA A test for comparing 2 or more means.
T-test A test for comparing 2 means
One-sample t-test Testen of het gemiddelde van één steekproef significant
verschilt van een bekend populatiegemiddelde of een
bepaalde theoretische waarden = kijken of
steekproefgroep afwijkt van een bepaalde norm.
Two-sample t-test Testen of er een significant verschil is tussen de
gemiddelden van twee onafhankelijke steekproeven.
,Within groups variance The variance of scores within each group averaged over
= residual variance the groups.
- There is only a good representation of variation
within each of the group if there is homogeneity
of variances, meaning that the within group
variances are not too different between the
groups
Between groups variance The variation of the group means, a measure of how
= explained variance different they are
F-statistics Goal is to answer the question: is the between group
variance large in comparison to the within group
variance?
Assumptions ANOVA 1. Within each group, the scores for the dependent
variable are normally distributed.
2. There are no outliers in the scores of the people
on the dependent variable.
3. The variance of the scores on the dependent
variable are the same in each group.
4. The scores of the people on the dependent
variable are mutually independent.
(2 & 4 are the most important)
Week 1: Bayes and MLR
Prior distribution The knowledge or belief about μ before we examine our
data.
Posterior A combination of the prior and the likelihood (data)
Conditional probabilities What is the probability that A will happen or is true,
given that we know B has happened or is true?
A = a hypothesis of interest
B = data we collected
P(A given B) represents the probability of our hypothesis,
given the data we observed in our study.
Definition P-value The probability of observing these (or more extreme)
data, given that the null hypothesis is true
- does not provide information about how likely it
is that the null is true given the data (only the
probability of observing the same or more
extreme data given that the null hypothesis is
true)
Confidence interval Frequentist
If we were to repeat this experiment many times and
calculate an interval each time, 95% of the intervals will
include the true parameter value (and 5% will not)
Credible interval Bayesian
There is 95% probability that the true value lies between
the interval
Bayesian probability Can provide information about this: How likely is the
null, or any other hypothesis, given the data we
observed?
- Bayesian measure the relative support for
hypotheses. Two hypotheses are compared, or
, tested against one another, using the Bayes
factor (BF)
BF12 = 10 means that the support for H1 is 10 times more than the
support for H2.
Prior model probabilities How likely is each hypothesis before seeing the data?
- Add up to 1
Assumptions about the measurement level of 1- the dependent variable is a continuous
variables in MLR: measure (interval or ratio level)
2- the independent variables are continuous or
dichotomous.
3- there are linear relationships between the
dependent variable and each of the continuous
independent variables.
4- no outliers
MLR A statistical technique used to examine the relationship
between one dependent variable (also called the
outcome variable) and two or more independent
variables (also known as predictors or explanatory
variables).
Independent variable De variabele die de onderzoeker manipuleert of
categoriseert om te zien welk effect deze heeft op iets
anders ➔ wat je verandert of selecteert als oorzaak
Dependent variable De variabele die je meet om te zien of deze beïnvloed
wordt door veranderingen in de onafhankelijke
variabelen ➔ wat je meet als mogelijk gevolg
Assumption 3 Can be checked using a scatterplot, a linear relationship
means that he scores in the scatterplot form a cloud
with an oval shape that can be described reasonably
well by a straight line.
Assumption 4 Looking at scatterplots
Assumptions multiple regression 1- Absence of outliers
2- Absence of multicollinearity
3- Homoscedasticity
4- Normally distributed residuals
1- Absence of outliers - Scatterplot for 2 variables at the time
- Histogram/boxplot for 1 variable at the time
- Standardized residuals; with this we check
whether there are outliers in the Y-space. As a
rule of thumb, it can be assumed that the
values must be between -3.3 and +3.3.
Those smaller than -3.3 or greater than +3.3,
indicate potential outliers.
- Cook’s distance; it is possible to check whether
there are outliers within the XY-space. As a rule
of thumb, we maintain that values for Cook’s
distance must be lower than 1. Values higher
than 1 indicate influential respondents
Correlation coefficent A standardized number to assess the strength of a linear
relationship.
Pearson:
- Scale between -1 and 1, 0 = no linear
relationship, 1 = maximum
- No causal relation!
Linear regression Used to make predictions about linear relations
B1 = slope, how much Y increases if X increases by 1
B0/constant/intercept = the point where the regression
line crosses the y-axis
Residual / error The difference between the true value Y and the
predicted value Y^
Least squares method Look for the line that will result in the smallest possible
sum of squared errors.
R-squared Determines the proportion of the variance of the
response variable that is ‘explained’ by the predictor
variable(s).
- Determines the ‘fit’
- Proportion between 0 and 1
Bayes factor Tells us how much more one hypothesis is supported in
comparison to another. Null-hypothesis versus an
alternative hypothesis
Construct validity The extent to which the measurement instruments
(operational definition) succeed in measuring the
concepts/constructs and thus fit the conceptual
definition. In experimental research, this is also about
the extent to which the intended manipulation
succeeded.
- About the correspondence between
operationalization and theoretical concept
Internal validity The extent to which the research method can eliminate
alternative explanations for an effect.
- About the ability to determine whether there is a
causal relationship
In principle: higher internal validity with experimental research than with qualitative or correlational
External validity The extent to which the research results can be
generalized to other groups, times and situations.
Statistical validity The extent to which the results of a statistical analysis
are accurate and well-founded
ANOVA A test for comparing 2 or more means.
T-test A test for comparing 2 means
One-sample t-test Testen of het gemiddelde van één steekproef significant
verschilt van een bekend populatiegemiddelde of een
bepaalde theoretische waarden = kijken of
steekproefgroep afwijkt van een bepaalde norm.
Two-sample t-test Testen of er een significant verschil is tussen de
gemiddelden van twee onafhankelijke steekproeven.
,Within groups variance The variance of scores within each group averaged over
= residual variance the groups.
- There is only a good representation of variation
within each of the group if there is homogeneity
of variances, meaning that the within group
variances are not too different between the
groups
Between groups variance The variation of the group means, a measure of how
= explained variance different they are
F-statistics Goal is to answer the question: is the between group
variance large in comparison to the within group
variance?
Assumptions ANOVA 1. Within each group, the scores for the dependent
variable are normally distributed.
2. There are no outliers in the scores of the people
on the dependent variable.
3. The variance of the scores on the dependent
variable are the same in each group.
4. The scores of the people on the dependent
variable are mutually independent.
(2 & 4 are the most important)
Week 1: Bayes and MLR
Prior distribution The knowledge or belief about μ before we examine our
data.
Posterior A combination of the prior and the likelihood (data)
Conditional probabilities What is the probability that A will happen or is true,
given that we know B has happened or is true?
A = a hypothesis of interest
B = data we collected
P(A given B) represents the probability of our hypothesis,
given the data we observed in our study.
Definition P-value The probability of observing these (or more extreme)
data, given that the null hypothesis is true
- does not provide information about how likely it
is that the null is true given the data (only the
probability of observing the same or more
extreme data given that the null hypothesis is
true)
Confidence interval Frequentist
If we were to repeat this experiment many times and
calculate an interval each time, 95% of the intervals will
include the true parameter value (and 5% will not)
Credible interval Bayesian
There is 95% probability that the true value lies between
the interval
Bayesian probability Can provide information about this: How likely is the
null, or any other hypothesis, given the data we
observed?
- Bayesian measure the relative support for
hypotheses. Two hypotheses are compared, or
, tested against one another, using the Bayes
factor (BF)
BF12 = 10 means that the support for H1 is 10 times more than the
support for H2.
Prior model probabilities How likely is each hypothesis before seeing the data?
- Add up to 1
Assumptions about the measurement level of 1- the dependent variable is a continuous
variables in MLR: measure (interval or ratio level)
2- the independent variables are continuous or
dichotomous.
3- there are linear relationships between the
dependent variable and each of the continuous
independent variables.
4- no outliers
MLR A statistical technique used to examine the relationship
between one dependent variable (also called the
outcome variable) and two or more independent
variables (also known as predictors or explanatory
variables).
Independent variable De variabele die de onderzoeker manipuleert of
categoriseert om te zien welk effect deze heeft op iets
anders ➔ wat je verandert of selecteert als oorzaak
Dependent variable De variabele die je meet om te zien of deze beïnvloed
wordt door veranderingen in de onafhankelijke
variabelen ➔ wat je meet als mogelijk gevolg
Assumption 3 Can be checked using a scatterplot, a linear relationship
means that he scores in the scatterplot form a cloud
with an oval shape that can be described reasonably
well by a straight line.
Assumption 4 Looking at scatterplots
Assumptions multiple regression 1- Absence of outliers
2- Absence of multicollinearity
3- Homoscedasticity
4- Normally distributed residuals
1- Absence of outliers - Scatterplot for 2 variables at the time
- Histogram/boxplot for 1 variable at the time
- Standardized residuals; with this we check
whether there are outliers in the Y-space. As a
rule of thumb, it can be assumed that the
values must be between -3.3 and +3.3.
Those smaller than -3.3 or greater than +3.3,
indicate potential outliers.
- Cook’s distance; it is possible to check whether
there are outliers within the XY-space. As a rule
of thumb, we maintain that values for Cook’s
distance must be lower than 1. Values higher
than 1 indicate influential respondents
