X- INDEPENDENT VARIABLE
Y- DEPENDENT VARIABLE
Mean square in ANOVA -> Sum of squares/df
T -value -> Unstandardized B/Standard error
Explained variance in the model -> SSm/SSt (SSm is the regression and SSt is the total)
Internal validity -> The degree of confidence that the causal relationship being tested is
trustworthy and not influenced by other factors.
External validity -> The extent to which results from a study can be applied to other situations.
Moderating variable M -> A moderating variable, also called a moderator variable or simply M,
changes the strength or direction of an effect between two variables x and y. In other words, it
affects the relationship between the independent variable or predictor variable and a dependent
variable or criterion variable. Moderating variables can be qualitative (non-numerical values like
race, socioeconomic class or sex) or quantitative (numerical values like weight, reward level or
age).
Mediating variable -> Mediation is a little more straightforward in its naming convention. A
mediator mediates the relationship between the independent and dependent variables –
explaining the reason for such a relationship to exist. Another way to think about a mediator
variable is that it carries an effect. In a perfect mediation, an independent variable leads to some
kind of change to the mediator variable, which then leads to a change in the dependent variable.
However, in practice, the relationships between the independent variable, mediator, and
dependent variable are not tested for causality, just a correlational relationship.
Moderating and Mediating Variables -> Another way to think about this issue is that a
moderator variable is one that influences the strength of a relationship between two other
variables, and a mediator variable is one that explains the relationship between the two other
variables.
- Variance -> N - 1
- Square root of variance = standard deviation
Covariance
- Measures of relationship between 2 variables: covariance and correlation. The
relationship can be: positive, negative or absent.
- Multiply the 2 deviation score (e.g. adverts watched and packets bought) ->
cross-product deviations.
- Covariance = add the cross-product deviations and divide by N - 1
- Covariance -> The extent to which deviations of one variable go hand in hand with
deviations of another variable.
- Disadvantage of covariance: if you use other units, the size of the covariance also
changes. We can’t use it as a measure of the strength of the relationship between 2
variables. That’s why we use correlation.
Correlation
- Relation between 2 variables.
- To get a measure of the strength of the correlation between 2 variables, we convert the
covariance into standard units (standardization).
- Standard units = standard deviations
, - If we divide each deviation from the mean by the SD, we get the distance to the mean in
standard deviations. In other words, we express the distance to the average in standard
deviations = units of SD.
- In other words we use z-scores -> Z = x - xbar/ S
- The correlation coefficient does not have a causal direction.
- The correlation coefficient is used as an indicator of the strength of an effect (effect size).
- The square of the correlation coef. (R-squared) is a measure of how much variance in
one variable is explained by the other.
WEEK 1
CAUSAL MODEL OF A SPURIOUS RELATION 1 (LECTURE)
Explanatory research: Causal Relations
- Explanatory research aims to argue if we can consider a causal relationship between
social phenomena X and Y assumed by theory is empirically tenable.
- We do this by testing the hypothesis on X -> in a critical way.
Step 1: Do you have logical arguments for the assumption that X is the cause of Y (X -> Y), and
not the other way around (Y -> X)?
- Is there a reasonable (theoretical) argument why X is the cause of Y and not the other
way around?
- Does X precede Y in time?
- Is Y changeable and X immutable (gender income)?
- Causal assumptions are not proof of causality, the point is whether it is logical to expect
that X can be the cause of Y and probably not the other way around.
Step 2: Have confounding variables been taken into account?
- If there are variables C that affect BOTH X and Y then part of the relationship between X
and Y is spurious.
- C is a confounding variable that needs to be controlled in order to draw conclusions on
the causal relation between X and Y.
,Correlation is not the same as causation
- Correlation -> Changes in one variable are related to changes in the other.
- Causation -> Changes in one variable cause changes in the other.
- With causation, you make very strong claims, so you have to be able to justify that well.
You do this by taking into account confounding variables.
CAUSAL MODEL - MEDIATION (LECTURE)
Explanatory research: Causal relations
- Once you have argued that a relationship is logically in this direction and when you have
taken into account confounding variables you can ask the question: How does X affect
Y? Via which mechanism?
Causal model of mediation
- Does X affect Y via an indirect relation, through mediator M?
- In the case of an indirect relationship, the causal influence is via an mediating variable M
(mediator), which lies between cause X and effect Y in time and causal order.
- If there is a causal relation (confounding variables taken into account) X -> Y (c), part of
this relation may go indirectly through M, which explains the relation between X and Y
partly. As a consequence the causal relation is split up in a direct part (c’) and an indirect
part (a * b), via M.
Statistical controls
- In models of spurious relations and in mediation models a third variable is taken into
account.
- Taking into account a third variable is similar to controlling, holding constant or
eliminating a third variable.
- This can be done via partial correlation (primitive method) or multivariate analysis (more
advanced method).
Holding constant confounding variable C
- Keeping C constant comes down to calculating the relation X -> Y for different values of
C, so if C is a dichotomous variable:
, C=0 C=1
- If the relationship between X and Y disappears, it is a spurious relation.
Holding constant mediating variable M
- Keeping M constant comes down to calculating the relation X -> Y for different values of
M, so if M is a dichotomous variable:
M=0 M=1
- If the relationship between X and Y disappears, it is mediated by M.
Holding constant variable that is not related to X
- Keeping X2 constant comes down to calculating the relation X -> Y for different values of
X2, so if X2 is a dichotomous variable:
X2 = 0 X2 = 1
- The relationship between X and Y will not change because there is no relation between
X1 and X2.
PARTIAL CORRELATION (LECTURE)
Statistical control: Partial and Semi- partial correlation
- The partial correlation and semi-partial correlation are ways to keep a third variable
constant.
- When you are interested in the correlation between X and Y through the partial
correlation you keep a third variable Z constant.
Y- DEPENDENT VARIABLE
Mean square in ANOVA -> Sum of squares/df
T -value -> Unstandardized B/Standard error
Explained variance in the model -> SSm/SSt (SSm is the regression and SSt is the total)
Internal validity -> The degree of confidence that the causal relationship being tested is
trustworthy and not influenced by other factors.
External validity -> The extent to which results from a study can be applied to other situations.
Moderating variable M -> A moderating variable, also called a moderator variable or simply M,
changes the strength or direction of an effect between two variables x and y. In other words, it
affects the relationship between the independent variable or predictor variable and a dependent
variable or criterion variable. Moderating variables can be qualitative (non-numerical values like
race, socioeconomic class or sex) or quantitative (numerical values like weight, reward level or
age).
Mediating variable -> Mediation is a little more straightforward in its naming convention. A
mediator mediates the relationship between the independent and dependent variables –
explaining the reason for such a relationship to exist. Another way to think about a mediator
variable is that it carries an effect. In a perfect mediation, an independent variable leads to some
kind of change to the mediator variable, which then leads to a change in the dependent variable.
However, in practice, the relationships between the independent variable, mediator, and
dependent variable are not tested for causality, just a correlational relationship.
Moderating and Mediating Variables -> Another way to think about this issue is that a
moderator variable is one that influences the strength of a relationship between two other
variables, and a mediator variable is one that explains the relationship between the two other
variables.
- Variance -> N - 1
- Square root of variance = standard deviation
Covariance
- Measures of relationship between 2 variables: covariance and correlation. The
relationship can be: positive, negative or absent.
- Multiply the 2 deviation score (e.g. adverts watched and packets bought) ->
cross-product deviations.
- Covariance = add the cross-product deviations and divide by N - 1
- Covariance -> The extent to which deviations of one variable go hand in hand with
deviations of another variable.
- Disadvantage of covariance: if you use other units, the size of the covariance also
changes. We can’t use it as a measure of the strength of the relationship between 2
variables. That’s why we use correlation.
Correlation
- Relation between 2 variables.
- To get a measure of the strength of the correlation between 2 variables, we convert the
covariance into standard units (standardization).
- Standard units = standard deviations
, - If we divide each deviation from the mean by the SD, we get the distance to the mean in
standard deviations. In other words, we express the distance to the average in standard
deviations = units of SD.
- In other words we use z-scores -> Z = x - xbar/ S
- The correlation coefficient does not have a causal direction.
- The correlation coefficient is used as an indicator of the strength of an effect (effect size).
- The square of the correlation coef. (R-squared) is a measure of how much variance in
one variable is explained by the other.
WEEK 1
CAUSAL MODEL OF A SPURIOUS RELATION 1 (LECTURE)
Explanatory research: Causal Relations
- Explanatory research aims to argue if we can consider a causal relationship between
social phenomena X and Y assumed by theory is empirically tenable.
- We do this by testing the hypothesis on X -> in a critical way.
Step 1: Do you have logical arguments for the assumption that X is the cause of Y (X -> Y), and
not the other way around (Y -> X)?
- Is there a reasonable (theoretical) argument why X is the cause of Y and not the other
way around?
- Does X precede Y in time?
- Is Y changeable and X immutable (gender income)?
- Causal assumptions are not proof of causality, the point is whether it is logical to expect
that X can be the cause of Y and probably not the other way around.
Step 2: Have confounding variables been taken into account?
- If there are variables C that affect BOTH X and Y then part of the relationship between X
and Y is spurious.
- C is a confounding variable that needs to be controlled in order to draw conclusions on
the causal relation between X and Y.
,Correlation is not the same as causation
- Correlation -> Changes in one variable are related to changes in the other.
- Causation -> Changes in one variable cause changes in the other.
- With causation, you make very strong claims, so you have to be able to justify that well.
You do this by taking into account confounding variables.
CAUSAL MODEL - MEDIATION (LECTURE)
Explanatory research: Causal relations
- Once you have argued that a relationship is logically in this direction and when you have
taken into account confounding variables you can ask the question: How does X affect
Y? Via which mechanism?
Causal model of mediation
- Does X affect Y via an indirect relation, through mediator M?
- In the case of an indirect relationship, the causal influence is via an mediating variable M
(mediator), which lies between cause X and effect Y in time and causal order.
- If there is a causal relation (confounding variables taken into account) X -> Y (c), part of
this relation may go indirectly through M, which explains the relation between X and Y
partly. As a consequence the causal relation is split up in a direct part (c’) and an indirect
part (a * b), via M.
Statistical controls
- In models of spurious relations and in mediation models a third variable is taken into
account.
- Taking into account a third variable is similar to controlling, holding constant or
eliminating a third variable.
- This can be done via partial correlation (primitive method) or multivariate analysis (more
advanced method).
Holding constant confounding variable C
- Keeping C constant comes down to calculating the relation X -> Y for different values of
C, so if C is a dichotomous variable:
, C=0 C=1
- If the relationship between X and Y disappears, it is a spurious relation.
Holding constant mediating variable M
- Keeping M constant comes down to calculating the relation X -> Y for different values of
M, so if M is a dichotomous variable:
M=0 M=1
- If the relationship between X and Y disappears, it is mediated by M.
Holding constant variable that is not related to X
- Keeping X2 constant comes down to calculating the relation X -> Y for different values of
X2, so if X2 is a dichotomous variable:
X2 = 0 X2 = 1
- The relationship between X and Y will not change because there is no relation between
X1 and X2.
PARTIAL CORRELATION (LECTURE)
Statistical control: Partial and Semi- partial correlation
- The partial correlation and semi-partial correlation are ways to keep a third variable
constant.
- When you are interested in the correlation between X and Y through the partial
correlation you keep a third variable Z constant.
