LECTURE 1: ANOVA
Interval-level variables. They assume that the distances are the same. Variables don’t have a ‘natural’
zero point. E.g. Degrees Celsius (because zero degrees is not the same as Fahrenheit)
Ratio-level variables. Data has a natural zero point. E.g. income, length, age
Continuous outcome: interval or ratio level outcomes.
Later on, logistic regression: differences in a dependent variable with only two categories (so
nominal).
Measurement level of explanatory level: specific or more general. How many explanatory variables
can we include in our model?
Complexity of associations
One-Way Between-Subjects Analysis of Variance
Important remark: we use the concepts ‘X variables’, ‘independent variables’, ‘explanatory variables’,
‘predictors’ interchangeably
1
,ANOVA deals with a very simple conceptual model. Only two variables, dependent (Y, continuous)
and independent (x, categorical).
Different measurement levels can be used:
1) Nominal level: Different categories and the numbers are used to express labels
1= male, 2= female
- Exhaustiveness: All possibilities are covered
- Mutually exclusiveness= One answer should only fit one answer category
For this measurement level the mean doesn’t say much because it is not interesting to know
(average gender, frequency can be interesting to know such as how many men where
included in the sample, but the mean does not say something)
2) Ordinal level: Different categories and the numbers are used to express labels
The numbers express an ordering between the categories
1= Low, 2= medium, 3= high
- The differences between these categories are not equal to each other
3) Scale level data: The numbers express quantity and have meaning
The differences between the groups are equal to each other
- Interval level: Does not have a natural zero point (Celsius, Fahrenheit)
- Ratio level: Does have a natural zero point (income, age)
Bivariate regression analysis
Team in which someone works(X) → Organizational Commitment (Y)
We can replicate the findings of an ANOVA with regression. Bivariate, only between two variables.
This model is important for a research paper, e.g. master thesis. A lot of independent variables,
X1X2X3. It is assumed that they are correlated ( r). So there is some association but not directional.
X1, to Y is directional.
There is an effect on salary on organizational commitment. Variable gender has a perpendicular
effect on this relationship. With regression we can investigate this interaction effect (or moderation).
This says on average there is some relation, but how this effect works will be different between men
and women.
In this model we have explanatory levels, that are categorical like gender or continuous like salary.
We can mix them.
2
,Multiple regression analysis
- This technique is most often used in the Research paper for the Master
- This research includes multiple independent variables which have an effect on Y=
dependent variable
- r indicates a correlation between variables = two sided arrows, so It means there is a
association/ correlation between variables but it does not have a particular direction
In this example Gender (X3) has a moderation effect = also called interaction effect
This means that X3 (gender) has an effect on the relationship between Salary X2 and
Organizational commitment Y
So X3 is a conditional effect: this means that X3 determines how strong the relationship
between X2 and Y is (so it could be that the relationship between salary and organizational
commitment is less strong for women than for men)
The difference is that in path analysis we have multiple dependent variables. We not only have
organizational commitment level but also salary (X2). If you look at the direction of the arrows you
will be able to identify the dependent variables. We still allow some kind of correlation. So this is an
extension between regression analysis.
Technique 3: Complexity of associations: Path analysis
This analysis can have two dependent variables (X2 and Y)
- If you look at the direction of the variables you can see which variables have an effect on
the other variables
- You see the arrows from Gender (X3) and Team in which someone works (X1) both have an
arrow with the direction to Salary (X2) So this is also a dependent variable
- The arrows of X1, X2, X3 all go to the direction of Y so this is also a dependent variable
3
, We apply this technique when we have a dependent variable that is actually only two categories.
Dependent becomes unemployed. It is not a continuous outcome, but nominal level outcome.
Multiple binary, also multiple independent variables.
Logic of ANOVA (chapter 6)
One-way between-subjects Analysis of Variance
Team in which someone works (X) → organizational commitment (Y)
Substantive hypothesis:
A person’s degree of organizational commitment (Y) depends on the team in which the person works
(X).
Question: If the hypothesis is correct, what would you expect to find with regard to differences in
average commitment between the teams? - We collected data in an organization along 3
teams, 2 scenarios with regard to the data
We are going to investigate the conceptual model. Hypotheses: does Y dependent on X?
In both teams’ the averages are the same.
Which scenario says systematic differences between the teams? Scenario 2, you can see much more
clearly the differences between the teams. They are smaller within group variance. The spread (dots
under) are smaller in scenario 2 than in 1.
4
Interval-level variables. They assume that the distances are the same. Variables don’t have a ‘natural’
zero point. E.g. Degrees Celsius (because zero degrees is not the same as Fahrenheit)
Ratio-level variables. Data has a natural zero point. E.g. income, length, age
Continuous outcome: interval or ratio level outcomes.
Later on, logistic regression: differences in a dependent variable with only two categories (so
nominal).
Measurement level of explanatory level: specific or more general. How many explanatory variables
can we include in our model?
Complexity of associations
One-Way Between-Subjects Analysis of Variance
Important remark: we use the concepts ‘X variables’, ‘independent variables’, ‘explanatory variables’,
‘predictors’ interchangeably
1
,ANOVA deals with a very simple conceptual model. Only two variables, dependent (Y, continuous)
and independent (x, categorical).
Different measurement levels can be used:
1) Nominal level: Different categories and the numbers are used to express labels
1= male, 2= female
- Exhaustiveness: All possibilities are covered
- Mutually exclusiveness= One answer should only fit one answer category
For this measurement level the mean doesn’t say much because it is not interesting to know
(average gender, frequency can be interesting to know such as how many men where
included in the sample, but the mean does not say something)
2) Ordinal level: Different categories and the numbers are used to express labels
The numbers express an ordering between the categories
1= Low, 2= medium, 3= high
- The differences between these categories are not equal to each other
3) Scale level data: The numbers express quantity and have meaning
The differences between the groups are equal to each other
- Interval level: Does not have a natural zero point (Celsius, Fahrenheit)
- Ratio level: Does have a natural zero point (income, age)
Bivariate regression analysis
Team in which someone works(X) → Organizational Commitment (Y)
We can replicate the findings of an ANOVA with regression. Bivariate, only between two variables.
This model is important for a research paper, e.g. master thesis. A lot of independent variables,
X1X2X3. It is assumed that they are correlated ( r). So there is some association but not directional.
X1, to Y is directional.
There is an effect on salary on organizational commitment. Variable gender has a perpendicular
effect on this relationship. With regression we can investigate this interaction effect (or moderation).
This says on average there is some relation, but how this effect works will be different between men
and women.
In this model we have explanatory levels, that are categorical like gender or continuous like salary.
We can mix them.
2
,Multiple regression analysis
- This technique is most often used in the Research paper for the Master
- This research includes multiple independent variables which have an effect on Y=
dependent variable
- r indicates a correlation between variables = two sided arrows, so It means there is a
association/ correlation between variables but it does not have a particular direction
In this example Gender (X3) has a moderation effect = also called interaction effect
This means that X3 (gender) has an effect on the relationship between Salary X2 and
Organizational commitment Y
So X3 is a conditional effect: this means that X3 determines how strong the relationship
between X2 and Y is (so it could be that the relationship between salary and organizational
commitment is less strong for women than for men)
The difference is that in path analysis we have multiple dependent variables. We not only have
organizational commitment level but also salary (X2). If you look at the direction of the arrows you
will be able to identify the dependent variables. We still allow some kind of correlation. So this is an
extension between regression analysis.
Technique 3: Complexity of associations: Path analysis
This analysis can have two dependent variables (X2 and Y)
- If you look at the direction of the variables you can see which variables have an effect on
the other variables
- You see the arrows from Gender (X3) and Team in which someone works (X1) both have an
arrow with the direction to Salary (X2) So this is also a dependent variable
- The arrows of X1, X2, X3 all go to the direction of Y so this is also a dependent variable
3
, We apply this technique when we have a dependent variable that is actually only two categories.
Dependent becomes unemployed. It is not a continuous outcome, but nominal level outcome.
Multiple binary, also multiple independent variables.
Logic of ANOVA (chapter 6)
One-way between-subjects Analysis of Variance
Team in which someone works (X) → organizational commitment (Y)
Substantive hypothesis:
A person’s degree of organizational commitment (Y) depends on the team in which the person works
(X).
Question: If the hypothesis is correct, what would you expect to find with regard to differences in
average commitment between the teams? - We collected data in an organization along 3
teams, 2 scenarios with regard to the data
We are going to investigate the conceptual model. Hypotheses: does Y dependent on X?
In both teams’ the averages are the same.
Which scenario says systematic differences between the teams? Scenario 2, you can see much more
clearly the differences between the teams. They are smaller within group variance. The spread (dots
under) are smaller in scenario 2 than in 1.
4
