Week 1: Conceptual models & Analysis of Variance
Terminology PV & OV
PV OV
- PV = Predictor variable = Independent variable
- OV = Outcome variable = Dependent variable
The predictor variable has an effect on the outcome variable.
The P-value stands for the probability of obtaining a result. This means when a P-value is low, it indicates
that the null hypothesis is unlikely. (P is low, H0 must go)
Conceptual Models
Conceptual models help to visualize your research question and provide a schematic overview of your
research. They help to build your hypothesis and to test research questions, and they also help to
determine what type of analysis is suitable.
Conceptual models are visual representations of relations between theoretical constructs (variables) of
interest. ( and typically also visualize the research question).
In research: By “model” we mean a simplified description of reality.
Measure scale of variables
Variables can be measures in different scales, such as:
- Categorical (nominal, ordinal) : Where subgroups are indicated by numbers.
- Quantitative ( discrete, interval, ratio) : Where we use numerical scales, with equal distances between
values (note: in social sciences we sometimes treat ordinal scales as (pseudo) intervals scales, e.g. Linkert
scales).
Example:
We are always interested in de cause and the effect of something, for example: a boring teacher, causes
boring children. What can be the research question? And conceptual model?
Research question: What factor determines student satisfaction?
Conceptual model:
What are the hypothesis suitable for this conceptual model and research question?
H0: Higher levels of teacher commitment do not lead to higher satisfaction levels (no relation)
H1: The more committed a teacher, the higher the satisfaction level of students.
During this course there are several types of conceptual models, those conceptual models help to choose
what type of analysis we use. We have moderation and mediation. Whereas moderation is something
that is often times investigated.
1
,Moderation, conceptual model (short intro)
An example is, what if the proposed effect is stronger in certain settings?
RQ: What is the effect of a teacher’s commitment on student satisfaction, and how is this relationship
moderated by a teacher’s communication skills?
In this case, communication skills is our moderator.
The communication skills has an effect on the effect
of commitment of teacher on student satisfaction.
Maybe the teacher has a lot of commitment but no
communication skills, therefore the students will not
be satisfied. On the other hand, if both commitment
of teacher and communication skills are positive,
most likely the students will be more satisfied.
The hypothesis are (moderation):
H0 = a Teacher’s communication skills will not influence the relationship between commitment of the
teachers and student satisfaction. (in this case, communication skills is not a moderator)
H1 = Teacher that are more committed will increase the satisfaction level of students, but only when they
have good communication skills.
Mediation, conceptual model (short intro, week 4 full)
But what if the proposed relationship “goes via” another variable?
RQ: What underlying mechanism drives the effect of teacher’s commitment on students satisfaction?
For example: quality of course material could be a
mediator. In this case the more committed the
teacher is, most likely the quality of course material
will be higher, which leads to a higher student
satisfaction. (so the effect of the PV on the mediator
on the OV)
The hypothesis are (Mediation):
H0 = The effect of teacher’s commitments on student satisfaction is not mediated by quality of the course
material.
H1 = The positive effect of teacher’s commitment on students satisfaction is mediated by quality of the
course material.
2
,ANOVA: Intuition and steps to take
ANOVA stands for: Analysis of Variance. It investigates with a certain level of (statistical) confidence,
what differences there might be between groups. It does so by comparing the variability between the
groups against the variability within the groups.
- In other words, does it matter in which group you are (which teaching method you receive) with
regard to your exam score?
ANOVA is a type of analysis to use to test main effect and if any moderating effect. These effects van be
tested by ANOVA provided that the outcome variable is quantitative and the predicted variable(s) are
categorical with two or more groups. This helps u to test your hypothesis.
Intuition Anova
Example: MRM2 students are assigned to thee subgroups, each group receives a different teaching
method. To determine which one is the best. To test which teaching method is the most effective, u can
potentially use the differences in scores on the exams between groups!
What might the distribution of exam scores of the
different groups look like?
We see different scores between the three groups. It’s
important to know that for the purple group it seems
that the teaching method is significantly better than the
other methods. ANOVA (and follow up analyses) can
investigate with a certain level of (statistical) confidence, what differences there might be between the
groups.
ANOVA does this by comparing the variability between the groups against the variability within the
groups. On other words, does it matter which group you are ( which teaching method you receive) with
regard to your exam score.
The idea of ANOVA: Analysis Of Variance:
- ANOVA statistically examines how much of the variability in our outcome variable (in the exam
results) can be explained by our predictor variable (teaching methods).
- It breaks down different measures of variability through calculating sums of squares.
- Via these calculations, ANOVA helps us to test if the mean scores of the groups are statically
different. (weather the purple group indeed has higher mean scores then the other group).
3
, We use the one-way between-subjects ANOVA when:
- Outcome Variable: (OV) = Quantitative
- Predictor Variable: (PV) = Categorical with more than 2
groups (levels)
One-way ANOVA: One predictor variable
Two-way ANOVA: Two predictor variables
Assumptions for ANOVA usage:
1. Variance is homogenous across groups. (So the variance between groups is pretty similar. So we
don’t want a high and low variance).
2. Residuals are normally distributed (Won’t be tested in MRM2)
3. Groups are roughly equally sized (In MRM2 they always are)
4. Our subjects can only be in one group ( between subjects design). A person can only receive one
teaching class.
When you do not adhere the assumptions, ANOVA can produce invalid outcomes!
Steps to use during ANOVA:
1. Data suited for ANOVA? Nature of the variables, assumptions etc.
2. Model as a whole makes sense? F-Test model, R2 (R square)
3. Which group means differ? Post hoc/ follow up tests
ANOVA: Example
RQ: Is there a relation between shopping platform and customer satisfaction?
Predictor Variable (PV) = shopping platform
(Categorical with three levels: 1. Brick- and-mortar
store. 2. Web shop. 3. Reseller)
Outcome Variable (OV) = customer satisfaction (
quantitative : score 1-50)
(Imagine that we have 10 observations…) The idea of ANOVA is to break down the total sum of squares
by a part that is explained by models and a part that is unexplained.
4
Terminology PV & OV
PV OV
- PV = Predictor variable = Independent variable
- OV = Outcome variable = Dependent variable
The predictor variable has an effect on the outcome variable.
The P-value stands for the probability of obtaining a result. This means when a P-value is low, it indicates
that the null hypothesis is unlikely. (P is low, H0 must go)
Conceptual Models
Conceptual models help to visualize your research question and provide a schematic overview of your
research. They help to build your hypothesis and to test research questions, and they also help to
determine what type of analysis is suitable.
Conceptual models are visual representations of relations between theoretical constructs (variables) of
interest. ( and typically also visualize the research question).
In research: By “model” we mean a simplified description of reality.
Measure scale of variables
Variables can be measures in different scales, such as:
- Categorical (nominal, ordinal) : Where subgroups are indicated by numbers.
- Quantitative ( discrete, interval, ratio) : Where we use numerical scales, with equal distances between
values (note: in social sciences we sometimes treat ordinal scales as (pseudo) intervals scales, e.g. Linkert
scales).
Example:
We are always interested in de cause and the effect of something, for example: a boring teacher, causes
boring children. What can be the research question? And conceptual model?
Research question: What factor determines student satisfaction?
Conceptual model:
What are the hypothesis suitable for this conceptual model and research question?
H0: Higher levels of teacher commitment do not lead to higher satisfaction levels (no relation)
H1: The more committed a teacher, the higher the satisfaction level of students.
During this course there are several types of conceptual models, those conceptual models help to choose
what type of analysis we use. We have moderation and mediation. Whereas moderation is something
that is often times investigated.
1
,Moderation, conceptual model (short intro)
An example is, what if the proposed effect is stronger in certain settings?
RQ: What is the effect of a teacher’s commitment on student satisfaction, and how is this relationship
moderated by a teacher’s communication skills?
In this case, communication skills is our moderator.
The communication skills has an effect on the effect
of commitment of teacher on student satisfaction.
Maybe the teacher has a lot of commitment but no
communication skills, therefore the students will not
be satisfied. On the other hand, if both commitment
of teacher and communication skills are positive,
most likely the students will be more satisfied.
The hypothesis are (moderation):
H0 = a Teacher’s communication skills will not influence the relationship between commitment of the
teachers and student satisfaction. (in this case, communication skills is not a moderator)
H1 = Teacher that are more committed will increase the satisfaction level of students, but only when they
have good communication skills.
Mediation, conceptual model (short intro, week 4 full)
But what if the proposed relationship “goes via” another variable?
RQ: What underlying mechanism drives the effect of teacher’s commitment on students satisfaction?
For example: quality of course material could be a
mediator. In this case the more committed the
teacher is, most likely the quality of course material
will be higher, which leads to a higher student
satisfaction. (so the effect of the PV on the mediator
on the OV)
The hypothesis are (Mediation):
H0 = The effect of teacher’s commitments on student satisfaction is not mediated by quality of the course
material.
H1 = The positive effect of teacher’s commitment on students satisfaction is mediated by quality of the
course material.
2
,ANOVA: Intuition and steps to take
ANOVA stands for: Analysis of Variance. It investigates with a certain level of (statistical) confidence,
what differences there might be between groups. It does so by comparing the variability between the
groups against the variability within the groups.
- In other words, does it matter in which group you are (which teaching method you receive) with
regard to your exam score?
ANOVA is a type of analysis to use to test main effect and if any moderating effect. These effects van be
tested by ANOVA provided that the outcome variable is quantitative and the predicted variable(s) are
categorical with two or more groups. This helps u to test your hypothesis.
Intuition Anova
Example: MRM2 students are assigned to thee subgroups, each group receives a different teaching
method. To determine which one is the best. To test which teaching method is the most effective, u can
potentially use the differences in scores on the exams between groups!
What might the distribution of exam scores of the
different groups look like?
We see different scores between the three groups. It’s
important to know that for the purple group it seems
that the teaching method is significantly better than the
other methods. ANOVA (and follow up analyses) can
investigate with a certain level of (statistical) confidence, what differences there might be between the
groups.
ANOVA does this by comparing the variability between the groups against the variability within the
groups. On other words, does it matter which group you are ( which teaching method you receive) with
regard to your exam score.
The idea of ANOVA: Analysis Of Variance:
- ANOVA statistically examines how much of the variability in our outcome variable (in the exam
results) can be explained by our predictor variable (teaching methods).
- It breaks down different measures of variability through calculating sums of squares.
- Via these calculations, ANOVA helps us to test if the mean scores of the groups are statically
different. (weather the purple group indeed has higher mean scores then the other group).
3
, We use the one-way between-subjects ANOVA when:
- Outcome Variable: (OV) = Quantitative
- Predictor Variable: (PV) = Categorical with more than 2
groups (levels)
One-way ANOVA: One predictor variable
Two-way ANOVA: Two predictor variables
Assumptions for ANOVA usage:
1. Variance is homogenous across groups. (So the variance between groups is pretty similar. So we
don’t want a high and low variance).
2. Residuals are normally distributed (Won’t be tested in MRM2)
3. Groups are roughly equally sized (In MRM2 they always are)
4. Our subjects can only be in one group ( between subjects design). A person can only receive one
teaching class.
When you do not adhere the assumptions, ANOVA can produce invalid outcomes!
Steps to use during ANOVA:
1. Data suited for ANOVA? Nature of the variables, assumptions etc.
2. Model as a whole makes sense? F-Test model, R2 (R square)
3. Which group means differ? Post hoc/ follow up tests
ANOVA: Example
RQ: Is there a relation between shopping platform and customer satisfaction?
Predictor Variable (PV) = shopping platform
(Categorical with three levels: 1. Brick- and-mortar
store. 2. Web shop. 3. Reseller)
Outcome Variable (OV) = customer satisfaction (
quantitative : score 1-50)
(Imagine that we have 10 observations…) The idea of ANOVA is to break down the total sum of squares
by a part that is explained by models and a part that is unexplained.
4
