Quantitative Data Analysis 2 (QDA2) notes based on lectures and knowledge clips given by Roger Pruppers. The summary is 89 pages and includes all the knowledge clips and lectures covered in the course 6012B0423Y at UvA.
Week 5: Regression Complications and Mediation 47
Knowledge Clip 1: Multicollinearity 47
Knowledge Clip 2: Categorical PVs 49
Knowledge Clip 3: Moderation and Mediation in Regression 51
Lecture 4a: Categorical PVs 53
Lecture 4b: Complications in Regression 57
Week 6: Logistic Regression & Hypothesis Formulation 59
Knowledge Clip 1: Concept of Logistic Regression 59
Knowledge Clip 2: Model Fit and Model Testing 61
Lecture 5a: Logistic Regression 63
Lecture 5b: Logistic Regression 67
Week 7: Principal Components Analysis & Reliability Analysis 71
Knowledge Clip 1: Concept of PCA & Initial Checks 71
Knowledge Clip 2: Main Analysis 73
Knowledge Clip 3: Follow-up Analyses 76
Lecture 6a: Principal Components Analysis & Reliability Analysis 81
Lecture 6b: Principal Components Analysis & Reliability Analysis 81
,Quantitative Data Analysis 2
Week 1: Conceptual Models & Analysis of Variance
Knowledge Clip 1: Conceptual Models
• OV = Outcome Variable (Field)
o DV = Dependent Variable → Test variable, variable to be explained
• PV = Predictor Variable (Field)
o IV = Independent Variable → Variable that explains
• PV → OV = IV → DV
• The p-value
o stands for the Probability of obtaining a result (or test-statistic value) equal to (or ‘more
extreme’ than) what was actually observed (the result you actually got), assuming that the
null hypothesis is true
o A low p value indicates that the null hypothesis is unlikely
• Conceptual models: Visual representations of relations between theoretical constructs (and variables)
of interest
• In research: by “model” we mean a simplified description of reality
o E.g. predictor variable has an effect on a outcome variable
• Variables can have different measurement scales:
o Categorical (nominal, ordinal) – subgroups are indicated by numbers.
o Quantitative (discrete, interval, ratio) – we use numerical scales, with equal distances
between values → able to run tests on the mean
o In social sciences we often treat ordinal scales as (pseudo) interval scales, e.g. Likert scales →
running tests on them with the mean
• E.g. Research question: What factors influence student satisfaction?
▪ Commitment of teacher
▪ Course content
▪ ...
o Conceptual model:
o H1 = Teacher commitment will increase students’
satisfaction level.
• Moderation/Interaction
o What if our proposed effect is stronger in certain settings?
o H2 = The positive effect of teacher commitment on student satisfaction (H1) is strengthened
by teachers’ level of communication skills.
▪ Teacher commitment is going to have a much larger
effect on student satisfaction if it is backed up by
communication skills.
o “Communication skills” is a moderating variable → one
variable moderates (changes) the relationship between two
other variables.
• Mediation
o What if the proposed relationship “goes via” another variable?
o H3 = The positive effect of teachers’ commitment on student
satisfaction is mediated by quality of the course material
o “Course material quality” is a mediating variable → one
variable mediates the relationship between two other
variables.
• Things can get complicated…
o Conceptual models can get complicated, but the following always applies:
▪ The boxes represent variables.
▪ Arrows represent relationships between variables.
• Arrows go from predictor variables to outcome variables.
,Quantitative Data Analysis 2
▪ Hypotheses refer to specific arrows → relationships/effects/differences
• Conceptual Models and Hypotheses
o Hypotheses are developed a priori: based on theory, previous research
o So not all potential relationships need to be hypothesized
▪ Every hypothesis refers to an arrow in the conceptual model
▪ But not every potential arrow refers to a hypothesis
• (red arrows) – we don’t see any theoretical reason to hypothesize here
o We will still test the effects, but not write hypotheses about them
o A hypothesis is a verbalized expression of an expected relationship between variables (i.e. an
arrow in the conceptual model)
▪ E.g. H1: Attribution of blame to a retail brand is higher in case of a service failure
than when there is no service failure.
▪ E.g. H2: The effect of service failure on attribution (H1) is stronger for the platform
brand than the seller.
• Models/Hypotheses and Analysis
o Appropriate way to test hypotheses depends on:
▪ 1. Nature of the relationship → derived from conceptual model
• Main effects, moderation/interaction, mediation
• (total, direct, indirect effects)
• The kind of relationships established in the conceptual model are a first
indication of the kind of tests that will be run
▪ 2. Nature of the data → not all of this derived from conceptual model as such
• Number of PVs, number of OVs → can be seen in conceptual model
• But, How are variables operationalized? Measured?
• Data type PV(s), data types OV(s)?
• If there are multiple groups: number of groups? relationship between them
((in)dependent)?
▪ Once we figured out nature of relationships and nature of data:
• What is the appropriate statistical analysis to test relationships/
hypotheses?
▪ Only THEN: how do you run the test, what comes out, what does that mean, what
are the implications etc.
Knowledge Clip 2: ANOVA
• But first: flashback to QDA1: Independent Samples T-test!
• When do you use it?
o One OV = Quantitative variable
o One PV = Categorical variable
▪ Number of categories = 2
▪ Participants = Different
• Q: What would we do
if participants = same?
• But what if we had sales figures for
o The Netherlands, UK and Germany? → 3
categories
o Or the Netherlands, UK, Germany, Spain, Italy, France etc.? → 5 categories
o i.e. number of categories = 2 or >2! → use ANOVA!
• ANOVA Basics
, Quantitative Data Analysis 2
o When do we use it?
▪ OV = Quantitative → so we can run tests on the mean
▪ PV = Categorical
• Number of categories = 2 or more!
• Participants = Different
o So independent, mutually exclusive samples!
o A.k.a. Between subjects design
▪ Further assumptions
• Variance is homogenous across groups.
• Residuals are normally distributed (in this class not tested further)
• Groups are roughly equally sized – in this class they usually are.
o NOT adhering to assumptions can produce invalid outcomes!
▪ But SPSS will still let you do it...
• Concepts & Terminology
o Focus
▪ Only 1 PV → One-way ANOVA
▪ Discuss n-way/factorial ANOVA in topic 2 (next week)
▪ Q: So a 3-way ANOVA would imply...?
o NB: Distinguish between
▪ Number of categories within one (categorical) predictor variable
• E.g. PV = gender → multiple categories
▪ Number of (predictor) variables
• E.g. PV gender, PV nationality, PV education level etc.
• ANOVA & F-test
o H0 (as tested in SPSS):
▪ No difference in OV mean across the different categories in PV
• PV with multiple categories, and those categories do
not differ in terms of their OV score
o H1 :
▪ There is at least one difference in OV mean score between PV categories
o Test statistic: F-test
▪ F-distribution looks different than t-distribution
▪ F-values are looking to explain variability
• Procedures are similar to the t-test
o ANOVA decomposes total variability observed in OV (aka DV)
▪ How much is caused by differences between groups?
• (explained variation) → makes sense, variations driven by differences
between groups can be explained by the model
▪ How much is caused by differences within groups?
• (unexplained variation) → multiple observations within the same group
will still differ in terms of the OV
• Variability measures
o Variance = the average of the squared differences from the Mean (average)
▪ Indication of variability
▪ If we have two data points with scores 2 and 3, the mean score = 2.5
(2−2.5)2 +(3−2.5)2
• Hence the variance = = 0.25
2
o Sum of squares = the sum of the squared differences from the Mean (average
o Q: Why do we use squared deviations for Variance?
• Sums of Squares
o Total Sum of Squares =
▪ Squared deviations from grand overall mean
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