Summary Premaster FALL: Causal Analysis Techniques

Causal analysis techniques (CAT)
Course goals
- To define key concepts which are relevant for using the techniques included in the obligatory
course materials (knowledge)

- To summarize the assumptions of the statistical techniques that are discussed in the course and
evaluate to what extent such assumptions have been fulfilled in a specific empirical application
(knowledge, evaluation).

- To explain how variance in observed scores in a One-Way Between-Subjects ANOVA and an OLS
or logistic regression analysis is dissected in a systematic and error component (comprehension)

- To, using SPSS, independently execute relevant data-manipulations (for examples, construct
dummy variables and interaction terms) and subsequently execute a data-analysis correctly (i.e.,
estimate (partial) correlations, execute a One-Way Between-Subjects ANOVA, execute a
sequential multiple OLS regression with dummy variables or interaction terms, estimate a path
model, and execute a sequential logistic regression analysis (application)

- To correctly interpret the SPSS output of such analyses (interpretation of model coefficients and
tests) and, if necessary, independently compute relevant statistics – for example, a total causal
effect in a path model (application, evaluation).

- To correctly apply the logic of the elaboration model to the results of a partial correlation
analysis or a sequential multiple OLS regression analysis and evaluate the type of association
between variables (evaluation)

The stati sti cal methods of this course
 One-Way Between-Subjects Analysis of Variance (ANOVA)
 Pearson’s (Partial) Correlation Coefficient
 Bivariate Regression
 Multiple Regression
 Elaboration Logic
 Path Analysis
 Logistic Regression Analysis

Choosing a method: Measurement level & number of variables




1

,LECTURE 1&2: ANOVA – ONE WAY BETWEEN SUBJECTS ANALYSIS OF VARIANCE
- In which situation ANOVA is applicable / When to use ANOVA
- What hypotheses can be tested with ANOVA
- The key logic behind ANOVA
- How to calculate the deviations from the mean(s)

LOGIC OF ANOVA
Hypothesis: A person’s degree of organizational commitment (Y) depends on the team in which the
person works (X)




When to use ANOVA?
 The dependent variable  We want to explain some of organization commitment (Y)
 The independent variable  The team in which someone works in (X)
*Team is categorical: you cannot necessarily put them in an order, and we assume there are more
than 2 teams.

 When in every team the commitment would be the same the average would be the same and it
doesn’t matter in which team you are.

Example from the hypothesis:

Is there a difference? Yes, we see a difference in
variance. We want to know this because it is
important to know if there is a difference in
means.

The average is the same in both scenarios.
Between the teams, there is a difference in
average.

Variance = a measure of variability

Better view from a visualization that there is significant
difference:




Key idea of ANOVA
ANOVA: ‘When there are 2 or more groups, can we make a statement about possible -significant-
differences between the mean scores of the groups?’

Intermezzo: ‘What could we do if there were only 2 groups?  T-test

ANOVA is the same as t-test but for many groups.




2

,Between and within groups
Between-group variance = about the group means
Within-group variance = all other variables that influences Y




Example:
 The between-group variance is the same because the average is the same (left)
 The within-group variance is different (right)




Important to realize:
 Any differences within a group cannot be due to differences between the groups because
everyone in a particular group has the same group score; so, within-group differences must be
due to systematic unmeasured factors (e.g., individual differences) or random measurement
error
 Any observed differences between groups are probably not only pure between-group
differences, but also differences due to systematic unmeasured factors or random measurement
error




Statistical null hypothesis of ANOVA:
Mean scores of k populations corresponding to the groups in the study are all equal to each other:

H0 = 1 = 2 = … = k

Reject H0 when at least one mean is significantly different from the other means.




3

, CALCULATIONS
F-statistic / F-distribution: In order to determine if a specific sample result is exceptional
(‘significant’) under the assumption that the statistical null hypothesis is correct, the test-statistic F
has to be calculated.

Strategy: Partition of scores into components
 Component of score that is associated with ‘group’
 Component of score that is not associated with ‘group’

Calculate the deviations scores:
1. Deviation of individual score from grand mean: Yij – My
2. Deviation of individual score from group mean: (Y ij – Mi) = ij
3. Deviation of group mean from grand mean: (Mi – My) α i
αi denotes the ‘effect of group i’




Example:


Calculating the grand mean




Calculating the differences within the
group and the group mean (within-
group)




Calculating the differences between
the group mean and the grand mean




But…




4