Exam Guide for Applied Multivariate Data Analysis – Get yourself a Wonderful Grade!
Summary of Statistics (IBC), Radboud University
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Erasmus Universiteit Rotterdam (EUR)
Liberal Arts And Sciences
Intermediate Statistics I
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1.5.5.2 Two types of variation
Unsystematic variation -> Variation resulting from random factors that exist between the
experimental conditions (such as natural differences in ability, the time of the day, etc.).
Systematic variation -> Variation due to the experimenter doing something in one condition but not
in the other condition.
In a repeated-measures design, differences between two conditions can be caused by only two
things: (1) the manipulation that was carried out on the participants, or (2) any other factors that
might affect the way in which an entity performs from one time to the next (likely to be fairly minor
compared to the influence of the experimental manipulation) -> ‘noise’ is kept to a minimum and so
the effect of the experiment is more likely to show up -> therefore have more power to detect effect
than independent designs.
In an independent design, differences between the two conditions can also be caused by one of two
things: (1) the manipulation, or (2) differences between the characteristics of the entities allocated to
each of the groups. The latter is likely to create considerable random variation both within each
condition and between them.
1.5.6. Randomization
In both repeated-measures and independent designs it is important to try to keep the unsystematic
variation to a minimum -> more sensitive measure of the experimental manipulation. Generally,
scientists use the randomization of entities to treatment conditions to achieve this goal.
Many statistical tests work by identifying the systematic and unsystematic sources of variation and
then comparing them. This comparison allows us to see whether the experiment has generated
considerably more variation than we would have got had we just tested participants without the
experimental manipulation.
Randomization is important because it eliminates most other sources of systematic variation, which
allows us to be sure that any systematic variation between experimental conditions is due to the
manipulation of the independent variable. We can use it in two different ways, depending on
whether we have a independent or repeated-measures design:
Repeated measurement design
- The two most important sources of systematic variation:
o Practice effects: participants may perform differently in the second condition because
of familiarity with the experimental situation and/or the measures being used.
o Boredom effects: participants may perform differently in the second condition because
they are tired or bored from having completed the first condition.
- Although it is impossible to eliminate them completely, we can ensure that they produce no
systematic variation between the conditions by counterbalancing the order in which a
person participates in a condition.
- We can use randomization to determine in which order the conditions are completed.
Independent designs
- Participants in different experimental conditions will differ in many respects (IQ, attention
span, etc.). We need to make sure that these variables contribute to the unsystematic
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