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Summary of Statistics for Pre-master DSS
The summary of all the covered chapters of the course
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Module 1. Relevance of statistics, research methodsWhy learn statistics and R?
- Develop your critical and analytical thinking skills
- Become an informed consumer (media, politics, etc.)
- Save money (don’t need to hire statistician)
- Effectively conduct research in terms of:
o Research design
o Data collection
o Data analysis
- To understand the state of the art for a given topic in data science/CSAI
o Nearly every empirical article you will find contains some form of statistics no matter the
topic: language, cognition, emotion, psychology, VR, robotics, etc.
Generating and testing theories
- Theory
o a hypothesized general principle or set of principles that explains known findings about the topic
and from which new hypotheses can be generated
- Hypothesis
o a prediction typically derived from theory observation
o e.g., people that have watched “a beautiful mind” have a higher IQ than those that have
not
- Falsification
o the act of disproving a theory or hypothesis.
Measurement
You have to conceptualize the question. After that you have H0 operationalize it, go to something
that can be observed.
,Scales of measurement
- Categorical scales (entities are divided into distinct categories):
• Binary variables: there are only 2 categories e.g., death or alive (can’t say one is
better than the other).
• Nominal variables: there are more than 2 categories e.g., whether someone is an
omnivore, vegetarian or vegan.
• Ordinal variable: the same as a nominal variable but the categories have a logical
order e.g., whether people got a fail, a pass, a merit or a distinction in their exam.
- Continuous scales (entities get a distinct score):
• Interval variable: equal intervals on the variable represent equal differences in the
property being measured (e.g., the difference between 6 and 8 is equivalent to the
difference between 13 and 15)
• Ratio variable: the same as an interval variable, but the ratios of the scores on the
scale must also make sense and have true zero scales (e.g., a score of 16 on an
anxiety scale means that the person is, in reality twice as anxious as someone
scoring 8. Temperature is not ratio because 0 degrees does not mean temperature
(there is no 0 temperature).
Examples:
Temperature in degrees Celsius: interval scale. The numerical value is genuinely meaningful. The
differences between the numbers are interpretable, but the variable does not have a “natural” zero
value.
Gender: nominal scale. It serves as “labels” only to identify an object. It usually deals with
nonnumeric variables where numbers have no value (e.g., averaging “male = 1” and “female = 2”
does not make any sense).
The order that runners cross the finish line in a marathon race: Ordinal scale. An ordinal scale
variable can be used to identify a natural, meaningful way to order the different possibilities, but you
cannot do anything else (e.g., you can say that the person who finished first was faster than the
person who finished second, but you cannot say that how much faster the first person was).
The amount of time bob took to solve a calculus problem: Ratio scale. The numerical value is
genuinely meaningful. The differences between the numbers are interpretable, and zero really means
zero; therefore, it is fine to multiply and divide the values.
Reliability of measures
- Reliability: the ability of the measure to produces the same results under the same
conditions (consistency).
- Test-retest reliability: the ability of a measure to produce consistent results when the same
entities are tested at two different points in time.
- Inter-rater reliability: consistency across people. Do they produce the same answer?
- Parallel forms reliability: do different measures that are supposed to measure the same
thing actually measure it the same? (two different eye trackers)
- Internal consistency reliability: do things that are supposed to measure the same thing
actually measure it? (multiple question measuring IQ)
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,Example
Inter-rater reliability: Tom and Edith are two judges measuring 50 speed skaters’ time in a short track
speed skating competition. If the results of the two judges were very similar, the results showed an
excellent inter-rater reliability
Test-retest reliability: Sue is a clinical psychologist and uses the Beck Depression Inventory (BDI) to
measure her client’s level of depression. If the scores of the BDI are consistent over multiple
occasions, the BDI has test-retest reliability
Internal consistency reliability: The following two items show good internal consistency reliability to
measure the level of satisfaction with life: “In most ways my life is close to my ideal” and “I am
satisfied with my life.” However, if the following item were part of the same measure, “I can control
my facial expressions”, it would have low internal consistency reliability to measure satisfaction with
life.
Parallel forms reliability: An experimenter developed a large set of word memory questions (i.e., list
of words). He split these questions into half, and administered them to a randomly selected half of a
target sample. If the results of the two sets of questions show a high correlation, this would be one
indicator that the tests have a good parallel forms reliability.
Some variable terminology
Common types of research
- Correlational research: observing what naturally goes on in the world, without directly
interfering with it.
- Cross-sectional research: data come from people at different age points, with different
people representing each age point. Could be quasi-experimental, case study, naturalistic
observations.
- Experimental research: one or more variable is systematically manipulated to see the effect
(alone or in combination) on an outcome variable; randomization (random assignment,
random sampling; statements can often be made out of cause and effect, but.
Must be careful for:
• Confounds = an unmeasured variable that could be related to the variables of the
interest.
• Artefacts = something that might threaten the external validity or construct validity
of your results (movement noise in an EEG signal
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, Types of validity
- Internal validity: the extent to which you are able to draw the correct conclusions about the
causal relationship between variables.
- External validity: the generalizability of you findings. To what extend do you expect to see
the same pattern of results in “real life” as you saw in your study.
- Construct validity: whether your actually measuring what you want to be measuring.
- Face validity: whether or not a measure “looks like” it’s doing what it’s supposed to.
- Ecological validity: the entire set up of the study should closely approximate the real world
scenario that’s being investigated (you cannot put an deathly experiment on people).
Example
Case(fictional) A researcher in psychology is conducting an experimental study about the effect of a
new type of cognitive behavioral therapy to treat depression among young Dutch women between
20-25 years old.
External validity: The extent to which we can generalize the results of this study to the real
population, namely young Dutch women between 20-25 years old with depression issues. When for
example just using undergraduate psychology students with small mental issues as the participants,
your sample has a high risk of not representative of the population. This experiment will carry a risk
of lacking external validity.
Internal validity: The extent to which we can draw the correct conclusions about the causal
relationship between the variables in the study. In this case we would like to study the causal
relationship between therapy and a change in depression levels among our population. We could
find a statistical significant result, due to certain correlation levels. However, a change in state of
depression could also be caused by other (confounding) variables, such as longer sleeping hours,
lower stress in daily life and new social relationships. These variables should be controlled for to
justify internal validity.
Construct validity: Construct validity is to show that the test is actually measuring what you want to
be measuring. If you are trying to examine the effect of cognitive therapy on depression, the research
should have the tools and the methods in order to somehow measure the concept of “depression”.
Ecological validity: The entire set up of the study should closely approximate the real world scenario
that is being investigated. In the above mentioned case, this should mean that the therapy session
that is considered to be the independent variable, should approximate “real world” therapy sessions.
This also applies to the environment where the participants are questioned about the change in
depression levels.
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