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Summary INTUITIVE SCIENTIST for Statistics 1 (Radboud University Nijmegen)
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This document covers a summary of the intuitive scientist literature relevant for the course Statistics 1.
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The intuitive scientistIntroduction:
-Kahneman and Tversky provided evidence for the view that people often trust heuristics (rules of
thumb) when assessing probabilities.
-Representativeness heuristic; availability heuristic; anchoring heuristic.
-Subject of the chapter lies at the interface of psychology and statistics.
1. Explain the limitations of everyday thought processes, using examples.
2. Describe empirical studies that proved the existence of these limitations.
3. Predict how these limitations will manifest themselves in everyday situations that are set out
in a given text.
Insensitivity to sample size→
-The mean of a large sample is usually much closer to the population mean than the mean of a small
sample.
-In the first instance, they put too much emphasis on the results of a small sample. In the second,
they are not sufficiently influenced by the results from a large sample.
-So, you can say that the sample mean becomes more reliable (as an estimate of the population
mean) if the sample increases in size.
-Square Root N Law: If you have a sample with N = 3, and I have a sample with N = 300, then my
sample mean is Wurzel aus 100 = 10 times as reliable.
-If N increases (as you go to the right in the figure), the sample mean approaches the population
mean more closely.
Limitations in intuitive thinking with sample size→
-People give too much weight to small samples and too little to large samples.
-One consequence of the Law of Large Numbers is that you should weigh the outcomes of large
samples more heavily (i.e., take them more seriously) than the outcomes of small samples.
-People are often influenced more by an extremely small rather than a large sample, because the
information from small samples is often presented in a more vivid way. A researcher with a large
sample is compelled by its mere size to present the information as statistics, like means and
percentages→boring.
-Fallacy→conscious process and attention error→unconscious.
Research studies into insensitivity to sample size→
Not fully informed: (Kahneman and Tversky 1972)
People not aware of the Law of Large Numbers→
Two hospitals were described to the subjects, one large and one small. On average 45 babies were
born per day in the large hospital, and an average of 15 per day in the small hospital. The question
was which hospital would have the most days on which 60% or more boys were born. Most of the
subjects thought that this would be equally probable for both hospitals. Among the remaining
subjects, the large hospital and the small hospital were chosen equally often. Subjects who had
followed a statistics course in general no longer made this error.
Vivid information: (Borgida and Nisbett 1977)
People can be influenced by small amounts of vivid information. Students selecting courses→It
turned out that they were influenced to a greater extent by the personal recommendations than by
the abstract means. But the means were based on a much larger sample.
, Everyday life: examples of insensitivity to sample size→
What happens if people have both types of knowledge: a small sample of vivid information,
comprising of personal experiences or nice stories, and a large sample of information presented in a
boring way, with lists and tables. The rational choice would be to base the decision on the large
sample, but the actual choice is usually that one bases one’s decision on the vivid information.
The interview illusion: (Nisbett and Ross 1980)
In interviews often more weight is given to the one hour interview than to report figures and written
recommendations, eventhough the latter sources are based on more information→Law of Large
Numbers is ignored.
Anecdotes:
For example, the anecdote about Uncle Charles who smoked like a chimney but lived to be 91 –
which is then used as a serious counterweight to dozens of research projects involving tens of
thousands of people.
Initial impressions:
Is very important eventhough it is based on very small sample of behavior. People are disinclined to
change their judgement when the sample gets a bit larger and the new information should actually
compel one to a different conclusion.
Rapid judgement: (Ambady and Rosenthal 1993)
The lecturers who were found likeable after two seconds were also considered good lecturers after a
full semester´s course→early judgement already passed.
Insensitivity to sample bias→
-Many samples that you encounter in everyday life are not random. Often all sorts of factors lead to
a particular selection, with the result that the sample is no longer representative, even if it is very
large. People usually pay too little attention to this in their intuitive assessments.
-A representative sample is a sample that is approximately equivalent to the population in its most
important characteristics (for example the mean). A biased sample deviates from the population on
important characteristics.
-Modern statistics is based on the principle that a sample should be randomly drawn and large; in
that case it will be probably approximately representative according to the Law of Large Numbers.
-If the method of selection is biased, taking a larger sample does not help: the mean will continue to
show the wrong value.
-With the unbiased samples, some of the sample means are below the correct value and others are
above it. So they are around the dotted line, and as N increases, they approach the dotted line more
closely. In the biased samples, the sample means are predominantly too small. They lie below the
dotted line, and as N increases, this error becomes more stable.
-You should prefer a small but unbiased sample to a large biased sample!!
Limitations in intuitive thinking with sample bias→
People in their intuitive everyday judgements pay too little heed to sample bias.
Insensitivity to sample bias means that the bias is not recognised, and that a conclusion is drawn as if
the sample is unbiased. In the example, this means that Xavier will simply conclude that he is more
likeable than Dr. Mean.
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