PSYC 180 Lucy Luo
How to Lie with Statistics
The Sample with the Build-in Bias
The sampling procedure: take a sample out of a big group and assume proportions from
that sample will be the same all through the group. If the sample is large enough and
selected properly, it will represent the whole well enough. If it is not, it may be far less
accurate than an intelligent guess.
One breed of sampling study, called market research, suggests that the assumption that
people sampled are telling the truth about their habits should not be taken at all.
The result of a sampling study is no better than the sample it is based on. By the time the
data have been filtered through layers of statistical manipulation and reduced to a
decimal-pointed average, the result begins to take on an aura of conviction that a closer
look at the sampling would deny.
To be worth much, a report based on sampling must use a representative sample, which is
one from which every source of bias has been removed.
The basic sample is the “random sample” – it is selected by pure chance from a
“universe” – the whole of which the sample is a part. Does every name or thing in the
whole group have an equal chance to be in the sample? But difficult and expensive. A
more economical substitute is the stratified random sampling – divide your universe into
several groups in proportion to their known prevalence.
The Well-Chosen Average
Average could be mean, median or mode.
Mean: add everything and divide it by the number there are of something.
Median: half have more and half have less
Mode: the most frequently met-with figure in a series.
Normal distribution: the mean, median and mode fall at the same point.
The median tells more about a situation than any other single figure does.
The Little Figures That Are Not There
The statistically inadequate sample: small number of subjects.
By operation of chance, the results will be what the experimenters want.
With a large group any difference produced by chance is likely to be a small one and
unworthy of big type. PSYC 180 Lucy Luo
How many is enough? It depends on how large and how varied a population you are
studying by sampling among other things.
Sometimes the number in the sample is not what it appears to be.
If the source of your information gives you also the degree of significance, it would be
better – it is the probability that the figures have a specified degree of precision. (one
figure that is not there)
Another figure that is not there is the one that tells the range of things or their deviation
from the average that is given.
Confusing “normal” with “desirable” is not good.
Place little faith in an average or a graph or a trend when numbers are missing on the axes
and the little figures are not there.
Much Ado about Practically Nothing
The IQ is a figure with a statistical error, like any other produce of the sampling method.
How accurately your sample can be taken to represent the whole field is a measure that
can be represented in figure: the probably error and the standard error.
Probable error: you decide your error from a few samples of error made by you (take the
average of error – say you had half overestimation and half underestimation) and then use
that error for future samples.
Most statisticians prefer to use another, but comparable, measurement called the standard
error. It takes in about 2/3 of the cases instead of exactly half and is considerably handier
in a mathematical way.
Comparisons between figures with small differences are meaningless. You must keep the
small probable error in mind.
The Gee-Whiz Graph
Graphs can chop off parts of the axes and change proportions to make their data look
significant – even when they’re not!
The middle of bar charts can be cut off
The One-Dimensional Picture
A pictorial graph has a chart on which a little man represents a million men or a
moneybag represents a billion dollars. It is capable of becoming a fluent, devious, and
successful liar. PSYC 180 Lucy Luo
A bar chart is capable of deceit too – they can change their widths and lengths while
representing a single factor of which they picture 3-D objects that have volumes which
are not easy to compa