Identify situations in which statistics can be misleading

Define "Statistics"

Statistics
include numerical facts and figures. For instance:

The largest earthquake measured 9.2 on the Richter scale.

Men are at least 10 times more likely than women to commit
murder.

One in every 8 South Africans is HIV positive.

By the year 2020, there will be 15 people aged 65 and over
for every new baby born.

The study of statistics involves math and relies upon calculations
of numbers. But it also relies heavily on how the numbers are
chosen and how the statistics are interpreted. For example,
consider the following three scenarios and the interpretations
based upon the presented statistics. You will find that the
numbers may be right, but the interpretation may be wrong. Try
to identify a major flaw with each interpretation before we
describe it.

1) A new advertisement for Ben and Jerry's ice
cream introduced in late May of last year resulted in a 30% increase
in ice cream sales for the following three months. Thus, the advertisement
was effective.

A major flaw is that ice cream consumption generally increases
in the months of June, July, and August regardless of advertisements.
This effect is called a history effect and leads people to interpret
outcomes as the result of one variable when another variable (in
this case, one having to do with the passage of time) is actually
responsible.

2) The more churches in a city, the more crime
there is. Thus, churches lead to crime.

A major flaw is that both increased churches
and increased crime rates can be explained by larger populations.
In bigger cities, there are both more churches and more crime.
This problem, which we discuss in more detail in the section on causality, refers to the third-variable problem. Namely, a third variable
can cause both situations; however, people erroneously believe
that there is a causal relationship between the two primary variables
rather than recognize that a third variable can cause both.

3) 75% more interracial marriages are occurring this year than
25 years ago. Thus, our society accepts interracial marriages.

A major flaw is that we don't have the information that we need.
What is the rate at which marriages are occurring? Suppose only
1% of marriages 25 years ago were interracial and so now 1.75%
of marriages are interracial (1.75 is 75% higher than 1). But
this latter number is hardly evidence suggesting the acceptability
of interracial marriages. In addition, the statistic provided
does not rule out the possibility that the number of interracial
marriages has seen dramatic fluctuations over the years and this
year is not the highest. Again, there is simply not enough information
to understand fully the impact of the statistics.

As a whole, these examples show that statistics
are not only facts and figures; they are something more than that.
In the broadest sense, "statistics" refers to a range
of techniques and procedures for analyzing, interpreting, displaying,
and making decisions based on data.