Behavioural Surveillance Surveys - The Wisdom of Whores

A glance at this table suggests that older
men were far more likely than younger men
to have no non-regular partners in the last
12 months, while younger men were more
likely than older men to have two or more
non-regular partners in that time frame.
However, we also note that there are far more
older men than younger men in the total
sample, and indeed only a handful of the total
sample (31 out of 562) are in the youngest age
category of teenagers. The way to determine
whether there is a statistically significant
relationship between age (the explanatory
variable) and non-regular sexual partnerships
(the outcome variable) is to calculate a χ 2 value.
The χ 2 value for this particular example is 40.8,
with a p-value of less than 0.001. We can
therefore conclude that age is significantly
related to number of sexual partners in this
population.
Tests for trend within bivariate analysis
If one variable in bivariate analysis is a
variable that can be divided into ordered
categories (such as the age categories in the
example above), and the other variable has
two possible values, it is possible to use a
χ 2 test for trend.
For example, if the category of numbers
of non-regular partners in the above example
were collapsed from four to just two (e.g. zero
vs. one or more), it would be possible to
determine if having more partners were
significantly associated with falling age.
The formula for this type of trend analysis
is found in all basic statistical textbooks.
In BSS, the most common test for trend is a
test for trends over time. The formula can be
found in any standard statistics textbook.
Bivariate analysis with binary variables:
a quick formula
When each of the variables in a bivariate
analysis is a binary variable with just two values
(for example male or female, or condom use
yes/no), then a quick formula can be used
in calculating the Chi-square distribution.
The variables are set up into a table as below,
this version of the table is known as a
“two by two table”. The table will look like this:
A B E
C D F
Column totals G H N
Row totals
The quick calculation formula for this type
of table is:
χ 2 = (AD - BC) 2 *N
EFGH
Once the chi-square statistic has been
calculated, the p-value can be found in a
chi-square table of any standard statistics
textbook and also contained in Appendix 5.
With two by two tables, the total number of
respondents (i.e. N) should be greater than 40.
The method is also valid if the number of
respondents lies between 20 and 40 and no
single expected value is less than 5.
B EHAV I OR A L S U R V EI L L A NC E SURV EY S CHAPTER 7
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