Behavioural Surveillance Surveys - The Wisdom of Whores

EXAMPLE : CALCULATING THE CHI-SQUARE STATISTIC BY HAND
The following illustrates a step-by-step process of calculating the chi-square statistic : Set up the
explanatory variable in columns, and the outcome variable in rows. Then calculate the row and
the column totals. Next, calculate the expected number of observations for each cell if there
were no difference in distribution according to the explanatory variable (i.e., if the null
hypothesis were true). Do this as follows :
Table of observed numbers
The expected number = row total * column total
overall total N
Chi-square is calculated by comparing the numbers actually observed with those expected
if there were no difference in distribution according to the explanatory variable. For every cell of
the table, calculate the difference between the expected and observed values (and square it to get
rid of any negatives) and then divide it by the expected value. Now add together the result of that
calculation for every cell of the table. The result is the chi-square value. In other words
χ 2 = SUM (observed - expected) 2
expected
Once the χ 2 value has been calculated, it can be compared with the Chi-square Table to determine
whether there is indeed a statistically significant association between the explanatory and the
outcome variables. Notice that the table uses the term degrees of freedom. The statistical
significance of χ 2 depends on how many categories there are in both the explanatory and the
outcome variables. The degrees of freedom (DF) can be calculated easily by looking at the table
laying out the variables, as follows :
DF = (number of rows - 1) * (number of columns - 1)
The steps below refer to the example provided in Chapter 7 of the analysis of the number of
non-regular sex partners by age group.
Step 1 : Set up the explanatory variable in columns, and the outcome variable in rows. Then
calculate the row and the column totals.
0 1 2 3+ Totals
< 20 years 12 4 6 9 31
20 - 24 87 36 21 27 171
25 - 29 75 29 11 18 133
30+ 177 26 11 13 227
Totals 351 95 49 67 562
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A PPEN DI X 5 B EHAV I OR A L SURV EI L L A NC E S U R V EY S