Biostatistics For Dummies, 2nd Edition (Monika Wahi, John Pezzullo)

164 PART 4 Comparing Groups

the expected counts. The rigorous proof behind this is too complicated for most

mathophobes (as well as some normal people) to understand. Nevertheless, a

simple informal explanation is based on the idea that random event occurrences

typically follow the Poisson distribution for which the SE of the event count equals

the square root of the expected count (as discussed in Chapter 10).

Summarizing and combining scaled differences

For the upper-left cell in the cross-tab (CBD–treated participants who experience

pain relief), you see the following:»

» ^{The observed count (Ob) is 33.»}

» ^{The expected count (Ex) is 25.8.»}

» ^{The difference (Diff) is}³³

25 8

. , or 7 2. .»

» ^{The SE of the difference is}^{25 8.}

or 5.08

You can “scale” the Ob-Ex difference (in terms of unit of SE) by dividing it by the

SE measurement unit, getting the ratio Diff / SE 7 2 5 08

. / .

, or 1.42. This means

that the difference between the observed number of CBD-treated participants who

experience pain relief and the number you would have expected if the CBD had no

effect on survival is about 1.42 times as large as you would have expected from

random sampling fluctuations alone. You can do the same calculation for the other

three cells and summarize these scaled differences. Figure 12-4 shows the differ-

ences between observed and expected cell counts, scaled according to the esti-

mated standard errors of the differences.

The next step is to combine these individual scaled differences into an overall

measure of the difference between what you observed and what you would have

expected if the CBD or NSAID use really did not impact pain relief differentially.

You can’t just add them up because the negative and positive differences would

cancel each other out. You want all differences (positive and negative) to contrib-

ute to the overall measure of how far your observations are from what you expected

under H0.

FIGURE 12-4:

Differences

between

observed and

expected cell

counts.