Statistical Analysis for Education and Psychology Researchers

p=probbnm1 (0.5, 66, 7);

put p=;

The probability is given in the Log File for example,

P=1.718532E–10

Note: The data set WORK. A has has 1 observations and 1

variables.

Note: The DATA statement used 39.1 seconds.

Note: E–10 means move the decimal point 10 places to

the left.

Interpretation of Computer Output

When P=Q=0.5 the normal approximation with correction for continuity provides a good
approximation as can be seen if the obtained Z-value of −6.27766 is evaluated using the
PROBNORM function in SAS. This function returns the one-tailed probability that a Z-
value is less than or equal to the value entered. For example, in the following SAS code a
Z-value of −6.27766 is entered,

data a;

p=probnorm (−6.27766);

put p=;

and a probability of p=1.718532E–10 is returned in the Log File. This value
(p=1.718532E–10) is the same as the exact probability that was returned by the binomial
probability function.

6.3 Fisher’s Exact Test

When to Use the Test

Fisher’s exact test is used to test the significance of any association or difference between
two independent samples. The test determines whether two independent groups differ
significantly in the proportions of observations that are classified by a dependent binary
variable. Suppose that in total twelve male subjects who had sustained upper limb injuries
were sampled. One group was a random sample of six males from a population who had
sustained their injuries before school age (injured when ≤6-years-old). The second
independent sample of six males was selected from a population who had sustained their
injuries when older (injured when >6-years-old). The dependent variable was handedness
(left or right). Investigators may want to know whether there is any association between
age when the injury occurred and handedness.
Fisher’s exact test is a useful alternative to the r×2 sample χ^2 test of association when
total sample sizes are small, n<20 or when expected frequencies in any of the four cells
of the contingency table are less than 5. The test provides an exact probability for
observing a particular frequency distribution in a 2×2 table.

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