The Fisher exact test of significance may be used in place of the chi-square test in 2-by-2 tables, particularly for small samples. Fisher exact test of significance tests the probability of getting a table as strong as or stronger than the observed, simply due to the chance of sampling, where "strong" is defined by the proportion of cases on the diagonal with the most cases. Though usually employed as a one-tailed test, Fisher exact test of significance may be computed as a two-tailed test as well.
The Fisher exact test of significance to r-by-c tables proposed by Fisher is also called the Fisher-Freeman-Halton test. Fisher exact test of significance to r-by-c tables are normally tested for significance using the chi-square test. For 2-by-2 small sample data, uncorrected chi-square tends to underestimate the probability of observed cell counts, which amounts to the increase in Type I errors. The corrected chi-square will normally lead to the same significance decision as the Fisher exact test of significance.
Fisher exact test of significance directly computes p, the probability of getting a table as strong as the observed table. Fisher exact test of significance can be computed by using a formula which has been explained below in a step-by-step manner.
The first step in Fisher exact test of significance is to specify the observed table and all stronger tables.
The second step in Fisher exact test of significance is to compute the probability by Fisher’s exact test which is given by Hypergeometric Distribution given below:
p = (r1!r2!c1!c2!)/n!a!b!c!d! where r1 = a+b , r2 = c+d , c1 = a+c and c2=b+d
Here ‘a,’‘b,’ ’c’ and ‘d’ are the marginal totals.
The third step in Fisher exact test of significance is to interpret Fisher’s p. Social scientists ordinarily consider .05 to be the cutoff for acceptability of significance levels, one can conclude that the distribution in the observed table in Fisher exact test of significance cannot be significantly different from chance.
In order to perform Fisher exact test of significance in SPSS, select “Analyze” from the menu, then from Analyze select “Descriptive Statistics” and from there select “Crosstabs.” In the Chi Square Tests output, one will get the value of Fisher exact test of significance along with the degree of freedom, Asymptotical Significance (2-sided) , Exact Significance (2-sided) and Exact Significance (1-sided).
Assumptions
We assume that the sample has been obtained by random sampling in Fisher exact test of significance.
A directional hypothesis is assumed in Fisher exact test of significance. A directional hypothesis is nothing but a one tailed hypothesis.
Independent observations are assumed in Fisher exact test of significance. This means that it is assumed that the value of the first person or unit sampled has no effect on the value for the second person or unit in Fisher exact test of significance.
The cases in Fisher exact test of significance must be mutually exclusive. This means that a given case may fall in only one cell of the table in Fisher exact test of significance.
A Dichotomous level of measurement must be assumed in Fisher exact test of significance.
The rationale for the Fisher exact test of significance assumes that the marginals are fixed by the researcher in advance when in an experiment. This assumption is widely ignored in practice.
