Statistical Analysis for Education and Psychology Researchers

2 3 3 6

50.00 50.00

50.00 75.00

Total 6 4 10

Statistics for table of row by col

Statistic DF Value Prob

Chi-Square 1 0.625 0.429

Continuity Adj. Chi-Square 1 0.017 0.895

Fisher’s Exact Test (Left) 0.929

(Right) 0.452

(2-Tail) 0.571

Simple Size=10

WARNING: 100% of the cells have expected counts less than 5. ChiSquare may not be a

valid test.

Figure 6.5: Output for Fisher’s exact

test

6.4 Proportions Test (or difference in percentages)

When to Use

When an investigator is interested in a simple difference in proportions between two
independent groups, rather than a relationship (when χ^2 would be used), the proportions
test is appropriate. This test procedure is used to compare the proportions of two
independent groups (such as boys and girls) with respect to a nominal variable of interest,
for example, blue eyes/brown eyes; IQ≥100/< 100; pass/fail. The groups are the result of
two independent random samples from specified populations and the sample sizes do not
have to be equal. The test procedure illustrated here is based on the confidence interval of
the difference between two population proportions which is estimated using the
difference between the observed proportions in the two random samples. The test is also
applicable to comparison of the difference between two percentages.

Statistical Inference and Null Hypothesis

Statistical inferences for this procedure relate to population proportions, the null
hypothesis is that these are equal. The test is based on a normal approximation to the
binomial distribution, the normal variate Z is used to evaluate a confidence interval for
the difference, D, between population proportions. To calculate the significance of this
difference, D, the standard error (standard deviation) of the observed difference is
calculated and an appropriate confidence interval for the difference, based on this
observed standard error, is evaluated. The unknown difference between population
proportions, D, is estimated using the observed difference in sample proportions, P 1 −P 2.
If the confidence interval excludes 0 we can be confident that the groups are significantly
different.

Statistical analysis for education and psychology researchers 184