Final answer:
When a statistically significant difference at the .05 level exists between VCI and PRI, it implies there's a true difference with 95% confidence and not due to sample variation.
Step-by-step explanation:
If a client shows a difference between VCI and PRI that is statistically significant at the .05 level, we can be confident that the difference is real and not due to random chance. Here, VCI stands for Verbal Comprehension Index, and PRI stands for Perceptual Reasoning Index, both of which are measures used in IQ testing. A statistically significant difference at the 0.05 level means that there is less than a 5 percent likelihood that the difference observed is due to random variation in the sample data. In other words, we are 95 percent confident that the observed difference represents a true difference in the population from which the sample was drawn.
To determine statistical significance, tests such as a t-test may be used to compare the scores. If the resulting p-value is less than the predetermined significance level (in this case, .05), we reject the null hypothesis that there is no difference between the two indexes and conclude that there is a statistically significant difference.