Does Type of Reward Influence Reaction to Task Disruption?
Pearson Chi-Squared Test Says NO! But Exact Test Says YES!

Researchers provided four types of rewards for successful completion of a block building task. The rewards may be categorized as achievement oriented, financial, socially reinforcing, and neural. Five subjects were assigned at random to each reward category. The subjects were instructed in advance about their respective reward structures, and then assigned to the block building task. Each subject was interrupted in a standard way while carrying out the task. The object of the experiment was to determine if the type of reward was related to the subject's reaction to task disruption. The data are displayed below:

The output from StatXact for Pearson's X2 test is displayed below:

Notice that the Pearson X2 = 11.56, which, when referred to a chi squared distribution with 6 degrees of freedom, yields an asymptotic p-value of 0.0727. But with data this sparse can you really trust the asymptotic p-value? Fortunately you don't need to. The exact p-value of the Pearson test is computed by StatXact to be 0.0398. You can feel secure that your experiment did indeed yield a statistically significant outcome, despite the small sample size. The type of reward does indeed affect one's reaction to task disruption.