A common mistake is to state the hypotheses in terms of sample statistics (e.g., sample mean) instead of population parameters (e.g., population mean). Hypotheses should always be about the population, not the sample.
Clearly understand the meaning of the level of significance (α). It represents the probability of rejecting the null hypothesis when it is actually true (Type I error). Choose an appropriate α based on the context of the problem. Common values are 0.05 or 0.01.
Failing to verify the assumptions required for a particular test statistic (e.g., normality for a t-test). If the assumptions are not met, the test results may be unreliable. Consider using non-parametric tests if assumptions are violated.
Many students incorrectly interpret the p-value as the probability that the null hypothesis is true. The p-value is the probability of observing a test statistic as extreme as, or more extreme than, the one computed, assuming the null hypothesis is true.
Ensure the critical region is consistent with the alternative hypothesis (one-tailed vs. two-tailed test). A one-tailed test has the critical region in only one tail of the distribution, while a two-tailed test has it in both tails.
A small sample size can lead to low power, increasing the chance of failing to reject a false null hypothesis (Type II error). Students should understand the relationship between sample size, power, and the probability of Type II error.
Students often conclude that accepting the null hypothesis means it is true. Failing to reject the null hypothesis only means there is insufficient evidence to reject it; it doesnt prove the null hypothesis is true.
Double-check the formula for degrees of freedom for the specific test you are using (e.g., t-test, chi-square test). Using the wrong degrees of freedom will lead to an incorrect p-value and conclusion.
When comparing variances, remember to use the F-test and ensure you are calculating the F-statistic correctly (ratio of the larger variance to the smaller variance).
Stating only the statistical significance without discussing the practical significance. While a result may be statistically significant, it may not be practically meaningful in the real-world context of the problem.