Final answer:
The p-value in hypothesis testing is influenced by the sample size, effect size, and alpha level and helps determine whether to reject or not reject the null hypothesis based on the comparison of the p-value to a predetermined alpha, commonly 0.05.
Step-by-step explanation:
When comparing an intervention versus a control, the p-value is affected by various factors such as sample size, effect size, alpha level, and the nature of the test (whether it is a one-tailed or two-tailed test).
- Sample Size: A larger sample size can lead to more precise estimates, thus potentially leading to a smaller p-value if there is a true effect.
- Effect Size: A larger effect size can make it easier to detect differences, hence lowering the p-value.
- Alpha Level: The alpha level or significance level is a threshold we set for rejecting the null hypothesis. A common alpha level is 0.05. If the p-value is less than the alpha level, we reject the null hypothesis.
For hypothesis testing, a systematic approach is used:
- State the null and alternative hypotheses.
- Calculate the test statistic based on your sample data.
- Determine the p-value which reflects the probability of observing your results assuming the null hypothesis is true.
- Compare the p-value to the alpha level to make a decision whether to reject or not reject the null hypothesis.
Common Errors in Hypothesis Testing
- Type I error: Rejecting the null hypothesis when it is actually true; this occurs when the p-value is less than the alpha level by chance.
- Type II error: Not rejecting the null hypothesis when it is false; this occurs when the p-value is larger than the alpha level but there is actually a true effect.
For example, if the p-value < 0.01, it suggests strong evidence against the null hypothesis and would typically lead to rejection of the null hypothesis at the 5 percent significance level.
If the calculated effect size is 0.625, this suggests a medium effect size as per Cohen's standards.