Welcome to understanding p-values! A p-value is a fundamental concept in statistics that measures the probability of observing data as extreme as your results, assuming the null hypothesis is true. For example, a p-value of zero point zero four means there's only a four percent chance of getting these results if the null hypothesis were actually correct.
A p-value is a fundamental concept in statistics. It represents the probability of observing test results at least as extreme as what we actually observed, assuming the null hypothesis is true. For example, a p-value of zero point zero four means there is only a four percent chance of getting results this extreme if the null hypothesis were actually true.
To determine if our results are statistically significant, we compare the p-value to our chosen significance level, called alpha. Common significance levels are zero point zero five and zero point zero one. The decision rule is simple: if the p-value is less than or equal to alpha, we reject the null hypothesis. Since our p-value of zero point zero four is less than zero point zero five, we reject the null hypothesis and conclude the results are statistically significant.
To summarize: A p-value of zero point zero four indicates there is only a four percent chance of observing such extreme results if the null hypothesis were true. At the standard significance level of zero point zero five, this p-value is statistically significant, leading us to reject the null hypothesis and accept the alternative hypothesis.
Now let's walk through the decision process for our p-value of zero point zero four. First, we set our significance level at zero point zero five. Next, we compare our p-value to this threshold. Since zero point zero four is less than or equal to zero point zero five, we reject the null hypothesis. This means our observed data provides sufficient evidence against the null hypothesis, and we conclude that the results are statistically significant at the five percent level.
It's important to understand what a p-value does NOT mean. A p-value is not the probability that the null hypothesis is true, nor is it the probability of making a wrong decision. The correct interpretation is that a p-value of zero point zero four means: if the null hypothesis were true, we would see results this extreme only four percent of the time. This distinction is crucial for proper statistical reasoning.
To summarize our understanding of p-values: A p-value of zero point zero four indicates there is only a four percent probability of observing such extreme results if the null hypothesis were true. Since this value is less than our significance level of zero point zero five, we conclude the results are statistically significant and reject the null hypothesis in favor of the alternative.