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A p-value more than the significance level (typically p > 0.05) is not statistically significant and indicates strong evidence for the null hypothesis. This means we retain the null hypothesis and reject the alternative hypothesis.
If the p-value is less than the significance level, then you reject the null hypothesis. If the p-value is not less than the significance level, then you fail to reject the null hypothesis. You can use the following clever line to remember this rule:
If the p-value is not less than .05, then we fail to reject the null hypothesis and conclude that we do not have sufficient evidence to say that the alternative hypothesis is true. The following examples explain how to interpret a p-value less than .05 and how to interpret a p-value greater than .05 in practice.
The smaller the p-value, the stronger the evidence that you should reject the null hypothesis. The observed value is statistically significant (p ≤ 0.05), so the null hypothesis (N0) is rejected, and the alternative hypothesis (Ha) is accepted.
No. The p-value only tells you how likely the data you have observed is to have occurred under the null hypothesis. If the p-value is below your threshold of significance (typically p < 0.05), then you can reject the null hypothesis, but this does not necessarily mean that your alternative hypothesis is true.
Here’s what it means in practice: If p < 0.05: This means that if the null hypothesis were true, we’d expect to see results as extreme as ours less than 5% of the time. In this case, we typically reject the null hypothesis and consider our results statistically significant.
When the p-value is less than 0.05, it’s significant, but there’s a vast difference if the p-value is 0.045 or 0.001. When the p-value is near 0.05, it can be significant but the evidence against the null is fairly weak.
Using P values and Significance Levels Together. If your P value is less than or equal to your alpha level, reject the null hypothesis. The P value results are consistent with our graphical representation. The P value of 0.03112 is significant at the alpha level of 0.05 but not 0.01.
If the p-value is less than or equal to 0.05, you reject the null hypothesis and conclude that sufficient evidence supports the alternative hypothesis. In other words, you are...
At P = 0.05, the bound suggests that our alternative hypothesis is at most 2.5 times more likely than the null (black dashed line). Also shown are the conventional Bayesian = 20 (blue...