Significance Test and Confidence Intervals In General:
You are reading an article in your field that reports several statistical analyses. The
article says that the P-value for a significance test is 0.045. Ifs the significant at
the 5% significance level?
To determine whether the result is significant at the 5% significance level, compare the p-value to the significance level. The significance level is typically set beforehand, often at 5%.
In this case, the given p-value is 0.045, which is less than the 5% significance level.
Therefore, the result is significant at the 5% significance level.
To determine if the result is significant at the 5% significance level, we need to compare the p-value to the significance level.
The significance level (also known as alpha) is the pre-determined threshold below which we consider a result to be statistically significant. In this case, the significance level is 5% or 0.05.
If the p-value is less than the significance level, it means that the result is statistically significant. In this case, the p-value is 0.045 which is less than 0.05. Hence, we can conclude that the result is significant at the 5% significance level.
Now, let me explain a bit about significance tests and p-values. In statistics, a significance test is a method used to determine if the results of a study are statistically significant or not. It helps us make inferences about a population based on a sample. The test compares the observed data from the sample to what would be expected under a null hypothesis.
The null hypothesis (H0) represents our default assumption that there is no significant difference or relationship between variables. The alternative hypothesis (Ha), on the other hand, is the claim we are trying to support with evidence.
The p-value is the probability of obtaining a result at least as extreme as the one observed if the null hypothesis is true. It quantifies the strength of evidence against the null hypothesis. If the p-value is small (below the significance level), it suggests that the observed result is unlikely to occur by chance if the null hypothesis is true, leading us to reject the null hypothesis in favor of the alternative hypothesis.
In summary, a p-value less than the significance level indicates that the result is statistically significant, meaning that it is unlikely to have occurred by chance under the null hypothesis.