Given the following p values which would be considered more significant?
a) p ≤ 0.3
b) p ≤ 0.02
c) p ≤ 0.25
The smallest is most significant.
To determine which p-value is more significant, we need to understand what a p-value represents in statistical hypothesis testing.
The p-value is a measure of the strength of the evidence against the null hypothesis. It quantifies the probability of observing the test statistic (or a more extreme value) given that the null hypothesis is true.
The smaller the p-value, the stronger the evidence against the null hypothesis, indicating that the observed result is unlikely to have occurred by chance alone.
Now, comparing the given p-values:
a) p ≤ 0.3: This means that the observed result has a probability of 0.3 or less of occurring by chance under the null hypothesis. While this indicates some evidence against the null hypothesis, it is not considered highly significant.
b) p ≤ 0.02: This means that the observed result has a probability of 0.02 or less of occurring by chance under the null hypothesis. This p-value is smaller than in (a), indicating stronger evidence against the null hypothesis. It is considered more significant than (a).
c) p ≤ 0.25: This means that the observed result has a probability of 0.25 or less of occurring by chance under the null hypothesis. This p-value is larger than in (b) but smaller than in (a). It indicates less evidence against the null hypothesis compared to (b), but it still suggests some level of significance.
Therefore, in terms of significance, the given p-values can be ranked as follows:
b) p ≤ 0.02 (most significant)
c) p ≤ 0.25
a) p ≤ 0.3 (least significant)