Question

What does p value mean at different levels and when do we reject or accept hypothesis

Answer 1

In statistical hypothesis testing, the p-value is a measure that helps determine the strength of evidence against the null hypothesis. The null hypothesis typically suggests that there is no effect or no difference between groups, while the alternative hypothesis suggests the presence of an effect or difference.

- **Interpretation of p-values:**

- If the p-value is low (typically ≤ 0.05 or 0.01), it indicates strong evidence against the null hypothesis. In this case, researchers might reject the null hypothesis and accept the alternative hypothesis. It suggests that the observed results are unlikely to have occurred under the assumption that there is no real effect or difference.

- If the p-value is high (e.g., ≥ 0.05), it suggests weak evidence against the null hypothesis. In such cases, researchers might fail to reject the null hypothesis, meaning there isn't enough evidence to conclude that there is a significant effect or difference.

- **Decision-making with p-values:**

- **Rejecting the null hypothesis:** When the p-value is below a chosen significance level (usually 0.05 or 0.01), researchers typically reject the null hypothesis. This means they conclude that there's enough evidence to support the alternative hypothesis.

- **Failing to reject the null hypothesis:** When the p-value is above the chosen significance level, researchers do not have enough evidence to reject the null hypothesis. They do not conclude that there's no effect or difference, but rather they don't have sufficient evidence to claim otherwise.

It's important to note that while the p-value provides information about the strength of evidence against the null hypothesis, it does not indicate the size or importance of the effect. Researchers should also consider effect sizes and the context of the study when drawing conclusions.

Answer 2

The p-value in statistical hypothesis testing indicates the likelihood of an event given that the null hypothesis is true. A small p-value signifies strong evidence against the null hypothesis, leading to its rejection when below a predetermined significance level (typically α = 0.05). The decision to reject or not also depends on whether the test is left, right, or two-tailed.

Step-by-step explanation:

The p-value is an important concept in hypothesis testing in statistics. It represents the probability that an event will happen purely by chance assuming the null hypothesis is true; the smaller the p-value, the stronger the evidence is against the null hypothesis. When you have calculated the p-value, the decision to reject or not reject the null hypothesis is based on a comparison with a preset alpha level (α), commonly set at 0.05.

To make this decision:

• If p-value < α, reject . This means there is sufficient evidence that the null hypothesis is incorrect, and the alternative hypothesis may be correct.
• If p-value ≥ α, do not reject . This indicates there is not enough evidence to dispute the null hypothesis.

The decision is affected by whether the test conducted is left, right, or two-tailed, which is determined by the alternative hypothesis. Hypothesis tests, including Cohen's d, provide measures of effect size and further interpretation of results beyond p-value assessment.

As a memory aid, one could use the phrase, "If the p-value is low, the null must go. If the p-value is high, the null must fly," to remember when to reject or not reject the null hypothesis based on the p-value in relation to the significance level.