Understanding the p-value in statistics | Measure of evidence against the null hypothesis

P- value Distribution when Ho is true

In statistics, the p-value is a measure of the strength of evidence against the null hypothesis (Ho)

In statistics, the p-value is a measure of the strength of evidence against the null hypothesis (Ho). The p-value gives the probability of obtaining a test statistic or a more extreme value if the null hypothesis is true.

When the null hypothesis is true, the test statistic follows a specific probability distribution known as the null distribution. The form of this distribution depends on the specific test being performed. Commonly used distributions include the normal distribution, t-distribution, chi-squared distribution, and F-distribution.

The p-value measures the likelihood of observing data as extreme or more extreme than what was observed, assuming the null hypothesis is true. A small p-value indicates strong evidence against the null hypothesis, suggesting that the observed data is unlikely to occur if the null hypothesis is true. On the other hand, a large p-value suggests weak evidence against the null hypothesis, indicating that the observed data is likely to occur even if the null hypothesis is true.

To determine the p-value, you calculate the probability of obtaining a test statistic as extreme or more extreme than the observed test statistic, under the assumption that the null hypothesis is true. This probability is then compared to a pre-determined significance level (usually denoted as alpha) to determine the strength of evidence against the null hypothesis.

If the p-value is less than or equal to the significance level (p ≤ alpha), then the observed data is considered statistically significant, and we reject the null hypothesis in favor of the alternative hypothesis. Conversely, if the p-value is greater than the significance level (p > alpha), then the observed data is not statistically significant, and we fail to reject the null hypothesis.

It is important to note that the p-value is not the probability of the null hypothesis being true or false. It merely provides a measure of the strength of evidence against the null hypothesis based on the observed data.

In summary, when the null hypothesis is true, the p-value distribution represents the probability of obtaining a test statistic as extreme or more extreme than the observed test statistic. This distribution is used to assess the strength of evidence against the null hypothesis and make decisions about whether to reject or fail to reject the null hypothesis.

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