How To Reject The Null Hypothesis With P Value?

Researchers use p-values to decide whether their findings are statistically significant. To reject the null hypothesis, you compare your p-value to a pre-set significance level, often 0.05. If the p-value is less than 0.05, you reject the null hypothesis and conclude that your result is statistically significant. This is the standard method taught in statistics and used across medical research.

What is the null hypothesis?

The null hypothesis is a statement that says there is no effect or no difference. For example, in a drug trial, the null hypothesis might be that the drug does not change blood pressure compared to a placebo. Researchers set up the null hypothesis as the default position. They then collect data to see if the evidence is strong enough to reject it.

Rejecting the null hypothesis does not mean you have proven your alternative hypothesis is true. It simply means the data are unlikely if the null hypothesis were true. This is an important distinction.

What does a p-value actually mean?

A p-value is the probability of getting a result as extreme as yours, or more extreme, if the null hypothesis were true. It is not the probability that the null hypothesis is true. It is not the probability that your alternative hypothesis is false. Many people misunderstand this.

For example, a p-value of 0.03 means that if there really were no effect, you would see a result this extreme about 3% of the time due to random chance alone. Because 3% is low, researchers often see this as evidence against the null. But a low p-value does not guarantee the effect is real or important.

What significance level should you use?

The significance level, often called alpha, is the threshold you set before collecting data. The most common value is 0.05. If your p-value is below 0.05, you reject the null hypothesis. Some fields use stricter thresholds like 0.01 or even 0.001, especially when the consequences of a false positive are high.

There is nothing special about 0.05. It is a convention. The choice should depend on the context. For a screening test where missing a real effect could be harmful, a higher alpha might be acceptable. For a confirmatory study, a lower alpha is better.

How do you calculate a p-value?

You do not usually calculate a p-value by hand. Statistical software like SPSS, R, or Python does it for you. The calculation depends on the type of test you run: a t-test for comparing two groups, an ANOVA for more than two groups, a chi-square test for categorical data, and so on.

Each test produces a test statistic (like t, F, or chi-square) based on your data. The p-value comes from comparing that statistic to a known distribution. The software gives you the p-value directly. What matters is whether that p-value is below your chosen alpha.

What are common mistakes when using p-values to reject the null?

A major mistake is treating p > 0.05 as proof that the null hypothesis is true. That is not correct. A non-significant result means the evidence is not strong enough to reject the null. It does not confirm the null. Similarly, a very small p-value does not prove that the effect is large or meaningful.

Another mistake is running many tests and only reporting the ones with p < 0.05. This is called p-hacking. If you run 20 tests, by chance alone you will likely find one significant result at the 0.05 level. Researchers should adjust for multiple comparisons using methods like Bonferroni correction or false discovery rate.

Also, p-values are sensitive to sample size. A very large study can find a tiny, unimportant effect with p < 0.001. A small study might miss a real, important effect because it lacks power. Statistical significance does not equal practical significance.

How to reject the null hypothesis with p value step by step

Here is a clear step-by-step process:

• State your hypotheses. Write out the null hypothesis (no effect) and the alternative hypothesis (an effect exists).
• Choose a significance level (alpha) before you collect data. Common choices: 0.05, 0.01.
• Collect your data and perform the appropriate statistical test.
• Get the p-value from the test output.
• Compare the p-value to alpha. If p < alpha, reject the null hypothesis. If p ≥ alpha, fail to reject the null (do not say "accept" the null).

Remember that this procedure only tells you about statistical significance. You still need to consider effect size, confidence intervals, and the quality of the study design before drawing conclusions.

What are alternatives to p-values?

Many statisticians recommend using confidence intervals and effect sizes alongside p-values. A confidence interval gives a range of plausible values for the true effect. If that interval does not include the null value (usually zero or one), it is equivalent to rejecting the null at that alpha level.

Effect sizes, like Cohen’s d or odds ratios, tell you the magnitude of the difference. A p-value alone cannot tell you whether the result matters. Reporting both gives a fuller picture. Some journals now require effect sizes and confidence intervals.

Are there situations where you should not rely on p-values?

Yes. When sample sizes are very small, p-values can be misleading. When you are testing many hypotheses at once, you need to correct for multiple comparisons. When the data are not independent or the assumptions of the test are violated, p-values may be invalid.

Also, p-values do not tell you the probability that your hypothesis is correct. That requires Bayesian statistics, which is a different framework. For most medical research, p-values are used alongside other measures, not alone.