Just because two or more values are different does not mean that they are differ

Question

Just because two or more values are different does not mean that they are different in a statistically significant manner. Researchers rely on the p values that are generated for each of their statistical tests to determine significance. If the p value is larger than the alpha, then they are not different in a statistically significant manner, and therefore the values are not considered different. In this journal activity, consider these concepts in terms of the differences between null and alternative hypotheses. What is the difference between failing to reject the null hypothesis and having evidence to support the hypothesis? Explain and give an example.

Explanation / Answer

Just because there is a difference in the mean values does not mean that the difference is large enough to be statistically significant, because it could have come just by chance and that is for what we perform the hypothesis testing at a particular confidence level or level of significance.

The p-value of the hypothesis testing actually is the probability of observing the given sample results in case the null hypothesis is true. In a hypothesis test, we initially assume that null hypothesis is true and then we try to find out the probability of obtaining the given sample results based on the null hypothesis, in case the probability of getting those results is too low, that is the p-value is lower than the level of significance, we then conclude that we have sufficient evidence to reject the null hypothesis, otherwise we fail to reject the null hypothesis and conclude that the sample results which we got were possible statistically given the null hypothesis was true.

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