Write a description of a situation where you might want lower p-values for signi

Question

Write a description of a situation where you might want lower p-values for significance and explain why. Then explain how p-values that are 0.05, 0.049, and 0.051, might be different when interpreting statistical results. Explain why p-values are significant in contributing to public health practice. Be specific and provide examples
Write a description of a situation where you might want lower p-values for significance and explain why. Then explain how p-values that are 0.05, 0.049, and 0.051, might be different when interpreting statistical results. Explain why p-values are significant in contributing to public health practice. Be specific and provide examples

Explanation / Answer

Solution:-

  P-value: “If the null hypothesis is true then, the probability of obtaining a result equal to or "more extreme" than what was actually observed is the p-value”.

  significance level:As the null hypothesis is assumed to be true in general and we only reject the null hypothesis when we have sufficient evidence against the null hypothesis so we reject the null hypothesis when it is smaller than some specified value which is known as “alpha” or “the significance level”. The significance level is basically the maximum possible Type I error probability.

What is Type I error and how is it related to p-value?

Type I error is basically the error of rejecting a true null hypothesis i.e. when the null hypothesis is actually true but the sample is tend to reject the null hypothesis. Most often it is observed that the Type I error is more serious than the Type II error thus we fix some maximum allowable value for this Type I error in a hypothesis test (known as the significance level) and test the hypothesis. If the observed p-value is smaller than the maximum allowable Type I error probability we reject the null hypothesis.

Where we might want lower p-values for significance:

As I already stated that most often the Type I error is more serious. For example lets consider an example, we are testing a lifesaving drug new version against old version. Now here the null hypothesis would be that the new version is equal or lower effective than old one and alternative would be that the old one is better. Here clearly the Type I error is more serious because if we conclude that the new one is better but it is not we may lose lots of life. Thus in these situations where the Type I error is more serious we choose a lower allowable maximum value for this probability i.e. basically we choose smaller alpha. And in the cases where the Type I error is not so serious we tend to loosen the grip by increasing alpha a little bit. As reducing alpha means basically reducing p-value for null hypothesis to be rejected thus basically where the Type I error is more serious we might want lower p-values for significance.

P-values and statistical results: Now, how is p-value related to the conclusion of a hypothesis test? As I stated above that we compare the p-value with the significance level to test the hypothesis. If the p-value is smaller than the significance level we reject the null hypothesis. Now for example suppose the significance level is 0.05. Then if the p-value is 0.05 or 0.51 we would not reject the null hypothesis but would reject it if the p-value is smaller than 0.05 say 0.049. Thus the p-value is essential in determination of rejection of the null hypothesis.

P-values in public health practice:

The last question that need to be answered is, “why p-values are significant in contributing to public health practice?”. The answer is pretty simple, because it determines the seriousness of the study. As I already stated earlier that in some cases, especially in health practices, a Type I error is more serious than Type II error and thus we want to control Type I error as much as possible. And for that reason a lower significance level is chosen so that we tend to reject the null hypothesis less often. Only when the p-value is sufficiently smaller we reject the null hypothesis and by this way we control the Type I error.

Thus p-values are essential in public health practice because it not only determines whether the test is significant or not but also ensures that the serious studies are actually considered seriously. So that there is no life loss rather the studies are done in such a manner that the acceptable error is very small and within limits.

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