What happens if your hypothesis is rejected

Such errors are troublesome, since they may be difficult to detect and cannot usually be quantified. The likelihood that a study will be able to detect an association between a predictor variable and an outcome variable depends, of course, on the actual magnitude of that association in the target population. Unfortunately, the investigator often does not know the actual magnitude of the association — one of the purposes of the study is to estimate it.

Instead, the investigator must choose the size of the association that he would like to be able to detect in the sample. This quantity is known as the effect size.

Selecting an appropriate effect size is the most difficult aspect of sample size planning. Sometimes, the investigator can use data from other studies or pilot tests to make an informed guess about a reasonable effect size. Thus the choice of the effect size is always somewhat arbitrary, and considerations of feasibility are often paramount.

When the number of available subjects is limited, the investigator may have to work backward to determine whether the effect size that his study will be able to detect with that number of subjects is reasonable.

After a study is completed, the investigator uses statistical tests to try to reject the null hypothesis in favor of its alternative much in the same way that a prosecuting attorney tries to convince a judge to reject innocence in favor of guilt. Depending on whether the null hypothesis is true or false in the target population, and assuming that the study is free of bias, 4 situations are possible, as shown in Table 2 below.

Truth in the population versus the results in the study sample: The four possibilities. The investigator establishes the maximum chance of making type I and type II errors in advance of the study. This is the level of reasonable doubt that the investigator is willing to accept when he uses statistical tests to analyze the data after the study is completed.

This represents a power of 0. Then 90 times out of , the investigator would observe an effect of that size or larger in his study. Ideally alpha and beta errors would be set at zero, eliminating the possibility of false-positive and false-negative results.

In practice they are made as small as possible. Reducing them, however, usually requires increasing the sample size. Sample size planning aims at choosing a sufficient number of subjects to keep alpha and beta at acceptably low levels without making the study unnecessarily expensive or difficult. Many studies s et al pha at 0.

These are somewhat arbitrary values, and others are sometimes used; the conventional range for alpha is between 0. In general the investigator should choose a low value of alpha when the research question makes it particularly important to avoid a type I false-positive error, and he should choose a low value of beta when it is especially important to avoid a type II error.

The null hypothesis acts like a punching bag: It is assumed to be true in order to shadowbox it into false with a statistical test. When the data are analyzed, such tests determine the P value, the probability of obtaining the study results by chance if the null hypothesis is true. The null hypothesis is rejected in favor of the alternative hypothesis if the P value is less than alpha, the predetermined level of statistical significance Daniel, For example, an investigator might find that men with family history of mental illness were twice as likely to develop schizophrenia as those with no family history, but with a P value of 0.

If the investigator had set the significance level at 0. Hypothesis testing is the sheet anchor of empirical research and in the rapidly emerging practice of evidence-based medicine. However, empirical research and, ipso facto, hypothesis testing have their limits. The empirical approach to research cannot eliminate uncertainty completely. At the best, it can quantify uncertainty. This uncertainty can be of 2 types: Type I error falsely rejecting a null hypothesis and type II error falsely accepting a null hypothesis.

The acceptable magnitudes of type I and type II errors are set in advance and are important for sample size calculations. We can only knock down or reject the null hypothesis and by default accept the alternative hypothesis. If we fail to reject the null hypothesis, we accept it by default. Source of Support: Nil.

Conflict of Interest: None declared. National Center for Biotechnology Information , U. Journal List Ind Psychiatry J v. Ind Psychiatry J. Amitav Banerjee , U. Chitnis , S.

Jadhav , J. Bhawalkar , and S. Chaudhury 1. Chitnis Department of Community Medicine, D. Jadhav Department of Community Medicine, D. Bhawalkar Department of Community Medicine, D. Author information Copyright and License information Disclaimer. The P-value was approximately 0. In this situation, the P-value is the probability that we will get a sample mean of 75 MBs or higher if the true mean is 62 MBs.

The result is rare enough that we question whether the null hypothesis is true. This is why we reject the null hypothesis. But it is possible that the null hypothesis hypothesis is true and the researcher happened to get a very unusual sample mean. In this case, the result is just due to chance, and the data have led to a type I error: rejecting the null hypothesis when it is actually true. Based on the sampling distribution, we estimated the P-value as 0.

In this situation, the P-value is the probability that we will get a sample proportion of 0. Which type of error is possible in this situation? In other words, we failed to accept an alternative hypothesis that is true. We definitely did not make a type I error here because a type I error requires that we reject the null hypothesis.

Of course we will not know if the null is true. This makes sense because we assume the null hypothesis is true when we create the sampling distribution. We look at the variability in random samples selected from the population described by the null hypothesis. The probability of a type I error, if the null hypothesis is true, is equal to the significance level. The probability of a type II error is much more complicated to calculate.

We can reduce the risk of a type I error by using a lower significance level. The best way to reduce the risk of a type II error is by increasing the sample size. In theory, we could also increase the significance level, but doing so would increase the likelihood of a type I error at the same time.

We discuss these ideas further in a later module. In the long run, a fair coin lands heads up half of the time. For this reason, a weighted coin is not fair. We conducted a simulation in which each sample consists of 40 flips of a fair coin. Here is a simulated sampling distribution for the proportion of heads in 2, samples.

Results ranged from 0. In general, if the null hypothesis is true, the significance level gives the probability of making a type I error. This is a problem! Moore in Basic Practice of Statistics 4th ed. Freeman, :. We do not know if the null is true or if it is false.

If the null is false and we reject it, then we made the correct decision. If the null hypothesis is true and we fail to reject it, then we made the correct decision. When doing hypothesis testing, two types of mistakes may be made and we call them Type I error and Type II error.

If we reject the null hypothesis when it is true, then we made a type I error. If the null hypothesis is false and we failed to reject it, we made another error called a Type II error. We can, however, define the likelihood of these events. However, we cannot decrease both. He is either guilty or not guilty. We found before that As you can see here, the Type I error putting an innocent man in jail is the more serious error.

Ethically, it is more serious to put an innocent man in jail than to let a guilty man go free. So to minimize the probability of a type I error we would choose a smaller significance level. An inspector has to choose between certifying a building as safe or saying that the building is not safe.

There are two hypotheses:. Therefore, they have an inverse relationship, i. Breadcrumb Home 6a 6a. Font size. Font family A A. Content Preview Arcu felis bibendum ut tristique et egestas quis: Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris Duis aute irure dolor in reprehenderit in voluptate Excepteur sint occaecat cupidatat non proident.

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