# Difference Between Null And Altenative Hypothesis Pdf

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In inferential statistics , the null hypothesis often denoted H 0 [1] is a default hypothesis that a quantity to be measured is zero null. Typically, the quantity to be measured is the difference between two situations, for instance to try to determine if there is a positive proof that an effect has occurred or that samples derive from different batches. The null hypothesis is effectively stating that a quantity of interest being larger or equal to zero AND smaller or equal to zero.

## Hypothesis testing, type I and type II errors

Hypothesis testing is an important activity of empirical research and evidence-based medicine. A well worked up hypothesis is half the answer to the research question. For this, both knowledge of the subject derived from extensive review of the literature and working knowledge of basic statistical concepts are desirable. The present paper discusses the methods of working up a good hypothesis and statistical concepts of hypothesis testing.

Karl Popper is probably the most influential philosopher of science in the 20 th century Wulff et al. Many scientists, even those who do not usually read books on philosophy, are acquainted with the basic principles of his views on science. Popper makes the very important point that empirical scientists those who stress on observations only as the starting point of research put the cart in front of the horse when they claim that science proceeds from observation to theory, since there is no such thing as a pure observation which does not depend on theory.

The first step in the scientific process is not observation but the generation of a hypothesis which may then be tested critically by observations and experiments. It is logically impossible to verify the truth of a general law by repeated observations, but, at least in principle, it is possible to falsify such a law by a single observation. Repeated observations of white swans did not prove that all swans are white, but the observation of a single black swan sufficed to falsify that general statement Popper, A good hypothesis must be based on a good research question.

It should be simple, specific and stated in advance Hulley et al. A simple hypothesis contains one predictor and one outcome variable, e. Here the single predictor variable is positive family history of schizophrenia and the outcome variable is schizophrenia.

A complex hypothesis contains more than one predictor variable or more than one outcome variable, e. Here there are 2 predictor variables, i. Complex hypothesis like this cannot be easily tested with a single statistical test and should always be separated into 2 or more simple hypotheses. A specific hypothesis leaves no ambiguity about the subjects and variables, or about how the test of statistical significance will be applied.

This is a long-winded sentence, but it explicitly states the nature of predictor and outcome variables, how they will be measured and the research hypothesis. Often these details may be included in the study proposal and may not be stated in the research hypothesis.

However, they should be clear in the mind of the investigator while conceptualizing the study. The hypothesis must be stated in writing during the proposal state.

The habit of post hoc hypothesis testing common among researchers is nothing but using third-degree methods on the data data dredging , to yield at least something significant. This leads to overrating the occasional chance associations in the study. For the purpose of testing statistical significance, hypotheses are classified by the way they describe the expected difference between the study groups.

The null hypothesis is the formal basis for testing statistical significance. By starting with the proposition that there is no association, statistical tests can estimate the probability that an observed association could be due to chance.

The proposition that there is an association — that patients with attempted suicides will report different tranquilizer habits from those of the controls — is called the alternative hypothesis.

The alternative hypothesis cannot be tested directly; it is accepted by exclusion if the test of statistical significance rejects the null hypothesis. A one-tailed or one-sided hypothesis specifies the direction of the association between the predictor and outcome variables. The prediction that patients of attempted suicides will have a higher rate of use of tranquilizers than control patients is a one-tailed hypothesis.

A two-tailed hypothesis states only that an association exists; it does not specify the direction. The prediction that patients with attempted suicides will have a different rate of tranquilizer use — either higher or lower than control patients — is a two-tailed hypothesis. The word tails refers to the tail ends of the statistical distribution such as the familiar bell-shaped normal curve that is used to test a hypothesis. One tail represents a positive effect or association; the other, a negative effect.

A one-tailed hypothesis has the statistical advantage of permitting a smaller sample size as compared to that permissible by a two-tailed hypothesis. Unfortunately, one-tailed hypotheses are not always appropriate; in fact, some investigators believe that they should never be used.

However, they are appropriate when only one direction for the association is important or biologically meaningful.

An example is the one-sided hypothesis that a drug has a greater frequency of side effects than a placebo; the possibility that the drug has fewer side effects than the placebo is not worth testing. Whatever strategy is used, it should be stated in advance; otherwise, it would lack statistical rigor.

Data dredging after it has been collected and post hoc deciding to change over to one-tailed hypothesis testing to reduce the sample size and P value are indicative of lack of scientific integrity. A hypothesis for example, Tamiflu [oseltamivir], drug of choice in H1N1 influenza, is associated with an increased incidence of acute psychotic manifestations is either true or false in the real world.

Because the investigator cannot study all people who are at risk, he must test the hypothesis in a sample of that target population. No matter how many data a researcher collects, he can never absolutely prove or disprove his hypothesis. There will always be a need to draw inferences about phenomena in the population from events observed in the sample Hulley et al. The absolute truth whether the defendant committed the crime cannot be determined.

Instead, the judge begins by presuming innocence — the defendant did not commit the crime. The judge must decide whether there is sufficient evidence to reject the presumed innocence of the defendant; the standard is known as beyond a reasonable doubt. A judge can err, however, by convicting a defendant who is innocent, or by failing to convict one who is actually guilty. In similar fashion, the investigator starts by presuming the null hypothesis, or no association between the predictor and outcome variables in the population.

Based on the data collected in his sample, the investigator uses statistical tests to determine whether there is sufficient evidence to reject the null hypothesis in favor of the alternative hypothesis that there is an association in the population.

The standard for these tests is shown as the level of statistical significance. Sometimes, by chance alone, a sample is not representative of the population. Thus the results in the sample do not reflect reality in the population, and the random error leads to an erroneous inference. A type I error false-positive occurs if an investigator rejects a null hypothesis that is actually true in the population; a type II error false-negative occurs if the investigator fails to reject a null hypothesis that is actually false in the population.

Although type I and type II errors can never be avoided entirely, the investigator can reduce their likelihood by increasing the sample size the larger the sample, the lesser is the likelihood that it will differ substantially from the population.

False-positive and false-negative results can also occur because of bias observer, instrument, recall, etc. Errors due to bias, however, are not referred to as type I and type II errors.

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.

## Null and Alternative Hypotheses

Hypothesis testing involves the careful construction of two statements: the null hypothesis and the alternative hypothesis. These hypotheses can look very similar but are actually different. How do we know which hypothesis is the null and which one is the alternative? We will see that there are a few ways to tell the difference. The null hypothesis reflects that there will be no observed effect in our experiment.

Generation of the hypothesis is the beginning of a scientific process. It refers to a supposition, based on reasoning and evidence. The researcher examines it through observations and experiments, which then provides facts and forecast possible outcomes. The hypothesis can be inductive or deductive, simple or complex, null or alternative. While the null hypothesis is the hypothesis, which is to be actually tested, whereas alternative hypothesis gives an alternative to the null hypothesis.

The null and alternative hypotheses are two mutually exclusive statements about a population. A hypothesis test uses sample data to determine whether to reject the null hypothesis. About the null and alternative hypotheses Learn more about Minitab Null hypothesis H 0 The null hypothesis states that a population parameter such as the mean, the standard deviation, and so on is equal to a hypothesized value. The null hypothesis is often an initial claim that is based on previous analyses or specialized knowledge. Alternative Hypothesis H 1 The alternative hypothesis states that a population parameter is smaller, greater, or different than the hypothesized value in the null hypothesis.

## Difference Between Null and Alternative Hypothesis

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