Estimating with Confidence 1.
Contact Us Null and Alternative Hypothesis Generally to understand some characteristic of the general population we take a random sample and study the corresponding property of the sample.
We then determine whether any conclusions we reach about the sample are representative of the population.
This is done by choosing an estimator function for the characteristic of the population we want to study and then applying this function to the sample to obtain an estimate. By using the appropriate statistical test we then determine whether this estimate is based solely on chance.
The hypothesis that the estimate is based solely on chance is called the null hypothesis. Thus, the null hypothesis is true if the observed data in the sample do not differ from what would be expected on the basis of chance alone.
The complement of the null hypothesis is called the alternative hypothesis. The null hypothesis is typically abbreviated as H0 and the alternative hypothesis as H1. Since the two are complementary i. H0 is true if and only if H1 is falseit is sufficient to define the null hypothesis.
Since our sample usually only contains a subset of the data in the population, we cannot be absolutely certain as to whether the null hypothesis is true or not. We can merely gather information via statistical tests to determine whether it is likely or not. We therefore speak about rejecting or not rejecting aka retaining the null hypothesis on the basis of some test, but not of accepting the null hypothesis or the alternative hypothesis.
Often in an experiment we are actually testing the validity of the alternative hypothesis by testing whether to reject the null hypothesis. When performing such tests, there is some chance that we will reach the wrong conclusion.
There are two types of errors: We use the following terminology: P-value the probability value is the value p of the statistic used to test the null hypothesis. Critical region is the part of the sample space that corresponds to the rejection of the null hypothesis, i. The significance level is the probability that the test statistic will fall within the critical region when the null hypothesis is assumed.
The typical approach for testing a null hypothesis is to select a statistic based on a sample of fixed size, calculate the value of the statistic for the sample and then reject the null hypothesis if and only if the statistic falls in the critical region.
One-tailed hypothesis testing specifies a direction of the statistical test. The null hypothesis is rejected only if the test statistic falls in the critical region, i. Figure 1 — Critical region is the right tail The critical value here is the right or upper tail. It is quite possible to have one sided tests where the critical value is the left or lower tail.
For example, suppose the cloud seeding is expected to decrease rainfall. Then the null hypothesis could be as follows: For the cloud seeding example, it is more common to use a two-tailed test. Here the null and alternative hypotheses are as follows.
To take care of this possibility, a two tailed test is used with the critical region consisting of both the upper and lower tails.
Figure 3 — Two-tailed hypothesis testing In this case we reject the null hypothesis if the test statistic falls in either side of the critical region. Thus power is the probability that you find an effect when one exists, i.
The general procedure for null hypothesis testing is as follows: What we have shown instead is that assuming the null hypothesis is true, the conditional probability that the sample data exhibits the obtained test statistic is 0.A non-directional alternative hypothesis is not concerned with either region of rejection, but, rather, it is only concerned that null hypothesis is not true.
References. So you can have a directional alternative hypothesis (therapy decreases depression) or a nondirectional alternative hypothesis (therapy has an effect on depression). you are trying to disprove the null hypothesis. Documents Similar To Notes on Directional and Non Directional.
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Uploaded by 4/4(5). In this case the researcher has phrased the alternative hypothesis as a directional would say that this alternative hypothesis is in the form of a non-directional question or hypothesis.
The null hypothesis in this case would, again, be the opposite of the In sum, the two-sample (independent samples) t-test is a choice between two. The research hypothesis can be written in a directional or non-directional manner.
Directional (one tailed) – specifics the direction of the expected relationship (e.g., H 0: µ 1 µ 2, H A: µ 1 > µ 2). Sometimes called a two-tailed test, a test of a nondirectional alternative hypothesis does not state the direction of the difference, it indicates only that a difference exists.
In contrast, a directional alternative hypothesis specifies the direction of the tested relationship, stating that one variable is predicted to be larger or smaller. A two-tailed non-directional hypothesis predicts that the independent variable will have an effect on the dependent variable, but the direction of the effect is not specified.
How to Write a Hypothesis. 1. To write the alternative and null hypotheses for an investigation, you need to identify the key variables in the study.