Introduction to the Hypothesis Testing - Research Paper Example

 Hypothesis Testing A hypothesis is a claim that is made about a population parameter such as the mean (µ), proportion (ρ), or standard deviation (σ) (Triola, p. 392). Hypothesis testing therefore involves testing claims, statements or assumptions about various properties of a population which is developed for testing purposes. It is one of the two main activities of inferential statistics (Triola, p. 392). During the process of hypothesis testing systematic procedures are utilized. These procedures involve the use of standard terms such as null hypothesis, alternative hypothesis, level of significance, test statistic; and conditions such as accept the null hypothesis if the statement is true or reject the null hypothesis if the statement is not true. When the rare event rule is used to test a hypothesis, an attempt is made to make a distinction between those results that happen by chance and those which are very unlikely to happen by chance. The explanation for a very unlikely result is that the fundamental assumption is incorrect or that a rare event has taken place. This type of reasoning can be applied to various statements or claims made about a population such as the proportion of males and females. The stages involved in hypothesis testing are shown in the diagram labeled - below. .. Five Step Hypothesis Testing Procedure (Extracted from: Mason and Lind 1996) The diagram shows the steps involved in carrying out a hypothesis test. NULL AND ALTERNATIVE HYPOTHESIS Morgan State University School of Engineering (Morgan.edu) indicates that in order to test a hypothesis data from a sample of a population is taken in order to form a conclusion about the population parameter or about its probability distribution. It involves making a claim about the parameter or distribution. This is a tentative assumption which is dependent on the results obtained from tests carried out on the sample. This assumption is described as the null hypothesis. In the book Elementary Statistics Triola indicates that the term null is an indication that there is no change, effect or difference (p. 395). It is a statement that the value of the population parameter is equal to a specific value. The null hypothesis is denoted as H0 and in relation to the population mean it usually reads as follows: H0: µ = 12 This is a claim that the population mean is equal to twelve (12). The assumption is that the claim is true and so it is tested in order to determine whether it is true and false and in so doing it is either accepted or rejected. If the null hypothesis is rejected it means that the alternative hypothesis which is denoted H1 is accepted. The alternative hypothesis to that indicated above would be: H1: µ ≠ 12 The alternative hypothesis in this case indicates that the population mean is not equal to twelve (12). This means that the value of the mean is different from what is stated in the null hypothesis. In a document entitled ‘Hypothesis Testing and written by Morgan State University School of Engineering, the author indicates that the alternative hypothesis is the opposite of what is written in the null hypothesis. It is a statement that is accepted once the sample tested provides sufficient evidence that H0 is not true. The alternative hypothesis can also be written as Ha and HA (Triola, p. 395). The null and alternative hypothesis for the population proportion would be written as follows for the population proportion: H0: ρ = 0.5 H1: ρ ≠ 0.5 In the case where H0: µ = 12 the alternative hypothesis could take any of the following forms: H1: µ < 12; H1: µ > 12; or H1: µ ≠ 12 as previously stated. LEVEL OF SIGNIFICANCE Hypothesis testing involves the use of samples and so there is a possibility that errors may occur. The level of significance is the probability of rejecting the hypothesis when it is true. It is denoted α and s referred to as the level of risk. There are two types of errors that can occur – Type I and Type II. A type I error occurs when the null hypothesis is rejected and it is actually true while a type II error occurs when the null hypothesis is accepted and it is really not true. In order to specify the probability of making a Type I error, hypothesis tests normally specify a probability of making such an error. This is described as the level of significance for the particular test. Frequently used levels of significance are 0.05, 0.01 and 0.1. These specify the level of confidence that the sample provides. Therefore, a significance level of 0.05 provides a 95% level of confidence, a 0.01 significance level provides a 99% level of confidence, and a 0.1 level of significance provides a 90% confidence level. The table below provides a very good summary of the decisions that one can make when performing hypothesis tests and the consequences of such decisions. Researcher Null Hypothesis Accepts H0 Rejects H0 If H0 is true and Correct decision Type I error If H0 s false and Type II error Correct decision Table - Researchers Decisions and possible consequences (Extracted from Mason and Lind 1996) TEST STATISTIC The test statistic is a value obtained from testing the sample that indicates whether to accept or reject the null hypothesis. In their book entitled Statistical Techniques in Business & Economics, Mason and Lind indicates that there are many test statistics (p. 349). Test statistics involves converting the sample statistic such as the sample mean (xbar) and the sample standard deviation (s) to a score such as z, t, F and χ2 (Chi Square). The symbols z, t, F and χ2 are test statistics. These are used to determine whether to accept or reject the null hypothesis. DECISION RULE This is a statement of the conditions that need to be met for the null hypothesis to be either accepted or rejected. A sampling distribution involving a one or two tailed test is normally used to determine this. The one tailed test may be a right or left tailed test whereby the rejection region is found to the right or left of a critical value of a normal distribution. DECISION The decision is to accept or reject the null hypothesis based on the results of the sample tested. The use of level of significance and critical values to serve as a means by which the confidence with which the null hypothesis is accepted or rejected and the dividing point between which the null hypothesis is accepted and the region where it is not accepted respectively. Some criticisms have been leveled at the use of hypothesis testing. In fact, Gardener and Altman in their article entitled Confidence intervals rather than P values: estimation rather than hypothesis testing indicates that over emphasizing hypothesis testing and using P-values to separate significant from insignificant results has detracted from the use of other useful ways of interpreting results such as estimation and the use of confidence intervals (p. 746). Works Cited Gardener, Martin J and Altman, Douglas G. Confidence intervals rather than P values: estimation rather than hypothesis testing. British Medical Journal, 292 (1986): 746 – 750, Print Hypothesis Testing. Morgan State University: School of Engineering. n.d. Web. 5 September 2012. < http://www.eng.morgan.edu/~slh/hypo.html> Mason, Robert D and Lind, Douglas A. Statistical Techniques in Business & Economics. 9th ed. USA: Irwin, 1996. Print Triola, Mario F. Elementary Statistics. 11th ed. USA: Addison Wesley, 2008. Print Read More