Testing of Hypothesis.pptx

Statistics

1. Testing of Hypothesis Dr.C.Hemamalini Assistant Professor Department of Economics Ethiraj College for women Chennai

2. Procedure of Testing Hypothesis Types of Errors Introduction Tail test of Hypothesis CONTENTS

3. Introduction Hypothesis testing was introduced by Ronald Fisher, Jerzy Neyman , Karl Pearson and Pearson’s son, Egon Pearson. Hypothesis testing is a statistical method that is used in making statistical decisions using experimental data. Hypothesis Testing is basically an assumption that we make about the population parameter. A premise or claim that we want to test.

4. Define According to Prof. Morris Hamburg “ A hypothesis in statistics is simply a quantitative statement about population” Palmer O Johnson has described hypothesis as “Islands in the uncharted seas of thought to be used as a bases for consolidation and recuperation as we have advance into the unknown”

5. Hypothesis Testing A hypotheses is a proposition which the researcher wants to verify. To test some hypothesis about parent population from which the sample is drawn Estimation to use the statistics obtained from sample as estimate of the unknown parameter of the population from which the sample is drawn .

6. Need for Testing Hypothesis To make a assumption of a future event that is likely going to happen. Without a hypothesis the researcher will be conducting studies will be able to obtain hypothetical results. By testing Hypothesis one may able to predict the information that is needed in the moment but it may not be a accurate result just an estimate .

7. Procedure of Testing Hypotheis 1.Formulate a hypothesis 2.Set up a suitable significance level 3.Choose a test criterion. 4.Compute 5.Make decisions

8. Formulate a Hypothesis To set up a hypothesis about a population parameter. The conventional approach to hypothesis testing is to set up two hypothesis instead of one in such a way that if one hypothesis is accepted , the other is rejected and viceversa. The two hypotheses are: i)Null hypothesis ii)Alternative hypothesis The term “null” means nothing or invalid. Let us assume that the mean of the population is u.

9. Formulate a Hypothesis Since we have assumed that the population has a mean µ 0, Then our null hypothesis is H : µ = µ 0, where H is the null hypothesis. The alternative hypotheses is H a : µ ≠µ 0. The rejection of the null hypothesis will show that the mean of the population is not µ 0. This implies that alternative hypothesis is accepted. It may be noted that one alternative hypothesis can be tested at one time against the null hypothesis.

10. Set Up a Suitable Significance Level The next step is to test its validity at a certain level of significance. The confidence with which a null hypothesis is rejected or accepted depends upon the significance level used for the purpose. A significance level of, say 5 percent, means that in the long run, the risk of making the wrong decision is about 5 percent. A significance level of, say 1 percent, implies that the researcher is running the risk of being wrong in accepting or rejecting the hypothesis in 1 out of every 100 occasions. Thus, a 1 percent, significance level provides greater confidence to the decision than a 5 percent significance level.

11. The diagram illustrates how to interpret a 5 percent level of significance. It may be noted that 2.5 percent of the area under the curve is located in each tail.

12. Setting a Test Criterion The next step in hypothesis testing procedure is to construct test criterion. This involves selecting an appropriate probability distribution for the particular test. There are many techniques from which one is to be chosen. The test criteria which are frequently used in hypothesis testing are Z, t, F, and Chi square test. When the hypothesis pertains to a large sample (30 or more), the Z-test implying normal distribution is used. When a sample is small (less than 30), the use of the Z-test will be inappropriate. Instead, the t-test will be more suitable.

13. Doing Computation The next step is the performance of various computations, necessary for the application of that particular test. These computations include the testing statistic as also its standard error.

14. Make Decisions The last step in hypothesis testing is to draw a statistical decision, involving the acceptance or rejection of the null hypothesis. This will depend on whether the computed value of the test criterion falls in the region of acceptance or in the region of rejection at a given level of significance. It may be noted that the statement rejecting the hypothesis is much stronger than the statement accepting the hypothesis. It is much easier to prove something false than to prove it true.

15. Concepts for Hypothesis Sample Distribution. Null Hypothesis. Alternative Hypothesis. Type I and Type II Error. One Tailed And Two Tailed Test

16. Sample Distribution When Population is very large and for collecting it’s information the resource requirement is high, so a representative sample ( i.e. a small number of elements of the population and which represents to an extent every major characteristics of the population .) is selected by the research conducting authorities and through the use of various methods information about the sample is collected which can be later applied on to the population.

17. Sample distribution The distribution so formed all possible values of a statistic is called the Sampling Distribution or the Probability distribution of that statistics. If instead of all the items of the universe we study only the small part of it. Sampling distribution is generated from a population distribution known or assumed

18. the same population may generate an infinite number of sampling distributions for the statistic each for special sample size n. Population may generate sampling distributions for two or more different statistics

19. Null Hypothesis The Hypothesis that are made with the intent of receiving a rejection Generally done to show that there is no relationship between two or more things. Alternative Hypothesis Rejection of null hypothesis leads to acceptance of alternative hypothesis. Thus stating that there is a relationship between two or more things.

20. Errors in Testing of Hypothesis Type I Error When Null Hypothesis is rejected but it is true. The hypothesis is true and our test accepts it. Probability of Type I error is α called level of significance. Type II Error When Null Hypothesis is accepted but it is false. The hypothesis is false and our test rejects it. Probability of Type Error is β called power of test.

21. Type I Error VS Type II Error Type I Type II Definition Type 1 error, in statistical hypothesis testing, is the error caused by rejecting a null hypothesis when it is true. Type II error is the error that occurs when the null hypothesis is accepted when it is not true. Also termed Type I error is equivalent to false positive. Type II error is equivalent to a false negative. Meaning It is a false rejection of a true hypothesis. It is the false acceptance of an incorrect hypothesis. Symbol Type I error is denoted by α. Type II error is denoted by β. T

22. Type I Type II Probability The probability of type I error is equal to the level of significance. The probability of type II error is equal to one minus the power of the test. Reduced It can be reduced by decreasing the level of significance. It can be reduced by increasing the level of significance. Cause It is caused by luck or chance. It is caused by a smaller sample size or a less powerful test. What is it? Type I error is similar to a false hit. Type II error is similar to a miss. Hypothesis Type I error is associated with rejecting the null hypothesis. Type II error is associated with rejecting the alternative hypothesis. When does it happen? It happens when the acceptance levels are set too lenient. It happens when the acceptance levels are set too stringent.

23. Tail Tests 1. One-Tailed. 2. Two-Tailed. One Tailed If the Null Hypothesis gets rejected when the value of a test statistic falls in one specific tale of the normal distribution. Two Tailed If null hypothesis gets rejected when a value of the test statistic falls in either one or the other of the two tails of its sampling distribution.

24. One -tailed tests One tail test because the rejection region will be located in one side One tail which may be either left or right depending upon alternative hypothesis formulated

25. Two-tailed Tests A two tailed test of hypothesis will reject the null hypothesis Two tail test the rejection region is located in both the tails, Testing hypothesis at 5 perecent level of significance the size of the acceptance region on each side of mean would be 0.475 and the size if the rejection region is 0.025 An area of 0.475 corresponds to 1.96 atandard error on each side the hypothetical mean and the acceptnace region. The acceptance and rejection regions for testing hypothesis st the .05 level of significance. Suitable for all categories business and personal presentation

26. To reduce the risk of committing an error Type I A hypothesis may be treated at .01 level of significance The probability of rejecting the hypothesis is 1 percent. The table areas under the normal curve an acceptance region of 0.495 is equal to 2.58 Standard Error The probability of rejecting or accepting hypothesis is 1 percent

27. Thank You Reference: Statistical Methods by S.P.Gupta