Hypothesis testing and parametric test

In the presentation, hypothesis test has been explained with scrap. Tree diagram is there to understand in which situation u can apply which parametric test

1. Hypothesis Testing Dr. Keerti Jain NIIT University, Neemrana

2. Some Important Terms Population Sample Population Parameter Sample Statistic Point Estimation Interval Estimation Confidence Interval 19-05-2019 Dr.Keerti Jain, NIIT University 2

3. Hypothesis A statistical hypothesis is a claim (assertion, statement, belief or assumption) about an unknown population parameter value. 19-05-2019 Dr.Keerti Jain, NIIT University 3

4. Hypothesis Testing The process that enables a decision maker to test the validity (or significance) of his claim by analysis the difference between the value of sample statistics and the corresponding hypothesized population parameter value, is called hypothesis testing. 19-05-2019 Dr.Keerti Jain, NIIT University 4

5. Steps of Hypothesis Testing Step1: State the Null Hypothesis and Alternate Hypothesis Step II: State the level of significance. Step III: Select the suitable test of significance or Test Statistic. Step IV: Interpretation (Decision). 19-05-2019 Dr.Keerti Jain, NIIT University 5

6. Errors in Hypothesis Testing Decision State of Nature Type I error ( α ) Correct decision with confidence (1- β ) Correct decision with confidence (1- α ) Type II error ( β ) 19-05-2019 Dr.Keerti Jain, NIIT University 6

7. Elements of a Hypothesis Test Null hypothesis – The null hypothesis represents the claim or statement made about the value or the population parameter. It is denoted by , where H stands for hypothesis and zero stands for no difference between sample statistic and parameter value Alternative hypothesis - Statement contradictory to the null hypothesis (will always contain an inequality). It is denoted by   19-05-2019 Dr.Keerti Jain, NIIT University 7

8. Directional Hypothesis (One tailed test) Example: :There is no difference between the average pulse rates of men and women. : Men have lower average pulse rates than women do. Non Directional Hypothesis (Two tailed test) Example: : There is no difference between the average pulse rates of men and women. :There is difference between the average pulse rates of men and women. : 19-05-2019 Dr.Keerti Jain, NIIT University 8

9. One Tailed Test (Directional) Left tailed test 19-05-2019 Dr.Keerti Jain, NIIT University 9  

10. Contd … Right tailed test 19-05-2019 Dr.Keerti Jain, NIIT University 10  

11. Two Tailed Test (Non Directional) 19-05-2019 Dr.Keerti Jain, NIIT University 11

12. 19-05-2019 Dr.Keerti Jain, NIIT University 12

13. Certain Critical Values for Sample Statistic Z Rejection Region Level of Significance, α per cent α = 0.10 α =0.05 α =0.01 α =0.005 One-tailed region Two -tailed region 19-05-2019 Dr.Keerti Jain, NIIT University 13

14. Contd … Test statistic = 19-05-2019 Dr.Keerti Jain, NIIT University 14

15. Formulate a Decision Rule to Accept Null Hypothesis The decision rules falls within the area of acceptance: If calculated absolute value of test statistic is less than or equal to its critical (tabulated) value, then accept the null hypothesis Otherwise reject null hypothesis. 19-05-2019 Dr.Keerti Jain, NIIT University 15

16. P - Value ………….???? It provides an alternative way to decide whether a null hypothesis is to be accepted. Probability Value or p - value is the probability of observing a sample outcome even more extreme than the observed value when the null hypothesis is true. The smaller the p - value, the smaller are the chances that variations are caused by chance/random factors. It is also called observed level of significance. 19-05-2019 Dr.Keerti Jain, NIIT University 16

17. P-value….??? Contd.. It has following advantages and that’s the reason mostly statistical softwares are giving printouts with p - values: It allows a decision maker to use his/her own level of significance and make decision accordingly once sample results are available with necessary statistic t provides very precise information about the highest level of significance at which the null hypothesis must be accepted . 19-05-2019 Dr.Keerti Jain, NIIT University 17

18. Example An auto company decided to introduce a new six cylinder car whose mean petrol consumption is claimed to be lower than that of the existing auto engine. It was found that the mean petrol consumption for 50 cars was 10 km per litre with a standard deviation of 3.5 km/ litre . Test for the company at 5 percent level of significance, the claim that in the new car petrol consumption is 9.5 km per litre on the average. 19-05-2019 Dr.Keerti Jain, NIIT University 18

19. Solution km/ litre km/litre Step 2: At 5% level of significance. Step 3: Given at α =0.05 level of significance. Thus using z-test statistics at α =0.05 level of significance.   19-05-2019 Dr.Keerti Jain, NIIT University 19

20. Contd.. Therefore null hypothesis is accepted. Hence the new car’s petrol consumption is 9.5 km/ litre . The p-value approach : The probability of finding is 0.3437 (from normal table). The p-value is the area to the right as well as left of the calculated value of z-test statistic (for two-tailed test). Since Therefore p-value = 2(0.1563)= 0.3126 > α =0.05, the null hypothesis is accepted.   19-05-2019 Dr.Keerti Jain, NIIT University 20

21. For every hypothesis-testing problem, we require a test which may be … PARAMETRIC NON PARAMETRIC 19-05-2019 Dr.Keerti Jain, NIIT University 21

22. Types of Variables Nominal Variable Ordinal Variable Interval Variable Ratio Variable 19-05-2019 Dr.Keerti Jain, NIIT University 22

23. PARAMETRIC TEST ... A PARAMETRIC test is a test whose model requires and specifies certain conditions about the parameters of the population from which the sample is drawn. Such tests makes certain assumptions about the nature of the underlying population like Normal Probability Distribution and their validity rests upon the validity of these assumptions. These test are more powerful and strong in their assertions and are usually applicable when data is interval scale or Ratio Scale. These tests are very much rich and developed. 19-05-2019 Dr.Keerti Jain, NIIT University 23

24. NON PARAMETRIC TESTS... These are the tests whose model does not specify conditions and assumptions about the parameters of the population; they lack parameters. These are widely used for nominal or ordinal data where no parametric tests is applicable. These tests are not very powerful and strong in their assertions. Non-parametric statistical tests are typically much easier to learn and apply than are parametric tests. These tests usually convert data into ranks or signs and thereby may loose some important information. 19-05-2019 Dr.Keerti Jain, NIIT University 24

25. TESTS RELATED TO INTERVAL/RATIO SCALE DATA – ONE SAMPLE ONE SAMPLE INTERVAL/RATIO SCALE DATA VARIATION TESTS CENTRAL TENDENCY TESTS c 2 USE Z-TEST or t-TEST 19-05-2019 Dr.Keerti Jain, NIIT University 25

26. Example of One Sample Has a visitor of the site placed an order. (Proportion test)- t-test or z-test. A study of incidence of heart diseases in the middle-age workers in Indian Managers. (Mean test)- t-test or z-test. It is claimed the Indian stock markets are not very risky as compared to other emerging markets. (Variability test)- Chi-Square test. 19-05-2019 Dr.Keerti Jain, NIIT University 26

27. TEST RELATED TO INTERVAL/RATIO SCALE – TWO SAMPLES TWO SAMPLES INTERVAL/RATIO SCALE DATA RELATED SAMPLES UNRELATED SAMPLES PAIRED t-TEST USE Z-TEST OR t-TEST FOR DIFFERENCES IN MEANS & PROPORTIONS VARIATION TEST F-TEST 19-05-2019 Dr.Keerti Jain, NIIT University 27

28. Examples of Two Samples Rozana is a retail chain. They have launched a special incentive point scheme in NCR region which run for last 6 months. To know whether such an incentive programme has any impact on sales. Related samples- (Difference in central tendency )- Paired t-test. The social conditions of Textile workers in India- A comparative study Delhi and Mumbai- Unrelated Samples- (Mean test)- z-test or t-test . Which stock exchange has more fluctuations in prices –BSE or NSE. Unrelated Samples- (Variability) - F-test . 19-05-2019 Dr.Keerti Jain, NIIT University 28

29. TEST RELATED TO INTERVAL/RATIO SCALE – MORE THAN TWO SAMPLES MORE THAN 2 SAMPLES INTERVAL/RATIO SCALE DATA ANALYSIS OF VARIANCE 19-05-2019 Dr.Keerti Jain, NIIT University 29

30. Reference J.K Sharma, Business Statistics, Pearson education. Srivastava, Rego , Statistics for Management, Tata Mcgrawhill . Johna S. Croucher , Statistics: Making Business Decisions, McGrawhill . Levin, Rubin, Statistics for Management, Pearson Prentice hall. Render, Stair, Hanna, Badri , Quantitative Analysis for Management, Pearson Prentice hall. http://www.graphpad.com/support/faqid/1089/ 19-05-2019 Dr.Keerti Jain, NIIT University 30

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