Hypothesis testing


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Hypothesis testing

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Hypothesis testing

  1. 1. Hypothesis Testing-Chi-Square Test <br />SHAMEER P.H<br />dept. of futures studies 2010-'12<br />
  2. 2. REWIND YOUR MIND<br />Hypothesis-<br /><ul><li>mere assumption to be proved or disproved
  3. 3. normal question that intends to resolve
  4. 4. tentative formulated for empirical testing
  5. 5. tentative answer to research question
  6. 6. point to start a research</li></ul>dept. of futures studies 2010-'12<br />
  7. 7. Research Questions and Hypotheses<br />Research question:<br />Non-directional:<br />No stated expectation about outcome<br />Example:<br />Do men and women differ in terms of conversational memory?<br />Hypothesis:<br />Statement of expected relationship<br />Directionality of relationship<br />Example:<br />Women will have greater conversational memory than men<br />dept. of futures studies 2010-'12<br />
  8. 8. The Null Hypothesis<br />Null Hypothesis - the absence of a relationship<br />E..g., There is no difference between men’s and women’s with regards to conversational memories<br />Compare observed results to Null Hypothesis<br />How different are the results from the null hypothesis?<br />We do not propose a null hypothesis as research hypothesis - need very large sample size / power<br />Used as point of contrast for testing<br />dept. of futures studies 2010-'12<br />
  9. 9. Hypotheses testing<br />When we test observed results against null:<br />We can make two decisions:<br />1. Accept the null<br />No significant relationship<br />Observed results similar to the Null Hypothesis<br />2. Reject the null<br />Significant relationship<br />Observed results different from the Null Hypothesis<br />Whichever decision, we risk making an error<br />dept. of futures studies 2010-'12<br />
  10. 10. Type I and Type II Error<br />1. Type I Error<br />Reality: No relationship<br />Decision: Reject the null<br />Believe your research hypothesis have received support when in fact you should have disconfirmed it<br />Analogy: Find an innocent man guilty of a crime<br />2. Type II Error<br />Reality: Relationship<br />Decision: Accept the null<br />Believe your research hypothesis has not received support when in fact you should have rejected the null.<br />Analogy: Find a guilty man innocent of a crime<br />dept. of futures studies 2010-'12<br />
  11. 11. Potential outcomes of testing<br /> Decision<br />Accept NullReject Null<br />R No <br />E Relationship<br />A<br />L<br />I <br />T<br />Y Relationship<br />Correct<br />decision<br />Type I Error <br />Correct<br />decision<br />Type II Error <br />dept. of futures studies 2010-'12<br />
  12. 12. Start by setting level of risk of making a Type I Error<br />How dangerous is it to make a Type I Error:<br />What risk is acceptable?:<br />5%? <br />1%?<br />.1%? <br />Smaller percentages are more conservative in guarding against a Type I Error<br />Level of acceptable risk is called “Significance level” :<br />Usually the cutoff - <.05<br />dept. of futures studies 2010-'12<br />
  13. 13. Steps in Hypothesis Testing<br /> State research hypothesis<br /> State null hypothesis<br />Decide the appropriate test criterion( eg. t test, χ2 test, F test etc.)<br />Set significance level (e.g., .05 level)<br /> Observe results<br /> Statistics calculate probability of results if null hypothesis were true<br /> If probability of observed results is less than significance level, then reject the null<br />dept. of futures studies 2010-'12<br />
  14. 14. Guarding against Errors<br />Significance level regulates Type I Error<br />Conservative standards reduce Type I Error:<br />.01 instead of .05, especially with large sample<br />Reducing the probability of Type I Error:<br />Increases the probability of Type II Error<br />Sample size regulates Type II Error<br />The larger the sample, the lower the probability of Type II Error occurring in conservative testing<br />dept. of futures studies 2010-'12<br />
  15. 15. Methods used to test hypothesis<br /><ul><li>T test
  16. 16. Z test
  17. 17. F test
  18. 18. χ2test
  19. 19. ……..</li></ul>dept. of futures studies 2010-'12<br />
  20. 20. Testing hypothesis for two nominal variables<br />Variables Null hypothesis Procedure<br />Gender <br /> Passing is not Chi-square<br /> related to gender <br />Pass/Fail<br />dept. of futures studies 2010-'12<br />
  21. 21. Testing hypothesis for one nominal and one ratio variable<br />Variables Null hypothesis Procedure<br />Gender <br /> Score is not T-test<br /> related to gender <br />Test score<br />dept. of futures studies 2010-'12<br />
  22. 22. Testing hypothesis for one nominal and one ratio variable<br />Variable Null hypothesis Procedure<br />Year in school <br /> Score is not <br /> related to year in ANOVA<br /> school <br />Test score<br />Can be used when nominal variable has more than two categories and can include more than one independent variable<br />dept. of futures studies 2010-'12<br />
  23. 23. Testing hypothesis for two ratio variables<br />Variable Null hypothesis Procedure<br />Hours spent <br />studying Score is not <br /> related to hours Correlation<br /> spent studying <br />Test score<br />dept. of futures studies 2010-'12<br />
  24. 24. Testing hypothesis for more than two ratio variables<br />Variable Null hypothesis Procedure<br />Hours spent <br />studying Score is positively <br /> related to hours <br />Classes spent studying and Multiple <br />missed negatively related regression<br /> to classes missed<br />Test score<br />dept. of futures studies 2010-'12<br />
  25. 25. Chi square (χ2 ) test<br />dept. of futures studies 2010-'12<br />
  26. 26. Used to:<br />Test for goodness of fit<br />Test for independence of attributes<br />Testing homogeneity<br />Testing given population variance<br />dept. of futures studies 2010-'12<br />
  27. 27. Chi-Square Test of Independence<br />dept. of futures studies 2010-'12<br />
  28. 28. Introduction (1)<br />We often have occasions to make comparisons between two characteristics of something to see if they are linked or related to each other.<br />One way to do this is to work out what we would expect to find if there was no relationship between them (the usual null hypothesis) and what we actually observe.<br />dept. of futures studies 2010-'12<br />
  29. 29. Introduction (2)<br />The test we use to measure the differences between what is observed and what is expected according to an assumed hypothesis is called the chi-square test.<br />dept. of futures studies 2010-'12<br />
  30. 30. For Example<br />Some null hypotheses may be:<br />‘there is no relationship between the subject of first period and the number of students absent in our class’.<br />‘there is no relationship between the height of the land and the vegetation cover’.<br />‘there is no connection between the size of farm and the type of farm’<br />dept. of futures studies 2010-'12<br />
  31. 31. Important<br />The chi square test can only be used on data that has the following characteristics:<br />The frequency data must have a precise numerical value and must be organised into categories or groups.<br />The data must be in the form of frequencies<br />The expected frequency in any one cell of the table must be greater than 5. <br />The total number of observations must be greater than 20.<br />dept. of futures studies 2010-'12<br />
  32. 32. Contingency table<br />Frequency table in which a sample from a population is classified according to two attributes, which are divided in to two or more classes<br />dept. of futures studies 2010-'12<br />
  33. 33. Degrees of Freedom<br /><ul><li>no of independent observations
  34. 34. Number of cells – no. of constraints </li></ul>dept. of futures studies 2010-'12<br />
  35. 35. Formula<br />χ2 = ∑ (O – E)2<br />E<br />χ2 = The value of chi square<br />O = The observed value<br />E = The expected value<br />∑ (O – E)2 = all the values of (O – E) squared then added together<br />dept. of futures studies 2010-'12<br />
  36. 36. Critical region:<br />dept. of futures studies 2010-'12<br />
  37. 37. dept. of futures studies 2010-'12<br />
  38. 38. Construct a table with the information you have observed or obtained.<br />Observed Frequencies (O)<br />dept. of futures studies 2010-'12<br />
  39. 39. Expected frequency = row total x column total<br />Grand total<br />Now<br />Work out the expected frequency.<br />dept. of futures studies 2010-'12<br />
  40. 40. (O – E)2<br />E<br />Now<br />For each of the cells calculate.<br />dept. of futures studies 2010-'12<br />
  41. 41. χ2Calc. = sum of all ( O-E)2/ E values in the cells. <br />Here χ 2Calc. =36.873<br />Find χ 2critical From the table with degree of freedom 2 and level of significance 0.05<br />χ 2Critical =5.99<br />dept. of futures studies 2010-'12<br />
  42. 42. Χ2table<br />dept. of futures studies 2010-'12<br />
  43. 43. Conclusion <br />Compareχ2Calc.and Χ2critical obtained from the table<br />Ifχ2Calc. Is larger thanχ2Critical.then reject null hypothesis and accept the alternative<br />Here since χ 2Calc.is much greater than χ 2Critical, we can easily reject null hypothesis<br /> that is ; there lies a relation between the gender and choice of selection.<br />dept. of futures studies 2010-'12<br />
  44. 44. Reference <br />RESEARCH METHODOLGIES <br /> - L R Potti<br />dept. of futures studies 2010-'12<br />