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Virtual Lecture-22: Inferential Statistics Recap and Problems

In this virtual lecture, Assistant Professor Ossam Chohan will recap the previous session and discuss problems related to Fisher's Exact test, test for homogeneity, and goodness of fit using Chi Square. Learn key concepts and examples.

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Virtual Lecture-22: Inferential Statistics Recap and Problems

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  1. Virtual COMSATSInferential StatisticsLecture-22 Ossam Chohan Assistant Professor CIIT Abbottabad

  2. Recap of last lecture • In our last sessions, we worked on: • Test for independence. • Practice problem. • Assessment Problems.

  3. Objective of lecture-22 • In this lecture, we will understand problems related to: • Fisher’s Exact test. • Test for homogeneity. • Goodness of fit. • Review of Chi Square.

  4. Fisher’s Exact test for 2*2 Contingency Table • When frequencies in a 2*2 contingency table are fairly small, typical chi square approach creates some doubts about adequacy. • An exact test is recommended by Fisher. • No comparison is made on observed and expected frequencies. • Exact test based on exact probabilities of each cell for all values. • More explanation in following example.

  5. Problem-20 • Use the Fisher’s exact test to test the hypothesis that inoculation is independent of immunity from attack among a population exposed to a certain disease, given the following data:

  6. Problem-20 Solution

  7. Problem-20 Solution

  8. Problem-20 Solution

  9. Assessment Problem-19 • Suppose that a number of patients were treated for cancer with results as in the following table: • Use Fisher’s exact test to test the independence.

  10. The chi square test of homogeneityBrandt-Snedecor formula • In a certain city, a random sample of 50 men and another sample of 50 women over 21 years of age were asked about their educational background, classified as Secondary, college or university education. The results were: • Test whether the two samples are homogeneous in respect of educational levels at 5% level of significance.

  11. Problem-21 Solution

  12. Cont…

  13. Goodness of Fit-Chi square A statistical method used to determine goodness of fit Goodness of fit refers to how close the observed data are to those predicted from a hypothesis Note: The chi square test does not prove that a hypothesis is correct It evaluates to what extent the data and the hypothesis have a good fit

  14. The Chi Square Test-Goodness of fit The general formula is (O – E)2 c2 =S E • With n-k-1 degrees of freedom • where • O = observed data in each category • E = observed data in each category based on the experimenter’s hypothesis • S = Sum of the calculations for each category

  15. Problem-22 • In the accounting department of a bank 100 accounts are selected at random and examined fro errors. The following results have been obtained. • Does this information verify that the errors are distributed according to Poisson probability law?

  16. Problem-22 Solution

  17. Problem-22 Solution

  18. Assessment Problem-20 • Suppose that 6 coins are tossed simultaneously 640 times and the following frequency distribution is observed: • Test the null hypothesis that the coins are well-balanced. Use 5% level of significance.

  19. Review of Chi-Square • In chi-square unit, we discussed the following points: • Hypothesis testing for variances. • Hypothesis testing for independence. • Special case of independence for 2*2. • Hypothesis testing for homogeneity. • Goodness of fit.

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