1 / 24

GOODNESS OF FIT TEST & CONTINGENCY TABLE

CHAPTER 6 BCT2053. GOODNESS OF FIT TEST & CONTINGENCY TABLE. 6.1 Introduction 6.2 Goodness of Fit Test 6.3 Contingency Table. Contents. Define the main situations when a chi-square distribution and significance test is used. 6.1 Introduction. Lesson outcomes:

deiter
Télécharger la présentation

GOODNESS OF FIT TEST & CONTINGENCY TABLE

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. CHAPTER 6BCT2053 GOODNESS OF FIT TEST &CONTINGENCY TABLE

  2. 6.1 Introduction 6.2 Goodness of Fit Test 6.3 Contingency Table Contents

  3. Define the main situations when a chi-square distribution and significance test is used. 6.1 Introduction Lesson outcomes: By the end of this topic you should be able to:

  4. When to use Chi-Square Distribution • Find confidence Interval for a variance or standard deviation • Test a hypothesis about a single variance or standard deviation • Tests concerning frequency distributions (Goodness of Fit) • Test the Independence of two variables (Contingency Table) • Test the homogeneity of proportions (Contingency Table)

  5. Test a distribution for goodness of fit using Chi-square 6.2 Goodness of Fit Test Lesson outcomes: By the end of this topic you should be able to:

  6. When to use Chi-Square Goodness of fit test • When you have some practical data and you want to know how well a particular statistical distribution, such as binomial or normal, models the data. • Example: To meet customer demands, a manufacturer of running shoes may wish to see whether buyers show a preference for a specific style. If there were no preference, one would expect each style to be selected with equal frequency.

  7. Hypothesis Null and Alternative • H0 : There is No difference or no change • Example: Buyers show no preference for a specific style. • H1 : There is a difference or change • Example: Buyers show a preference for a specific style.

  8. Formula and Assumptions • Formula • Where O = observed frequency E = expected frequency (equal frequency = 1/category) • With degree of freedom equal to the number of categories minus 1 • Assumptions • The data are obtained from a random sample • The expected frequency for each category must be 5 or more

  9. Procedure • State the hypothesis and identify the claim, • Compute the test value. • Find the critical value. The test is always right-tailed since O – E are square and always positive. • Make the decision – reject Ho if • Summarize the result.

  10. Why this test is called goodness of fit • If the graph between observed values and expected values is fitted, one can see whether the values are close together or far apart. • When observed values and expected values are close together: • the chi-square test value will be small. • Decision must be not reject Ho (accept Ho). • Hence there is a “good fit”. • When observed values and expected values are far apart: • the chi-square test value will be large. • Decision must be reject Ho (accept H1). • Hence there is a “not a good fit”.

  11. Example 1 : goodness of fit test • A market analyst whished to see whether consumers have any preference among five flavors of a new fruit soda. A sample of 100 people provided these data. Is there enough evidence to reject the claim that there is no preference in the selection of fruit soda flavors at 0.05 significance level?

  12. Another Applications • H0 is that the particular distributions does provide a model for the data. • Example: state the claim distribution • H1 is that it does not. • Example: The distribution is not same as stated in the null hypothesis Expected value (E) = given percentage × sample size

  13. Example 2 : goodness of fit test • The adviser of an ecology club at a college believes that the group consists of 10% freshmen, 20% sophomores, 40% juniors, and 30% seniors. The membership for the club this year consisted of 14 freshmen, 19 sophomores, 51 juniors, and 16 seniors. At α = 0. 10, test the adviser’s conjecture.

  14. Example 3 : goodness of fit test • According to a particular genetic theory, the colour of strains (pink, white and blue) in a certain flower should appear in the ratio 3:2:5. In 200 randomly chosen plants, the corresponding numbers of each colour were 48, 28 and 124. Test at the 1% significance level, whether the theory is true.

  15. EXCEL application • Insert – functions - CHITEST P-value Reject H0 if P-value ≤ α

  16. Test two variables for independence using Chi-square Test proportions for homogeneity using Chi-square 6.3 Contingency Table Lesson outcomes: By the end of this topic you should be able to:

  17. The Chi-Square Independence Test • To test the independence of two tests • H0 : The tests are independent (x has no relationship with y) • H1 : The tests are not independent (x has relationship with y) • Reject H0 if where and I = ROW (x) J =COLUMN (y) Row sum Column sum Grand total Observed values Expected values

  18. Example 4: Chi-Square Independence Test • The data below shows the number of insomnia patient according to their smoking habit in Malaysia. At α = 0.01, Can we say that insomnia is independent with smoking habit?

  19. Example 5: Chi-Square Independence Test • A researcher wishes to see if the way of people obtain information is not related with their educational background. A survey of 400 high school and college graduates yielded the following information. At α = 0.05, can the researcher conclude that the way people obtain information is not related with their educational background?

  20. Example 6 : Chi-Square Independence Test • A sociologist wishes to see whether the number of years of college a person has completed is related to his or her place of residence. A sample of 88 people is selected and classified as shown. At 0.05 significance level, can the sociologist conclude that the years of college education are dependent on the person’s location?

  21. Test for Homogeneity of Proportions • Samples are selected from several different populations and the researcher is interested in determining whether the proportions of elements that have a common characteristics are the same for each population. • H0 : • H1 : At least one proportion is different from the others • Reject H0 if where and

  22. Example 7 : Homogeneity Test for Proportions • A researcher selected a sample of 50 seniors from each of three area high schools and asked each senior, “ Do you drive to school in a car owned by either you or your parent?”. The data are shown in the table. At 0.05 , test the claim that the proportion of students who drive their own or their parents’ car is the same at all three schools.

  23. SUMMARY • Three uses of the Chi-Square distribution were explained in this chapter: • Test a distribution for goodness of fit using Chi-square • Test two variables for independence using Chi-square • Test proportions for homogeneity using Chi-square • The test is always a right tailed test:

  24. THE END

More Related