1 / 17

Ch 26 – Comparing Counts Day 1 - The Chi-Square Distribution

Part VII – Exploring and Understanding Data. Ch 26 – Comparing Counts Day 1 - The Chi-Square Distribution. The Chi-Square Test. The Chi-square test has two uses: Goodness of fit: to determine if data fits a given distribution

marioneal
Download Presentation

Ch 26 – Comparing Counts Day 1 - The Chi-Square Distribution

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. Part VII – Exploring and Understanding Data Ch 26 – Comparing CountsDay 1 - The Chi-Square Distribution

  2. The Chi-Square Test • The Chi-square test has two uses: • Goodness of fit: to determine if data fits a given distribution • Independence: to determine if there is a relationship between two categorical variables

  3. The Chi-square test statistic • The basic idea behind chi-square is to see if what really happened is significantly different from what you expected to happen • The formula for a chi-square test statistic is:

  4. Decisions using Chi-square • We use chi-square only for hypothesis tests – no confidence intervals • Once we get a test statistic, we use the chi-square table to make a decision as to whether or not to reject H0 • The table works in a similar way to the t-table

  5. Goodness of Fit Test • A botanist wants to know if a certain insect has a preference in the color of roses it eats. She records the number of insects who infest each color in her study.

  6. Hypotheses • For this type of test there are no symbols in the hypotheses, only words • The null hypothesis basically states that there is nothing unusual going on • In this case: H0: the insects have no color preference Ha: the insects do have a color preference

  7. Type of Test • Chi-square test for goodness of fit • α = .05 • df = 3 • For goodness of fit tests: df = # of categories – 1

  8. Make sure you show your expected counts somewhere in your problem Conditions for Chi-square

  9. Expected Values • The expected values are based on your null hypothesis • In this problem, if our null hypothesis was true, all cells would have the same value

  10. Conditions for Chi-square(This problem)

  11. The test statistic

  12. Conclusion • Since p < .05, reject H0. There is enough evidence to conclude that the insects do have a color preference.

  13. Another example… • An anatomy teacher hypothesizes that the final grades in her classes are distributed as 10% A’s, 23% B’s, 45% C’s, 14% D’s and 8% F’s. At the end of the semester, a random sample of her students has the following grades. Was her hypothesis correct?

  14. Expected Values • 10% A’s, 23% B’s, 45% C’s, 14% D’s and 8% F’s • Total in sample = 53 5.3 12.19 23.85 7.42 4.24

  15. H0: The distribution does fit the teacher’s hypothesisHa: The distribution doesn’t fit the teacher’s hypothesis Χ2 test for goodness of fit, α=.05, df =4 Stated Since p >.05, fail to reject H0. There is not enough evidence to conclude that the teacher’s grades do not fit her hypothesis. No – one count is < 5 this concerns us, but we will proceed

  16. Homework 26-1 • GOF WS

More Related