Ch 15 - Chi-Squared _Categorical Data_


Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: tistic Our measure of how close the observed counts are to what we expect under the null hypothesis. 21 33.352 36 19.97 2 30 23.682 48 35.652 26 32.032 19 25.322 X2 33.35 29.97 23.68 35.65 32.03 25.32 14.5 Do you think a value of X 2 14.5 is large enough to reject H0? The next step is to find the p‐value, the probability of getting an X 2 test statistic value as large or larger than the one we observed, assuming H0 is true. To do this we need to know the distribution of the X 2 test statistic under the null hypothesis. If H0 is true, then X 2 has the 2 distribution with degrees of freedom = (r‐1)(c‐1) 217 Aside: Using our frame of reference for chi‐square distributions. If H0 were true, we would expect the X 2 test statistic to be about 2 give or take about sqrt(2*2) = 2 . About how many standard deviations is the observed X 2 value of 14.5 from the expected value under H0? What do you think the decision will be? (14.5 – 2)/2 = 6.25 about 6 standard deviations above the expected value under H0. Find the p‐value for our factory worker example: Observed X 2 test statistic value = 14.5 df = 2 Find the p‐value and use it to determine if the results are statistically significant at the 1% significance level. Sketch the distribution to show the bounds are: p‐value < 0.001 So the results are statistically significant at the 1% level. Conclusion at a 1% level: It appears that .... there is an association between smoking and hypertension for the population of factory workers represented by this sample. Test of Independence Summary Assume: We have 1 random sample of size n . We measure 2 discrete responses: X which has r possible outcomes and Y which has c possible outcomes. Test: H0: The two variables X and Y are independent for the population. Test Statistic: X 2 observed - expected2 expected (row total)(column total) where expected Total n If H0 is true, then X 2 has a 2 distribution with ( r 1)(c 1) degrees of freedom. The necessary conditions are: at least 80% of the expected counts are greater than 5 and none are less than 1. 218 Relationship between Age Group and Appearance Satisfaction Are you satisfied with your overall appearance? A random sample of 150 women were surveyed. Their answer to this question (Yes or No) was recorded along with their age category (1 = under 30, 2 = 30 to 50, and 3 = over 50). SPSS was used to generate the following output from the data. Are You Satisfied? * Age Group Crosstabulation Count Are You Satisfied? Yes No Total under 30 38 10 48 Age Group 30 to 50 30 29 59 over 50 34 9 43 Total 102 48 150 Chi-Square Tests Pearson Chi-Square Likelihood Ratio Linear-by-Linear Association N of Valid Cases Value 13.149 13.039 .018 df 2 2 Asymp. Sig. .001 .001 1 .893 150 a. Give the name of the test to be used for assessing if there is a relationship between age group and appearance satisfaction. __ Chi‐squared test of independence ______________________ b. Assuming there is no relationship between age group and app...
View Full Document

This document was uploaded on 02/25/2014 for the course STATS 250 at University of Michigan.

Ask a homework question - tutors are online