Stat 13 UCLA, Statistics Statistical Methods for Life and Health Sciences I.D. Dinov, M. Zheng, J. Miller ChiChiChiChi----square Goodnesssquare Goodnesssquare Goodnesssquare Goodness----ofofofof----fit testfit testfit testfit test For this lab, we are going to see how STATA performs the Chi-square goodness-of-fit test. About the data . use http://www.ats.ucla.edu/stat/stata/notes/hsb2 The data used here is called hsb2, high school and beyond. This data file contains 200 observations from a sample of high school students with demographic information about the students, such as their gender (female), socio-economic status (ses) and ethnic background (race). It also contains a number of scores on standardized tests, including tests of reading (read), writing (write), mathematics (math) and social studies (socst). Today’s Lab First of all, look at the dataset: . describe Let’s look at “race”, which is the variable we are interested in. Here, please note that race is stored using real (floating point) numbers not strings. . sort race . list race so we can see that race==1 denotes Hispanic, race==2 denotes Asian, race==3 denotes African-American, and race==4 denotes white. Q1: What is the proportion of students of each race?Stat 13 UCLA, Statistics Statistical Methods for Life and Health Sciences I.D. Dinov, M. Zheng, J. Miller Now suppose the true proportion of the races is 10% for Hispanic and 10% for Asian, and 10% for African-American, and 70% for whites. We are going to test whether there is statistical evidence that there is significant difference between the given true proportions and the observed sample proportions. In STATA the Chi-Square (χ2) goodness of fit test is invoked by csgof: . csgof race, expperc(10 10 10 70) We obtain a p-value is 0.16. How do you interpret these findings and what are your conclusions, based on this result? Q2: What are your conclusions about the test reuslts? What should the null & the alternative hypotheses be? What is the degree of freedom? Next, let’s look at ses ( socio-economic status) variable. In the sample, are the proportions in each social-economic group the same. Q3: What should be the expected proportions in this case? We now perform a Chi-Square (χ2) goodness of fit test to investigate equal proportions: . csgof ses, expperc(33.3333,33.3333,33.3334) Q4: What do you think about our belief now? What should H0 and H1 be? What is the degree of freedom? Q5: Investigate if there are differences between the reading and writing literacy
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