BUSN5000 HW5 Part B

9/25/23, 5 : 37 PM Homework 5: Measurement Error and Sample Selection Page 1 of 10 https://chris-cornwell.shinyapps.io/Assignment_5/#section-b.-empirical-exercise B. Empirical exercise Using the Project Star data provided in the AER package, you will estimate the e ! ect of class size on student achievement. Substantively, you will be replicating the Column (1) results in Table V of Krueger (1999), except with testing data reported in raw scores, not percentiles. Thus, the scale of your estimated e ! ects will be di ! erent. A few provenance questions Using the STAR data vignette located here (https://cran.r- project.org/web/packages/AER/AER.pdf) answer a few questions about the provenance of the data you we using in this exercise. Question 1: The data set has _____ observations and _____ variables. The data set has _____ observations and _____ variables. The data set has _____ observations and _____ variables. The data set has _____ observations and _____ variables. 11598, 47 Correct! Question 2: The STAR experiment assigned students to three class types: The STAR experiment assigned students to three class types: The STAR experiment assigned students to three class types: The STAR experiment assigned students to three class types: _____, _____, and _____.(Place them in order of class size _____, _____, and _____.(Place them in order of class size _____, _____, and _____.(Place them in order of class size _____, _____, and _____.(Place them in order of class size smallest to largest) smallest to largest) smallest to largest) smallest to largest) small, regular, regular+aide Correct! Question 3: A small class was defined as having between _____ and _____ A small class was defined as having between _____ and _____ A small class was defined as having between _____ and _____ A small class was defined as having between _____ and _____ students. students. students. students. 13, 17 Correct! Homework 5: Homework 5: Measurement Measurement Error and Error and Sample Sample Selection Selection A. Short answer (https://chris- cornwell.shinyapps.io/Assignment_5/#section- a.-short- answer) B. Empirical exercise (https://chris- cornwell.shinyapps.io/Assignment_5/#section- b.- empirical- exercise) Submission Start Over

9/25/23, 5 : 37 PM Homework 5: Measurement Error and Sample Selection Page 2 of 10 https://chris-cornwell.shinyapps.io/Assignment_5/#section-b.-empirical-exercise Question 4: A regular class was defined as having between _____ and _____ A regular class was defined as having between _____ and _____ A regular class was defined as having between _____ and _____ A regular class was defined as having between _____ and _____ students. students. students. students. 22, 25 Correct! Continue Estimating class-size effects using original and new students Now let’s turn to the estimation of class-size e ! ects, comparing the findings for the original kindergartners with the larger sample that includes new students who entered the experiment in later grades. The first order of business is to attach the data and create the test score variables. Section 2 of the slide deck can help with this. R Code ! Start Over ▶ Run Code ge ge… <fct> ethnicity ethnicity <fct> birth birth <yearqtr> stark stark <fct> star1 star1 <fct> star2 star2 <fct> 1122 female afam 1979 Q3 # load the library with the data data(STAR) # load the specific dataset STAR2 <- STAR %>% mutate( scorek= readk + mathk, # create the kinderga score1= read1 + math1, # create the 1st grad score2= read2 + math2, # create the 2nd grad score3= read3 + math3 # create the 3rd grad ) STAR2 NA NA NA 1 2 3 4 5 6 7 8 9 10

9/25/23, 5 : 37 PM Homework 5: Measurement Error and Sample Selection Page 4 of 10 https://chris-cornwell.shinyapps.io/Assignment_5/#section-b.-empirical-exercise Test scores by class type, Kindergarten grade stark stark regular regular small small regular+aide regular+aide Variable Variable N Mean Mean SD SD N Mean Mean SD SD N Mean Mean SD SD scorek 2005 918 73 1738 932 76 2043 918 71 Test scores by class type, 1st grade stark stark regular regular small small regular+aide regular+aide Variable Variable N Mean Mean SD SD N Mean Mean SD SD N Mean Mean SD SD score1 1456 1057 91 1339 1076 95 1503 1054 91 Test scores by class type, 2nd grade stark stark regular regular small small regular+aide regular+aide Variable Variable N Mean Mean SD SD N Mean Mean SD SD N Mean Mean SD SD score2 1201 1179 83 1080 1189 85 1183 1175 83 Test scores by class type, 3rd grade stark stark regular regular small small regular+aide regular+aide Variable Variable N Mean Mean SD SD N Mean Mean SD SD N Mean Mean SD SD score3 1047 1247 70 937 1258 73 1021 1247 73 #Generate summary statistics for Kindergarten st(STAR2, vars=c('scorek'), group='stark', title="Test scores by class type, Kindergarte #Generate summary statistics for 1st grade st(STAR2, vars=c('score1'), group='stark', title="Test scores by class type, 1st grade") #Generate summary statistics for 2nd grade st(STAR2, vars=c('score2'), group='stark', title="Test scores by class type, 2nd grade") 1 2 3 4 5 6 7 8 9 10

9/25/23, 5 : 37 PM Homework 5: Measurement Error and Sample Selection Page 5 of 10 https://chris-cornwell.shinyapps.io/Assignment_5/#section-b.-empirical-exercise Question 6: The di ! erence is average test scores between regular and small The di ! erence is average test scores between regular and small The di ! erence is average test scores between regular and small The di ! erence is average test scores between regular and small classes for kindergartners amounts to roughly _____ of a classes for kindergartners amounts to roughly _____ of a classes for kindergartners amounts to roughly _____ of a classes for kindergartners amounts to roughly _____ of a regular-class standard deviation. (Round to the nearest decile regular-class standard deviation. (Round to the nearest decile regular-class standard deviation. (Round to the nearest decile regular-class standard deviation. (Round to the nearest decile percentage.) percentage.) percentage.) percentage.) 20% Correct! Question 7: The largest di ! erence in average test scores between small and The largest di ! erence in average test scores between small and The largest di ! erence in average test scores between small and The largest di ! erence in average test scores between small and regular classes is in _____ grade. regular classes is in _____ grade. regular classes is in _____ grade. regular classes is in _____ grade. first Correct! Question 8: Between kindergarten and first grade, sample size _____ by Between kindergarten and first grade, sample size _____ by Between kindergarten and first grade, sample size _____ by Between kindergarten and first grade, sample size _____ by _____ students. _____ students. _____ students. _____ students. increases, 593 Correct! Question 9: The largest di ! erence in average test scores between regular The largest di ! erence in average test scores between regular The largest di ! erence in average test scores between regular The largest di ! erence in average test scores between regular and regular+aide classes is _____ points, which occurs in _____ and regular+aide classes is _____ points, which occurs in _____ and regular+aide classes is _____ points, which occurs in _____ and regular+aide classes is _____ points, which occurs in _____ grade. grade. grade. grade. 12, 1st Correct! Next, create a table of tests like in Section 6 of the slide deck for the null of no di ! erence between the average scores of small and regular classes in kindergarten, first, second, and third grades using all students. However, only report the grade level, di ! erence in means and the statistic value. t t

9/25/23, 5 : 37 PM Homework 5: Measurement Error and Sample Selection Page 7 of 10 https://chris-cornwell.shinyapps.io/Assignment_5/#section-b.-empirical-exercise first Correct! Question 12: The di ! erences in means in Table 5 are _____ than those The di ! erences in means in Table 5 are _____ than those The di ! erences in means in Table 5 are _____ than those The di ! erences in means in Table 5 are _____ than those reported in Section 6 of the deck, which compares only the reported in Section 6 of the deck, which compares only the reported in Section 6 of the deck, which compares only the reported in Section 6 of the deck, which compares only the _____ STAR participants. _____ STAR participants. _____ STAR participants. _____ STAR participants. greater, original Correct! Question 13: The di ! erences in means reported in Section 6 of the deck are The di ! erences in means reported in Section 6 of the deck are The di ! erences in means reported in Section 6 of the deck are The di ! erences in means reported in Section 6 of the deck are statistically _____ at the 5-percent level. statistically _____ at the 5-percent level. statistically _____ at the 5-percent level. statistically _____ at the 5-percent level. significant Correct! Continue Do aides matter? Up to this point, we have not considered whether teachers’ aides matter. Focusing on the kindergartners, replicate Figure 1 in the deck, comparing regular and regular+aid class types. R Code ! Start Over ▶ Run Code ggplot(data = subset(STAR2, stark=="regular" | st aes(x=scorek, fill=as.factor(stark), color=as.factor(stark))) + geom_density(alpha=0.4) + labs( title="Figure 1. Empirical test score distrib x="Kindergarten test score", y="Density" ) 1 2 3 4 5 6 7 8 9

9/25/23, 5 : 37 PM Homework 5: Measurement Error and Sample Selection Page 8 of 10 https://chris-cornwell.shinyapps.io/Assignment_5/#section-b.-empirical-exercise Finally, conduct a test of the null that there is no di ! erence in the average test scores of regular and regular+aide classes. Warning: Removed 377 rows containing non-finit Warning: Removed 377 rows containing non-finit e values (`stat_density()`). e values (`stat_density()`). t R Code ! Start Over ▶ Run Code Welch Two Sample t-test Welch Two Sample t-test data: scorek by stark data: scorek by stark t = -0.13824, df = 4038.2, p-value = 0.8901 t = -0.13824, df = 4038.2, p-value = 0.8901 alternative hypothesis: true difference in mea alternative hypothesis: true difference in mea ns between group regular and group regular+aid ns between group regular and group regular+aid e is not equal to 0 e is not equal to 0 95 percent confidence interval: 95 percent confidence interval: -4.766247 4.138376 -4.766247 4.138376 sample estimates: sample estimates: mean in group regular mean in group regul mean in group regular mean in group regul ar+aide ar+aide 918.0429 9 918.0429 9 18.3568 18.3568 t.test(scorek~ stark, data = subset(STAR2, stark= 1 2 3

9/25/23, 5 : 37 PM Homework 5: Measurement Error and Sample Selection Page 10 of 10 https://chris-cornwell.shinyapps.io/Assignment_5/#section-b.-empirical-exercise