STATA OUTPUT AND GRAPHS FOR FINAL EXAM
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STATA OUTPUT AND GRAPHS FOR FINAL EXAM
Instructions for the materials
This material packet contains 22 “exhibits” – Stata output, graphs, or tables – for four research questions. The final exam will ask questions about these exhibits. Not all exhibits will necessarily be covered in the final exam and the final exam may ask questions about topics not directly examined in the materials. You may take notes on this packet in any way that you wish. There are two blank pages at the end of the packet for additional notes. You may not add any more pages – your material packet should have a total of single sided 23 pages.
A suggestion to use this material packet: Examine the output and graphs presented here in the context of the material covered in class. And think about what questions could be asked about them, using the problem sets and class slides as guides.
Data and Research Questions: Two Data sets are used for the exam: California school districts data and ECLS -K-2011.
1. The exam will use California school districts data (posted in Canvas) for the research questions 1 and 2 on non-linearity and interactions. We will examine these with this data and output/graphs presented in exhibits 20-22. The data description and variables are presented below. Exhibits 20-22 will be used for the questions for this data.
Key Variables
dist_code: district Code;
Read_scr: avg Reading Score;
Math_scr: avg Math Score;
County : county;
District: District;
gr_span: grade span of district;
enrl_tot : total enrollment;
teachers: number of teachers;
computer: number of computers;
testscr: avg test score (= (read_scr+math_scr)/2 );
comp_stu: computers per student ( = computer/enrl_tot);
expn_stu: expentitures per student ($’s);
str: student teacher ratio (enrl_tot/TEACHERS);
el_pct: percent of English Learners;
Meal_pct: Percent qualifying for reduced-price lunch;
cAlw_pct: Percent qualifying for CalWorks;
avGinc: district average income (in $1000's);
Research Questions:
1. Are there nonlinear effects of class size reduction on test scores? That is, does a reduction from 35 to 30 have same effect as a reduction from 20 to 15?
2. Are there non-linear interactions between PctEL (percent of English Learners) and STR (student teacher ratio)? (Are small classes more effective when there are many English learners?)
2. The exam uses data from ECLS-K-2011 to examine the relationship between private school attendance and teacher perceptions of student behavior. The third research question will ask you to describe the type of students that attend private school. The fourth research question will ask you to investigate the relationship between private school attendance and teacher perceptions of student behavior. The materials also include some relevant exploratory data analysis, and are generally organized as follows:
· Exhibits 1-9: Exploratory data analysis and relevant descriptive statistics (relevant to both research questions)
· Exhibits 10-13: Exhibits relevant to Research Question 3
· Exhibits 14-19: Exhibits relevant to Research Question 4
Key variables:
X2TCHCON teacher reported self control (spring)
X2TCHPER teacher reported interpersonal skills (spring)
X2ATTNFS teacher reported attentional focus (spring)
X2INBCNT teacher reported inhibitory control (spring)
Fall versions of these variables that begin with X1
ZBEHAVE2 (spring) and ZBEHAVE1 (fall) indices of teacher perceived behavior standardized in the analysis sample. Stata Code for the construction of these variables:
**Generate standardized indices of teacher perceptions of student behavior**
foreach v of varlist X2TCHCON X2TCHPER X2ATTNFS X2INBCNT X1TCHCON X1TCHPER X1ATTNFS X1INBCNT {
egen std_`v'=std(`v')
}
egen behave2=rowmean(std_X2*)
egen behave1=rowmean(std_X1*)
center behave2 , standardize gen(ZBEHAVE2)
center behave1 , standardize gen(ZBEHAVE1)
label var ZBEHAVE2 "Teacher Perceptions of Behavior (Spring, Z-scored)"
label var ZBEHAVE1 "Teacher Perceptions of Behavior (Fall, Z-scored)"
PRIVATE dummy variable indicating if a child attends kindergarten in a private school
ASIAN, BLACK, LATINO, MULTIRACIAL, NATAMER, WHITE dummy variables for racial groups constructed from the RACE6 variable provided by ECLS-K
ZSES socioeconomic status, standardized in the analysis sample
FEMALE a dummy variable for indicating that the child is a girl
NONENGL a dummy variable indicating that the child’s home language is not English
DISABILTY a dummy variable indicating that the child has a disability
Sample restrictions: The sample is restricted to students with non-missing data for all of the above variables (or the variables used to construct the above variables)
Research question 3: What type of students attend private schools?
Research question 4: Do teachers’ perceptions of student behavior differ across school sectors (public vs. private)?
Exhibit 1: Principal components analysis of spring teacher reported self control, interpersonal skills, attentional focus, and inhibitory control (X2TCHCON X2TCHPER X2ATTNFS X2INBCNT)
pca X2TCHCON X2TCHPER X2ATTNFS X2INBCNT, means
Principal components/correlation Number of obs = 8921
Number of comp. = 4
Trace = 4
Rotation: (unrotated = principal) Rho = 1.0000
--------------------------------------------------------------------------
Component | Eigenvalue Difference Proportion Cumulative
-------------+------------------------------------------------------------
Comp1 | 3.05158 2.47495 0.7629 0.7629
Comp2 | .576633 .366531 0.1442 0.9071
Comp3 | .210102 .048416 0.0525 0.9596
Comp4 | .161686 . 0.0404 1.0000
--------------------------------------------------------------------------
Principal components (eigenvectors)
--------------------------------------------------------------------
Variable | Comp1 Comp2 Comp3 Comp4 | Unexplained
-------------+----------------------------------------+-------------
X2TCHCON | 0.5057 -0.4715 -0.3810 0.6138 | 0
X2TCHPER | 0.5004 -0.4890 0.5653 -0.4370 | 0
X2ATTNFS | 0.4748 0.6538 0.4443 0.3869 | 0
X2INBCNT | 0.5181 0.3334 -0.5812 -0.5316 | 0
--------------------------------------------------------------------
Exhibit 2: Screeplot of the eigenvalues after the above PCA (spring variables)
Exhibit 3: Principal components analysis of fall teacher reported self control, interpersonal skills, attentional focus, and inhibitory control (X1TCHCON X1TCHPER X1ATTNFS X1INBCNT)
pca X1TCHCON X1TCHPER X1ATTNFS X1INBCNT, means
Principal components/correlation Number of obs = 8921
Number of comp. = 4
Trace = 4
Rotation: (unrotated = principal) Rho = 1.0000
--------------------------------------------------------------------------
Component | Eigenvalue Difference Proportion Cumulative
-------------+------------------------------------------------------------
Comp1 | 3.0154 2.43384 0.7538 0.7538
Comp2 | .581558 .354863 0.1454 0.8992
Comp3 | .226695 .0503479 0.0567 0.9559
Comp4 | .176347 . 0.0441 1.0000
--------------------------------------------------------------------------
Principal components (eigenvectors)
--------------------------------------------------------------------
Variable | Comp1 Comp2 Comp3 Comp4 | Unexplained
-------------+----------------------------------------+-------------
X1TCHCON | 0.5030 -0.4766 -0.5136 0.5060 | 0
X1TCHPER | 0.4972 -0.5030 0.6214 -0.3373 | 0
X1ATTNFS | 0.4826 0.6188 0.3804 0.4893 | 0
X1INBCNT | 0.5167 0.3700 -0.4532 -0.6251 | 0
--------------------------------------------------------------------
Exhibit 4: Screeplot of the eigenvalues after the above PCA (fall variables)
Exhibit 5: Summary statistics of key variables for the analysis
sum ZBEHAVE2 ZBEHAVE1 PRIVATE ZSES FEMALE WHITE BLACK LATINO ASIAN ///
NATAMER MULTI NONENGL DISABILITY , sep(0)
Variable | Obs Mean Std. Dev. Min Max
-------------+--------------------------------------------------------
ZBEHAVE2 | 8921 -2.28e-10 1 -3.487666 1.575331
ZBEHAVE1 | 8921 3.82e-10 1 -3.67505 1.800834
PRIVATE | 8921 .137989 .3449078 0 1
ZSES | 8921 -2.24e-09 1 -2.905879 2.957004
FEMALE | 8921 .4914247 .4999545 0 1
WHITE | 8921 .5529649 .4972147 0 1
BLACK | 8921 .1080596 .3104731 0 1
LATINO | 8921 .2106266 .4077765 0 1
ASIAN | 8921 .0671449 .2502869 0 1
NATAMER | 8921 .0110974 .104764 0 1
MULTIRACIAL | 8921 .0501065 .2181769 0 1
NONENGL | 8921 .1512162 .3582796 0 1
DISABILITY | 8921 .1972873 .3979733 0 1
Exhibit 6: Distribution of ZBEHAVE2 by school, for a subset of schools and Stata code used to generate the graph
sort SCHID
graph box ZBEHAVE2 if SCHID>=1300&SCHID<=1400 , ///
over(SCHID, label(angle(45) labsize(tiny))) ///
nooutsides name(behaveXschool,replace)
Exhibit 7: Cross tabulations of private school status with demographic characteristics
Key
|----------------|
| frequency |
| row percentage |
+----------------+
| CHILD ATTENDS PRIVATE SCHOOL
ASIAN | PUBLIC PRIVATE | Total
-----------+----------------------+----------
No | 7,193 1,129 | 8,322
| 86.43 13.57 | 100.00
-----------+----------------------+----------
Yes | 497 102 | 599
| 82.97 17.03 | 100.00
-----------+----------------------+----------
BLACK | PUBLIC PRIVATE | Total
-----------+----------------------+----------
No | 6,820 1,137 | 7,957
| 85.71 14.29 | 100.00
-----------+----------------------+----------
Yes | 870 94 | 964
| 90.25 9.75 | 100.00
-----------+----------------------+----------
LATINO | PUBLIC PRIVATE | Total
-----------+----------------------+----------
No | 5,983 1,059 | 7,042
| 84.96 15.04 | 100.00
-----------+----------------------+----------
Yes | 1,707 172 | 1,879
| 90.85 9.15 | 100.00
-----------+----------------------+----------
MULTIRACIAL| PUBLIC PRIVATE | Total
-----------+----------------------+----------
No | 7,312 1,162 | 8,474
| 86.29 13.71 | 100.00
-----------+----------------------+----------
Yes | 378 69 | 447
| 84.56 15.44 | 100.00
-----------+----------------------+----------
NAT.AMERICAN| PUBLIC PRIVATE | Total
-----------+----------------------+----------
No | 7,604 1,218 | 8,822
| 86.19 13.81 | 100.00
-----------+----------------------+----------
Yes | 86 13 | 99
| 86.87 13.13 | 100.00
-----------+----------------------+----------
WHITE | PUBLIC PRIVATE | Total
-----------+----------------------+----------
No | 3,538 450 | 3,988
| 88.72 11.28 | 100.00
-----------+----------------------+----------
Yes | 4,152 781 | 4,933
| 84.17 15.83 | 100.00
-----------+----------------------+----------
Total | 7,690 1,231 | 8,921
| 86.20 13.80 | 100.00
Key
|----------------|
| frequency |
| row percentage |
+----------------+
| CHILD ATTENDS PRIVATE SCHOOL
LANGUAGE | PUBLIC PRIVATE | Total
-----------+----------------------+----------
ENGLISH | 6,449 1,123 | 7,572
| 85.17 14.83 | 100.00
-----------+----------------------+----------
NON-ENGLISH| 1,241 108 | 1,349
| 91.99 8.01 | 100.00
-----------+----------------------+----------
DISABILITY | PUBLIC PRIVATE | Total
-----------+----------------------+----------
NO | 6,120 1,041 | 7,161
| 85.46 14.54 | 100.00
-----------+----------------------+----------
YES | 1,570 190 | 1,760
| 89.20 10.80 | 100.00
-----------+----------------------+----------
GENDER | PUBLIC PRIVATE | Total
-----------+----------------------+----------
MALE | 3,923 614 | 4,537
| 86.47 13.53 | 100.00
-----------+----------------------+----------
FEMALE | 3,767 617 | 4,384
| 85.93 14.07 | 100.00
-----------+----------------------+----------
Total | 7,690 1,231 | 8,921
| 86.20 13.80 | 100.00
Exhibit 8: Distribution of ZBEHAVE1 and ZBEHAVE2, by private school status
bys PRIVATE: su ZBEHAVE1
-> PUBLIC
Variable | Obs Mean Std. Dev. Min Max
-------------+---------------------------------------------------------
ZBEHAVE1 | 7,690 -.0201468 1.007677 -3.67505 1.800834
-> PRIVATE
Variable | Obs Mean Std. Dev. Min Max
-------------+---------------------------------------------------------
ZBEHAVE1 | 1,231 .1258559 .9413133 -2.907247 1.800834
bys PRIVATE: su ZBEHAVE2
-> PUBLIC
Variable | Obs Mean Std. Dev. Min Max
-------------+---------------------------------------------------------
ZBEHAVE2 | 7,690 -.0049717 1.005333 -3.487666 1.575331
-> PRIVATE
Variable | Obs Mean Std. Dev. Min Max
-------------+---------------------------------------------------------
ZBEHAVE2 | 1,231 .0310581 .9658383 -3.292697 1.575331
Exhibit 9: Kernel densities of ZBEHAVE1 and ZBEHAVE2 by private school status
Exhibit 10: The probability of attending private school by SES for locally weighted scatterplot smoothing (“LOWESS”) and the fitted values from a logistic regression with private school as the outcome and ZSES as the predictor
Exhibit 11: Stata output from a logistic regression of private school status on SES, indicators for race/ethnicity, home language, disability status, gender, and the interactions between SES and race/ethnicity groups
Log-odds:
Logistic regression Number of obs = 8,921
LR chi2(14) = 619.90
Prob > chi2 = 0.0000
Log likelihood = -3270.0123 Pseudo R2 = 0.0866
------------------------------------------------------------------------------------
PRIVATE | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------------+----------------------------------------------------------------
ZSES | .6452725 .0464642 13.89 0.000 .5542044 .7363406
BLACK | -.1698165 .1279719 -1.33 0.185 -.4206368 .0810038
LATINO | -.0199731 .1053526 -0.19 0.850 -.2264604 .1865141
ASIAN | -.0802641 .1831387 -0.44 0.661 -.4392093 .2786811
NATAMER | .1520036 .332461 0.46 0.648 -.499608 .8036151
MULTIRACIAL | -.0140527 .1650163 -0.09 0.932 -.3374787 .3093733
BLACK#c.ZSES | .446846 .1335925 3.34 0.001 .1850096 .7086824
LATINO#c.ZSES | .370618 .1018251 3.64 0.000 .1710446 .5701915
ASIAN#c.ZSES | -.0282525 .1274395 -0.22 0.825 -.2780292 .2215243
NATAMER#c.ZSES | .8569835 .4880388 1.76 0.079 -.099555 1.813522
MULTIRACIAL#c.ZSES | .0733108 .142324 0.52 0.606 -.2056392 .3522609
FEMALE | .0300211 .0641863 0.47 0.640 -.0957819 .155824
NONENGL | -.151067 .1339794 -1.13 0.260 -.4136618 .1115277
DISABILITY | -.3117393 .0871495 -3.58 0.000 -.4825491 -.1409294
_cons | -1.900224 .0614793 -30.91 0.000 -2.020721 -1.779726
------------------------------------------------------------------------------------
Odds-ratios:
Logistic regression Number of obs = 8,921
LR chi2(14) = 619.90
Prob > chi2 = 0.0000
Log likelihood = -3270.0123 Pseudo R2 = 0.0866
------------------------------------------------------------------------------------
PRIVATE | Odds Ratio Std. Err. z P>|z| [95% Conf. Interval]
-------------------+----------------------------------------------------------------
ZSES | 1.906506 .0885843 13.89 0.000 1.740556 2.08828
BLACK | .8438196 .1079852 -1.33 0.185 .6566285 1.084375
LATINO | .980225 .1032692 -0.19 0.850 .7973509 1.205042
ASIAN | .9228726 .1690136 -0.44 0.661 .6445459 1.321386
NATAMER | 1.164164 .3870392 0.46 0.648 .6067685 2.233601
MULTIRACIAL | .9860456 .1627136 -0.09 0.932 .7135672 1.362571
BLACK#c.ZSES | 1.563374 .2088549 3.34 0.001 1.20323 2.031313
LATINO#c.ZSES | 1.44863 .1475068 3.64 0.000 1.186544 1.768606
ASIAN#c.ZSES | .9721429 .1238894 -0.22 0.825 .7572747 1.247978
NATAMER#c.ZSES | 2.356043 1.14984 1.76 0.079 .9052402 6.132006
MULTIRACIAL#c.ZSES | 1.076065 .1531499 0.52 0.606 .8141268 1.422279
FEMALE | 1.030476 .0661425 0.47 0.640 .9086622 1.168621
NONENGL | .8597901 .1151941 -1.13 0.260 .6612246 1.117985
DISABILITY | .7321724 .0638085 -3.58 0.000 .617208 .8685506
_cons | .1495352 .0091933 -30.91 0.000 .1325599 .1686843
------------------------------------------------------------------------------------
Exhibit 12: The probability of attending a private school by SES, for students of different race/ethnicity groups, controlling for home language, disability, and gender
Note: If you have difficulty distinguishing the lines, use the regression output from Exhibit 12 to guide you.
2021-12-25