Evaluated on behalf of Borough Hall and New Dorp High School by Fil Babalievsky and Atishay Sehgal
This is a replication file for Babalievsky and Sehgal (2018), an evaluation of Project SPARK.
First we load prerequisite pack and set our working directory to the path with the data (not a local file--we cannot store the data in a public repo.)
setwd("~/Dropbox/New SI Stuff/SPARK Eval")
knitr::opts_knit$set(root.dir = "~/Dropbox/New SI Stuff/SPARK Eval")
#install.packages("tidyverse")
#install.packages("stargazer")
#install.packages("Rcurl")
#install.packages("dplyr")
#install.packages("readxl")
#install.packages("anonymizer")
library(tidyverse)## ── Attaching packages ────────────────────────────────────────────────────── tidyverse 1.2.1 ──
## ✔ ggplot2 3.0.0.9000 ✔ purrr 0.2.5
## ✔ tibble 1.4.2 ✔ dplyr 0.7.5
## ✔ tidyr 0.8.1 ✔ stringr 1.3.1
## ✔ readr 1.1.1 ✔ forcats 0.3.0
## ── Conflicts ───────────────────────────────────────────────────────── tidyverse_conflicts() ──
## ✖ dplyr::filter() masks stats::filter()
## ✖ dplyr::lag() masks stats::lag()library(dplyr)
library(stargazer)##
## Please cite as:
## Hlavac, Marek (2018). stargazer: Well-Formatted Regression and Summary Statistics Tables.
## R package version 5.2.2. https://CRAN.R-project.org/package=stargazerlibrary(RCurl)## Loading required package: bitops
##
## Attaching package: 'RCurl'
## The following object is masked from 'package:tidyr':
##
## completelibrary(readxl)
library(anonymizer)Next we import a function for clustered standard errors.
# import the function from repository
# thanks https://economictheoryblog.com/2016/12/13/clustered-standard-errors-in-r/
url_robust <- "https://raw.githubusercontent.com/IsidoreBeautrelet/economictheoryblog/master/robust_summary.R"
eval(parse(text = getURL(url_robust, ssl.verifypeer = FALSE)),
envir=.GlobalEnv)First we import data for the ninth graders in the Health Sciences SLC in New Dorp High who are enrolled in SPARK. Note that there are 57 students in SPARK and 37 students in New Dorp's 9th grade class not in SPARK. The seventh tab of the Excel file holds data for SPARK students in their first marking periods in English, math, and science. There are 171 observations, 3 classes times 51 students.
hs_spark_1<-read_excel("SPARK 2017 HN copy.xlsx", sheet = 7, col_names = FALSE)
names(hs_spark_1)<-c("StudentID", "Course", "Mark1")
nrow(hs_spark_1)## [1] 171#dummy for Spark participation
hs_spark_1$Spark<-1
#dummy for New Dorp High School students
hs_spark_1$HS<-1Next we import data for ninth graders who are in the Health Sciences SLC in New Dorp High School but not in SPARK. There are 111 observations, 3 classes times 37 students.
hs_nonspark_1<-read_excel("SPARK 2017 HN copy.xlsx", sheet = 8, col_names = FALSE)
names(hs_nonspark_1)<-c("StudentID", "Course", "Mark1")
#dummy for SPARK non-participation
hs_nonspark_1$Spark<-0
#dummy for New Dorp High School Students
hs_nonspark_1$HS<-1
nrow(hs_nonspark_1)## [1] 111Here we combine the results from the first marking period with those of the second marking period.
first<-rbind(hs_spark_1, hs_nonspark_1)
all_mp_2<-read_excel("SPARK MP2 Grades copy.xlsx", sheet = 1)
names(all_mp_2)## [1] "StudentID" "Course" "Mark"names(all_mp_2)<-c("StudentID", "Course", "Mark2")
total<-left_join(first, all_mp_2, by=c("StudentID", "Course"))
total$diff<-as.numeric(as.character(total$Mark2))-as.numeric(as.character(total$Mark1))## Warning: NAs introduced by coerciontotal_hs<-total[total$HS==1,]
nrow(total_hs[total_hs$Spark==0,])## [1] 111nrow(total_hs[total_hs$Spark==1,])## [1] 171Next we look at the data from marking periods 3 and 4 and try to merge them with the data from periods 1 and 2.
three_and_four_again<-read_excel("SPARK 2017 Term 2 MP3 and MP4 copy.xlsx", sheet = 1)
names(three_and_four_again)<-c("StudentID", "Blank1", "Blank2", "Course", "Blank3", "Blank4", "Blank5", "Blank6", "MP3", "MP4", "Final")
total_hs<-total[total$HS==1,]
total_hs$firsfour<-substr(total_hs$Course, 1, 4)
total_hs$lastthree<-substr(total_hs$Course, 6, 8)
total_hs$Course<-paste(total_hs$firsfour, total_hs$lastthree, sep="2")
nrow(total_hs)## [1] 282Final<-left_join(total_hs, three_and_four_again, by=c("StudentID", "Course"))
nrow(Final)## [1] 282nrow(Final[Final$Spark==0,])## [1] 111nrow(Final[Final$Spark==1,])## [1] 171Final$Final <- NULLNext we run our regressions. All our observations are at the student-subject level. The first three regressions have the following format:
Δ=α+β×SPARK
Here Δ is the difference in grades for a student-subject between marking period 1 and a subsequent marking period, α is a constant, and β is the coefficient on a dummy variable taking value 1 if and only if the student is in SPARK. The next three regressions have the format:
Δ=α+∑i(βi×SPARK×Classi)+∑i(γi×Classi)
Here, γ is the coefficient on a specific subject--Math, English, or Science. A high value for, say γm, the coefficient on math, tells us that student performance declined less in math than in the "default" subject (here chosen as science.) A high value for βm would therefore imply that students in SPARK saw even smaller decreases in math performance than non-SPARK students.
Final$diff1<-as.numeric(as.character(Final$Mark2))-as.numeric(as.character(Final$Mark1))## Warning: NAs introduced by coercionFinal$diff2<-as.numeric(as.character(Final$MP3))-as.numeric(as.character(Final$Mark1))## Warning: NAs introduced by coercionFinal$diff3<-as.numeric(as.character(Final$MP4))-as.numeric(as.character(Final$Mark1))## Warning: NAs introduced by coercionsummary(Final$diff1)## Min. 1st Qu. Median Mean 3rd Qu. Max. NA's
## -29.000 -9.000 -5.000 -4.905 0.000 23.000 9lm1<-lm(diff1~Spark,data=Final)
summary(lm1)##
## Call:
## lm(formula = diff1 ~ Spark, data = Final)
##
## Residuals:
## Min 1Q Median 3Q Max
## -25.0059 -4.0059 0.3846 3.9941 26.9941
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -6.3846 0.7333 -8.707 3.13e-16 ***
## Spark 2.3905 0.9320 2.565 0.0109 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 7.478 on 271 degrees of freedom
## (9 observations deleted due to missingness)
## Multiple R-squared: 0.0237, Adjusted R-squared: 0.0201
## F-statistic: 6.579 on 1 and 271 DF, p-value: 0.01086summary(lm1, cluster=c("StudentID"))##
## Call:
## lm(formula = diff1 ~ Spark, data = Final)
##
## Residuals:
## Min 1Q Median 3Q Max
## -25.0059 -4.0059 0.3846 3.9941 26.9941
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -6.385 NA NA NA
## Spark 2.391 NA NA NA
##
## Residual standard error: 7.478 on 271 degrees of freedom
## (9 observations deleted due to missingness)
## Multiple R-squared: 0.0237, Adjusted R-squared: 0.0201
## F-statistic: NaN on 1 and 0 DF, p-value: NAlm2<-lm(diff2~Spark,data=Final)
summary(lm2)##
## Call:
## lm(formula = diff2 ~ Spark, data = Final)
##
## Residuals:
## Min 1Q Median 3Q Max
## -39.713 -6.165 0.835 7.287 24.835
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -8.8350 0.9733 -9.077 <2e-16 ***
## Spark 0.5475 1.2479 0.439 0.661
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 9.878 on 261 degrees of freedom
## (19 observations deleted due to missingness)
## Multiple R-squared: 0.0007368, Adjusted R-squared: -0.003092
## F-statistic: 0.1925 on 1 and 261 DF, p-value: 0.6612lm3<-lm(diff3~Spark,data=Final)
summary(lm3)##
## Call:
## lm(formula = diff3 ~ Spark, data = Final)
##
## Residuals:
## Min 1Q Median 3Q Max
## -33.413 -4.192 0.029 4.587 24.587
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -6.0291 0.7667 -7.864 9.86e-14 ***
## Spark 1.4416 0.9829 1.467 0.144
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 7.781 on 261 degrees of freedom
## (19 observations deleted due to missingness)
## Multiple R-squared: 0.008174, Adjusted R-squared: 0.004374
## F-statistic: 2.151 on 1 and 261 DF, p-value: 0.1437Final$coursechar<-as.character(Final$Course)
Final$Type<-substr(Final$coursechar, 1, 1)
Final$Spark_math<-0
Final$Spark_math[Final$Spark==1&Final$Type=="M"]<-1
Final$Spark_sci<-0
Final$Spark_sci[Final$Spark==1&Final$Type=="S"]<-1
Final$Spark_eng<-0
Final$Spark_eng[Final$Spark==1&Final$Type=="E"]<-1
Final$math<-0
Final$math[Final$Type=="M"]<-1
Final$sci<-0
Final$sci[Final$Type=="S"]<-1
Final$eng<-0
Final$eng[Final$Type=="E"]<-1
lm1_subj<-lm(diff1~Spark_math+Spark_sci+Spark_eng+math+eng,data=Final)
summary(lm1_subj)##
## Call:
## lm(formula = diff1 ~ Spark_math + Spark_sci + Spark_eng + math +
## eng, data = Final)
##
## Residuals:
## Min 1Q Median 3Q Max
## -24.6429 -3.8214 0.1786 3.7059 25.4737
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -8.0857 1.2577 -6.429 5.9e-10 ***
## Spark_math 3.2322 1.6124 2.005 0.0460 *
## Spark_sci 2.9071 1.6033 1.813 0.0709 .
## Spark_eng 0.9857 1.6033 0.615 0.5392
## math 2.3798 1.7917 1.328 0.1852
## eng 2.7429 1.7787 1.542 0.1242
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 7.441 on 267 degrees of freedom
## (9 observations deleted due to missingness)
## Multiple R-squared: 0.04771, Adjusted R-squared: 0.02987
## F-statistic: 2.675 on 5 and 267 DF, p-value: 0.02224summary(lm1_subj, cluster=c("StudentID"))##
## Call:
## lm(formula = diff1 ~ Spark_math + Spark_sci + Spark_eng + math +
## eng, data = Final)
##
## Residuals:
## Min 1Q Median 3Q Max
## -24.6429 -3.8214 0.1786 3.7059 25.4737
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -8.0857 NA NA NA
## Spark_math 3.2322 NA NA NA
## Spark_sci 2.9071 NA NA NA
## Spark_eng 0.9857 NA NA NA
## math 2.3798 NA NA NA
## eng 2.7429 NA NA NA
##
## Residual standard error: 7.441 on 267 degrees of freedom
## (9 observations deleted due to missingness)
## Multiple R-squared: 0.04771, Adjusted R-squared: 0.02987
## F-statistic: NaN on 5 and 0 DF, p-value: NAlm2_subj<-lm(diff2~Spark_math+Spark_sci+Spark_eng+math+eng,data=Final)
summary(lm2_subj)##
## Call:
## lm(formula = diff2 ~ Spark_math + Spark_sci + Spark_eng + math +
## eng, data = Final)
##
## Residuals:
## Min 1Q Median 3Q Max
## -38.396 -5.396 0.333 5.252 23.604
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -3.3714 1.5492 -2.176 0.030452 *
## Spark_math 0.2778 2.0251 0.137 0.891008
## Spark_sci 0.2394 1.9963 0.120 0.904656
## Spark_eng 1.3962 1.9963 0.699 0.484924
## math -8.9619 2.2239 -4.030 7.36e-05 ***
## eng -7.6286 2.1909 -3.482 0.000585 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 9.165 on 257 degrees of freedom
## (19 observations deleted due to missingness)
## Multiple R-squared: 0.153, Adjusted R-squared: 0.1365
## F-statistic: 9.282 on 5 and 257 DF, p-value: 3.854e-08summary(lm2_subj, cluster=c("StudentID"))##
## Call:
## lm(formula = diff2 ~ Spark_math + Spark_sci + Spark_eng + math +
## eng, data = Final)
##
## Residuals:
## Min 1Q Median 3Q Max
## -38.396 -5.396 0.333 5.252 23.604
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -3.3714 NA NA NA
## Spark_math 0.2778 NA NA NA
## Spark_sci 0.2394 NA NA NA
## Spark_eng 1.3962 NA NA NA
## math -8.9619 NA NA NA
## eng -7.6286 NA NA NA
##
## Residual standard error: 9.165 on 257 degrees of freedom
## (19 observations deleted due to missingness)
## Multiple R-squared: 0.153, Adjusted R-squared: 0.1365
## F-statistic: NaN on 5 and 0 DF, p-value: NAlm3_subj<-lm(diff3~Spark_math+Spark_sci+Spark_eng+math+eng,data=Final)
summary(lm3_subj)##
## Call:
## lm(formula = diff3 ~ Spark_math + Spark_sci + Spark_eng + math +
## eng, data = Final)
##
## Residuals:
## Min 1Q Median 3Q Max
## -32.113 -4.560 -0.463 4.368 25.887
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -3.42857 1.30296 -2.631 0.00902 **
## Spark_math 2.85690 1.70323 1.677 0.09469 .
## Spark_sci 0.08895 1.67894 0.053 0.95779
## Spark_eng 1.45606 1.67894 0.867 0.38661
## math -3.96537 1.87038 -2.120 0.03496 *
## eng -3.91429 1.84267 -2.124 0.03460 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 7.708 on 257 degrees of freedom
## (19 observations deleted due to missingness)
## Multiple R-squared: 0.04149, Adjusted R-squared: 0.02284
## F-statistic: 2.225 on 5 and 257 DF, p-value: 0.05233summary(lm3_subj, cluster=c("StudentID"))##
## Call:
## lm(formula = diff3 ~ Spark_math + Spark_sci + Spark_eng + math +
## eng, data = Final)
##
## Residuals:
## Min 1Q Median 3Q Max
## -32.113 -4.560 -0.463 4.368 25.887
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -3.42857 NA NA NA
## Spark_math 2.85690 NA NA NA
## Spark_sci 0.08895 NA NA NA
## Spark_eng 1.45606 NA NA NA
## math -3.96537 NA NA NA
## eng -3.91429 NA NA NA
##
## Residual standard error: 7.708 on 257 degrees of freedom
## (19 observations deleted due to missingness)
## Multiple R-squared: 0.04149, Adjusted R-squared: 0.02284
## F-statistic: NaN on 5 and 0 DF, p-value: NAWe next run three regressions, again with subject dummies, but this time we compare performance between:
Final$diff_intermediate1<-as.numeric(as.character(Final$MP3))-as.numeric(as.character(Final$Mark2))
lm_intermediate1<-lm(diff_intermediate1~Spark_math+Spark_sci+Spark_eng+math+eng,data=Final)
summary(lm_intermediate1)##
## Call:
## lm(formula = diff_intermediate1 ~ Spark_math + Spark_sci + Spark_eng +
## math + eng, data = Final)
##
## Residuals:
## Min 1Q Median 3Q Max
## -30.9259 -4.8056 0.5833 5.8286 22.0741
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 4.806 1.472 3.264 0.00124 **
## Spark_math -3.783 1.917 -1.973 0.04949 *
## Spark_sci -2.880 1.901 -1.515 0.13092
## Spark_eng -0.287 1.901 -0.151 0.88006
## math -10.634 2.097 -5.072 7.45e-07 ***
## eng -10.389 2.082 -4.990 1.10e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 8.833 on 263 degrees of freedom
## (13 observations deleted due to missingness)
## Multiple R-squared: 0.2472, Adjusted R-squared: 0.2329
## F-statistic: 17.27 on 5 and 263 DF, p-value: 8.895e-15Final$diff_intermediate2<-as.numeric(as.character(Final$MP4))-as.numeric(as.character(Final$MP3))
lm_intermediate2<-lm(diff_intermediate2~Spark_math+Spark_sci+Spark_eng+math+eng,data=Final)
summary(lm_intermediate2)##
## Call:
## lm(formula = diff_intermediate2 ~ Spark_math + Spark_sci + Spark_eng +
## math + eng, data = Final)
##
## Residuals:
## Min 1Q Median 3Q Max
## -12.5185 -3.5556 0.0278 2.4815 20.2037
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.02778 0.74732 -0.037 0.970378
## Spark_math 2.86138 0.97301 2.941 0.003566 **
## Spark_sci -0.17593 0.96478 -0.182 0.855450
## Spark_eng 0.37037 0.96478 0.384 0.701369
## math 4.68492 1.06439 4.402 1.56e-05 ***
## eng 3.58333 1.05686 3.391 0.000805 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 4.484 on 263 degrees of freedom
## (13 observations deleted due to missingness)
## Multiple R-squared: 0.2852, Adjusted R-squared: 0.2717
## F-statistic: 20.99 on 5 and 263 DF, p-value: < 2.2e-16Final$diff_ends<-as.numeric(as.character(Final$MP4))-as.numeric(as.character(Final$Mark2))
lm_ends<-lm(diff_ends~Spark_math+Spark_sci+Spark_eng+math+eng,data=Final)
summary(lm_ends)##
## Call:
## lm(formula = diff_ends ~ Spark_math + Spark_sci + Spark_eng +
## math + eng, data = Final)
##
## Residuals:
## Min 1Q Median 3Q Max
## -25.9074 -3.7222 0.9444 4.2222 17.0926
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 4.77778 1.16935 4.086 5.84e-05 ***
## Spark_math -0.92116 1.52251 -0.605 0.545681
## Spark_sci -3.05556 1.50963 -2.024 0.043976 *
## Spark_eng 0.08333 1.50963 0.055 0.956020
## math -5.94921 1.66548 -3.572 0.000421 ***
## eng -6.80556 1.65371 -4.115 5.18e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 7.016 on 263 degrees of freedom
## (13 observations deleted due to missingness)
## Multiple R-squared: 0.1101, Adjusted R-squared: 0.09319
## F-statistic: 6.509 on 5 and 263 DF, p-value: 1.001e-05plot(Final$Mark1)## Warning in xy.coords(x, y, xlabel, ylabel, log): NAs introduced by coercion
plot(Final$Mark2)
plot(Final$MP3)
plot(Final$MP4)
Next, we note that a small number of kids are in a more advanced math course. The first letter of the course identifier indicates the broad subject, whereas the second indicates the specific course. A second letter "E" indicates algebra 1, whereas a second letter "G" indicates a more advanced geometry course. We add dummies for this higher level math course and for its interaction with SPARK. Nothing important changes.
The number of students in a different science level was tiny, so we do not bother cutting up the sample along that dimension.
All students were at the same level of English.
Final$Type2<-substr(Final$coursechar, 1, 2)
Final$adv_math<-0
Final$adv_math[Final$Type2=="MG"]<-1
Final$Spark_adv_math<-0
Final$Spark_adv_math[Final$Spark==1&Final$Type2=="MG"]<-1
lm3_subj_adv<-lm(diff3~Spark_math+Spark_sci+Spark_eng+math+eng+adv_math+Spark_adv_math,data=Final)
summary(lm3_subj_adv)##
## Call:
## lm(formula = diff3 ~ Spark_math + Spark_sci + Spark_eng + math +
## eng + adv_math + Spark_adv_math, data = Final)
##
## Residuals:
## Min 1Q Median 3Q Max
## -32.113 -4.524 -0.113 4.343 25.887
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -3.42857 1.30788 -2.621 0.00928 **
## Spark_math 2.73505 1.78113 1.536 0.12588
## Spark_sci 0.08895 1.68528 0.053 0.95795
## Spark_eng 1.45606 1.68528 0.864 0.38841
## math -3.91518 1.89248 -2.069 0.03957 *
## eng -3.91429 1.84962 -2.116 0.03529 *
## adv_math -1.65625 7.85751 -0.211 0.83322
## Spark_adv_math 2.13995 8.39795 0.255 0.79907
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 7.738 on 255 degrees of freedom
## (19 observations deleted due to missingness)
## Multiple R-squared: 0.04175, Adjusted R-squared: 0.01545
## F-statistic: 1.587 on 7 and 255 DF, p-value: 0.1394Next we look at the kids who left our sample after Marking Period 2. Note that the SPARK students who dropped out of the sample had high MP1 grades, and an MP1 to MP2 drop that was not unusually great. We do not know why they left the sample. The overall number of kids leaving the sample was not great.
dropouts <- Final[which(is.na(Final$MP4)),]
dropouts$anonID<-anonymize(dropouts$StudentID, .n_chars = 5, .algo = "crc32")
myvars<-c("anonID", "Mark1", "Mark2", "MP3", "MP4", "Spark")
dropouts_anon<-dropouts[myvars]
dropouts_anon## # A tibble: 13 x 6
## anonID Mark1 Mark2 MP3 MP4 Spark
## <chr> <chr> <chr> <chr> <chr> <dbl>
## 1 b4d27052 84 80 <NA> <NA> 1
## 2 b4d27052 80 70 <NA> <NA> 1
## 3 b4d27052 85 83 <NA> <NA> 1
## 4 281c8b1c 89 80 <NA> <NA> 1
## 5 281c8b1c 85 87 <NA> <NA> 1
## 6 281c8b1c 88 85 <NA> <NA> 1
## 7 8e773d69 99 94 <NA> <NA> 1
## 8 8e773d69 98 97 <NA> <NA> 1
## 9 8e773d69 93 88 <NA> <NA> 1
## 10 2a98d8da 65 65 <NA> <NA> 0
## 11 95e6d8a7 99 <NA> <NA> <NA> 0
## 12 95e6d8a7 99 <NA> <NA> <NA> 0
## 13 95e6d8a7 97 <NA> <NA> <NA> 0as.numeric(dropouts$Mark2)-as.numeric(dropouts$Mark1)## [1] -4 -10 -2 -9 2 -3 -5 -1 -5 0 NA NA NAsummary(as.numeric(dropouts$Mark2)-as.numeric(dropouts$Mark1))## Min. 1st Qu. Median Mean 3rd Qu. Max. NA's
## -10.00 -5.00 -3.50 -3.70 -1.25 2.00 3summary(as.numeric(Final$Mark2)-as.numeric(Final$Mark1))## Warning in summary(as.numeric(Final$Mark2) - as.numeric(Final$Mark1)): NAs
## introduced by coercion
## Min. 1st Qu. Median Mean 3rd Qu. Max. NA's
## -29.000 -9.000 -5.000 -4.905 0.000 23.000 9mean(dropouts$diff)## [1] NAwrite.csv(Final, file = "Final_Spark.csv")