## student_id plan_id name Grade Weekly_Assessments_Given
## 1 1 584 T1 Rational Counting PK 0
## 2 1 589 T1 Rhyme PK 1
## 3 1 1097 T1 Quantification PK 0
## 4 1 1173 T1 Syllables PK 0
## 5 1 1696 T1 Number Symbols PK 0
## 6 1 1908 T1 Phonemes PK 3
## Number.of.Exit.Exam preclass_exit_exam first_exit_exam second_exit_exam
## 1 1 NA 80 NA
## 2 1 NA 100 NA
## 3 1 NA NA 100
## 4 1 NA 100 NA
## 5 1 NA NA 30
## 6 2 NA 100 100
## third_exit_exam Maximum_Exit_Score Pass_Exam_or_Not
## 1 NA 80 Pass
## 2 NA 100 Pass
## 3 NA 100 Pass
## 4 NA 100 Pass
## 5 NA 30 Fail
## 6 NA 100 Pass##
## Call:
## glm(formula = factor(Pass) ~ factor(Grade) + factor(NumExit),
## family = binomial(link = "logit"), data = exit2)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -1.8978 0.6009 0.6009 0.7221 0.8667
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 1.62029 0.05424 29.872 < 2e-16 ***
## factor(Grade)PS -0.40908 0.06724 -6.084 1.17e-09 ***
## factor(NumExit)2 -0.01716 0.08234 -0.208 0.8349
## factor(NumExit)3 -0.37083 0.21605 -1.716 0.0861 .
## factor(NumExit)4 -0.42556 0.53536 -0.795 0.4267
## factor(NumExit)5 10.94577 187.49087 0.058 0.9534
## factor(NumExit)6 -14.18635 324.74370 -0.044 0.9652
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 5706.9 on 5698 degrees of freedom
## Residual deviance: 5661.7 on 5692 degrees of freedom
## AIC: 5675.7
##
## Number of Fisher Scoring iterations: 11In this result, Grade has a great impact on passing exit exam, and the number of exit exam also has a great impact on students’ exit exam performance.In this case, I don’t consider the effect of plans. Next, we will only consider several frequently used plan to investigate the relationship between the number of exit exams and student’s overall performance in exit exam(s)
## T1 Addition Strategies T1 Classification/Sorting
## 159 19
## T1 Comparative Value T1 Compound Words
## 85 256
## T1 Conversations T1 Expression: Ask & Answer
## 36 73
## T1 Expression: Descriptive Language T1 Final Sounds
## 293 2
## T1 Initial Sounds T1 Number Symbols
## 30 423
## T1 One-to-One T1 Oral Comprehension
## 324 200
## T1 Ordering T1 Patterns
## 9 10
## T1 Phonemes T1 Quantification
## 268 567
## T1 Rational Counting T1 Rhyme
## 929 786
## T1 Rote Counting T1 Shape Composition
## 255 12
## T1 Shape Identification T1 Spatial Awareness
## 27 14
## T1 Subtraction Strategies T1 Syllables
## 37 336
## T1 Word Awareness T2 Rote Counting
## 534 13
## T2 Word Awareness
## 2## PK PS
## 696 767## 1 2 3 4 6
## 1060 358 32 12 1##
## Call:
## glm(formula = factor(Pass) ~ factor(Grade) + factor(NumExit),
## family = binomial(link = "logit"), data = data1)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -2.0440 -1.2574 0.6646 0.8746 1.0995
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 1.3978 0.1040 13.445 < 2e-16 ***
## factor(Grade)PS -0.6339 0.1250 -5.073 3.92e-07 ***
## factor(NumExit)2 0.2072 0.1466 1.413 0.158
## factor(NumExit)3 0.5590 0.4955 1.128 0.259
## factor(NumExit)4 -0.5779 0.5951 -0.971 0.331
## factor(NumExit)6 -13.9639 324.7437 -0.043 0.966
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 1650.3 on 1462 degrees of freedom
## Residual deviance: 1615.3 on 1457 degrees of freedom
## AIC: 1627.3
##
## Number of Fisher Scoring iterations: 11Only grade signficant affects students’ performance of passing exit exam. However,the Number of Exit exams doesn’t
model2 <- glm(factor(Pass) ~ factor(Weekly_Assessments_Given),family=binomial(link='logit'),data=data1)
summary(model2)##
## Call:
## glm(formula = factor(Pass) ~ factor(Weekly_Assessments_Given),
## family = binomial(link = "logit"), data = data1)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -2.0393 -1.5518 0.7954 0.7954 0.8446
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 0.98852 0.07279 13.581 <2e-16 ***
## factor(Weekly_Assessments_Given)1 0.29713 0.18016 1.649 0.0991 .
## factor(Weekly_Assessments_Given)2 0.40469 0.19993 2.024 0.0430 *
## factor(Weekly_Assessments_Given)3 -0.14122 0.27079 -0.522 0.6020
## factor(Weekly_Assessments_Given)4 0.95739 0.53945 1.775 0.0759 .
## factor(Weekly_Assessments_Given)5 0.95739 1.07152 0.893 0.3716
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 1650.3 on 1462 degrees of freedom
## Residual deviance: 1639.3 on 1457 degrees of freedom
## AIC: 1651.3
##
## Number of Fisher Scoring iterations: 4when the number of weekly assessment is 2, it has significant effect on students’ performance in exit exam
model3 <- glm(factor(Pass) ~ factor(NumExit),family=binomial(link='logit'),data=data1[data1$Grade=='PS',])
summary(model3)##
## Call:
## glm(formula = factor(Pass) ~ factor(NumExit), family = binomial(link = "logit"),
## data = data1[data1$Grade == "PS", ])
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -1.6719 -1.5015 0.8849 0.8849 1.2735
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 0.73571 0.08966 8.206 2.3e-16 ***
## factor(NumExit)2 0.37794 0.19552 1.933 0.0532 .
## factor(NumExit)3 0.36291 0.67267 0.540 0.5895
## factor(NumExit)4 -0.95885 0.67679 -1.417 0.1565
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 946.85 on 766 degrees of freedom
## Residual deviance: 940.41 on 763 degrees of freedom
## AIC: 948.41
##
## Number of Fisher Scoring iterations: 4model4 <- glm(factor(Pass) ~ factor(NumExit),family=binomial(link='logit'),data=data1[data1$Grade=='PK',])
summary(model4)##
## Call:
## glm(formula = factor(Pass) ~ factor(NumExit), family = binomial(link = "logit"),
## data = data1[data1$Grade == "PK", ])
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -2.1460 0.6512 0.6512 0.6512 0.6576
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 1.44316 0.11468 12.585 <2e-16 ***
## factor(NumExit)2 -0.02177 0.22050 -0.099 0.921
## factor(NumExit)3 0.75407 0.75413 1.000 0.317
## factor(NumExit)4 13.12291 509.65214 0.026 0.979
## factor(NumExit)6 -16.00922 882.74338 -0.018 0.986
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 676.13 on 695 degrees of freedom
## Residual deviance: 670.29 on 691 degrees of freedom
## AIC: 680.29
##
## Number of Fisher Scoring iterations: 13In a word, after strafying on Grade, we can see that when the grade is PK, the number of exit exam has no obviously effect on passing exit exams, while when the grade is PS, the number of exit exams has some effect on passing exit exam,which means that NumExit=2 will increase the odds of passing exit exam(s) to 1.46 when other varialbes hold constant.