1 What are the highest math classes that students took?

As seen in the graph and table in the tabs below, the most frequent highest math course taken is MTH 231 in both 2019 and 2020. This course represents 36.8% and 41.0% of the maximum math courses taken in 2019 and 2020, respectively, out of courses that range from MTH 103 to MTH 432.

1.1 Highest Math Course Graph

1.2 Highest Math Course Table


	2019		2020
MTH	N	%	N	%
103	0	0.0%	1	0.2%
107	3	0.6%	4	0.8%
111	4	0.8%	2	0.4%
114	3	0.6%	1	0.2%
121	51	10.7%	47	9.6%
131	51	10.7%	42	8.6%
132	1	0.2%	0	0.0%
141	9	1.9%	10	2.0%
231	176	36.9%	201	41.0%
241	30	6.3%	20	4.1%
242	38	8.0%	25	5.1%
305	1	0.2%	0	0.0%
331	2	0.4%	0	0.0%
341	14	2.9%	21	4.3%
405	1	0.2%	1	0.2%
425	0	0.0%	1	0.2%
426	0	0.0%	1	0.2%
432	1	0.2%	1	0.2%
No Record	92	19.3%	112	22.9%
Total	477	100.0%	490	100.0%

2 When did they take their highest math?

The heatmap displays the most frequent term in which the highest math class was taken, by year. The colors/values correspond to the counts/frequencies that are greater than the median count value (excluding zeros). The median frequency across all year and MTH course combinations for 2019 was 7 and was 6 for 2020 (excluding zeros). Most students took their highest math class within 4 semesters of taking GN 311. For GN 311 2019, the semester where most students took their highest MTH course was the 2018 Spring Term. For GN 311 2020, the 2019 Spring Term contained the highest frequencies of maximum MTH course taken.

NOTE: Students that may have taken their highest math class more than once are counted only once according to the semester in which their grade points were highest (which generally corresponds to the latest enrollment), and then by latest enrollment if grade points were the same across different semesters.

2.1 Graphs of Highest Math by Year Taken

2.2 2019 Table

	107	111	114	121	131	132	141	231	241	242	305	331	341	405	432	Total
2020 Spring Term	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
2019 Fall Term	1	0	0	2	4	1	1	14	3	4	0	1	2	0	0	33
2019 Summer Term 2	0	0	0	0	2	0	0	1	0	0	0	0	0	0	0	3
2019 Summer Term 1	0	0	0	1	1	0	0	1	0	0	0	0	1	0	0	4
2019 Spring Term	0	0	0	6	7	0	0	40	2	9	1	0	1	0	1	67
2018 Fall Term	0	0	2	10	9	0	3	32	9	10	0	0	3	0	0	78
2018 Summer Term 2	0	0	0	1	0	0	0	1	0	0	0	0	0	0	0	2
2018 Summer Term 1	0	0	0	0	0	0	0	1	0	2	0	0	1	0	0	4
2018 Spring Term	0	1	0	13	10	0	1	47	7	9	0	0	1	1	0	90
2017 Fall Term	2	0	1	7	11	0	1	21	4	3	0	1	0	0	0	51
2017 Summer Term 1	0	0	0	0	0	0	0	0	1	0	0	0	0	0	0	1
2017 Spring Term	0	1	0	3	1	0	1	10	3	0	0	0	5	0	0	24
2016 Fall Term	0	0	0	7	4	0	0	5	1	0	0	0	0	0	0	17
2016 Spring Term	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
2015 Fall Term	0	0	0	1	2	0	1	0	0	1	0	0	0	0	0	5
2015 Summer Term 2	0	1	0	0	0	0	0	0	0	0	0	0	0	0	0	1
2014 Fall Term	0	0	0	0	0	0	1	0	0	0	0	0	0	0	0	1
2014 Spring Term	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0	1
2013 Fall Term	0	1	0	0	0	0	0	0	0	0	0	0	0	0	0	1
2013 Spring Term	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
2011 Summer Term 2	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
2011 Spring Term	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0	1
2010 Fall Term	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0	1
Total	3	4	3	51	51	1	9	176	30	38	1	2	14	1	1	385

2.3 2020 Table

	103	107	111	114	121	131	141	231	241	242	341	405	425	426	432	Total
2020 Spring Term	1	1	1	0	2	7	0	21	1	4	3	0	0	1	0	42
2019 Fall Term	0	0	0	0	3	3	1	43	2	7	1	1	1	0	0	62
2019 Summer Term 2	0	1	0	0	0	0	0	0	0	0	0	0	0	0	0	1
2019 Summer Term 1	0	0	0	0	0	2	0	1	0	1	0	0	0	0	0	4
2019 Spring Term	0	0	1	0	7	9	1	45	5	3	6	0	0	0	1	78
2018 Fall Term	0	1	0	0	12	5	3	35	2	6	1	0	0	0	0	65
2018 Summer Term 2	0	0	0	0	0	1	0	1	0	0	0	0	0	0	0	2
2018 Summer Term 1	0	0	0	0	0	0	0	0	1	0	1	0	0	0	0	2
2018 Spring Term	0	1	0	0	9	5	0	28	3	0	4	0	0	0	0	50
2017 Fall Term	0	0	0	0	10	8	4	12	2	3	3	0	0	0	0	42
2017 Summer Term 1	0	0	0	0	0	0	0	0	1	0	0	0	0	0	0	1
2017 Spring Term	0	0	0	0	2	0	0	7	2	0	1	0	0	0	0	12
2016 Fall Term	0	0	0	1	1	2	0	5	1	0	0	0	0	0	0	10
2016 Spring Term	0	0	0	0	0	0	0	0	0	0	1	0	0	0	0	1
2015 Fall Term	0	0	0	0	0	0	0	0	0	1	0	0	0	0	0	1
2015 Summer Term 2	0	0	0	0	1	0	0	0	0	0	0	0	0	0	0	1
2014 Fall Term	0	0	0	0	0	0	1	0	0	0	0	0	0	0	0	1
2014 Spring Term	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
2013 Fall Term	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0	1
2013 Spring Term	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0	1
2011 Summer Term 2	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0	1
2011 Spring Term	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
2010 Fall Term	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
Total	1	4	2	1	47	42	10	201	20	25	21	1	1	1	1	378

3 How many students have taken ST 311? (prior to enrollment in GN 311)

193 students took ST 311 prior to taking GN 311 in the fall of 2019. 213 students took ST 311 prior to taking GN 311 in the spring of 2020. This table excludes students that took ST 311 during their enrollment in GN 311.

NOTE: Students that may have taken ST 311 more than once are counted only once according to the semester in which their grade points were highest (which generally corresponds to the latest enrollment), and then by latest enrollment if grade points were the same across different semesters.

3.1 Table

	2019		2020
Term	N	%	N	%
2019 Fall Term	0	0.0%	67	31.5%
2019 Summer Term 2	2	1.0%	0	0.0%
2019 Summer Term 1	3	1.6%	3	1.4%
2019 Spring Term	50	25.9%	51	23.9%
2018 Fall Term	62	32.1%	45	21.1%
2018 Summer Term 1	3	1.6%	2	0.9%
2018 Spring Term	33	17.1%	23	10.8%
2017 Fall Term	20	10.4%	10	4.7%
2017 Summer Term 2	1	0.5%	0	0.0%
2017 Spring Term	12	6.2%	9	4.2%
2016 Fall Term	4	2.1%	2	0.9%
2016 Spring Term	0	0.0%	1	0.5%
2015 Fall Term	1	0.5%	0	0.0%
2014 Fall Term	1	0.5%	0	0.0%
2011 Fall Term	1	0.5%	0	0.0%
Total	193	100.0%	213	100.0%

4 How many people are currently taking ST 311? (while enrolled in GN 311)

36 students were enrolled in ST 311 while taking GN 311 during the fall of 2019. 28 students are currently enrolled in ST 311 and GN 311 for the spring, 2020.

NOTE: Few students may have also taken ST 311 prior to current ST 311 course enrollment with respect to their GN 311 cohort.

4.1 Table

	Enrolled		Not Enrolled
	N	%	N	%
2019	36	8.2%	441	92.5%
2020	28	5.7%	462	94.3%

5 What was the average GPA for ST 311?

The average GPA for students who took ST 311 and GN 311 during Fall 2019 (indicated by the ‘Current (2019)’ row) is 3.0. The average GPA for students who did not take (or are not taking) ST 311 concurrently with GN 311, in 2019 and 2020 (middle row), is 3.3. The overall average GPA including all students (see notes below) is 3.1.

5.1 Table

	Min	Q1	Median	Mean	Q3	Max	N
Current (2019)	1.0	2.7	3.0	3.0	3.3	4.0	36
Prior	1.0	3.0	3.3	3.3	4.0	4.3	404
Overall	0.0	2.7	3.3	3.1	4.0	4.3	468

6 How many students got Homework 1 question 10 correct? How many got Homework 2 question 9 correct?

The table below displays 2020 in blue. The counts and percentages of correct, incorrect, and ‘No Record’ responses are indicated in the columns below.

6.1 Table

	2019						2020
	Correct		Incorrect		No Record		Correct		Incorrect		No Record
	N	%	N	%	N	%	N	%	N	%	N	%
Q9	343	71.9%	114	23.9%	20	4.2%	378	77.1%	95	19.4%	17	3.5%
Q10	321	67.3%	139	29.1%	17	3.6%	320	65.3%	154	31.4%	16	3.3%
Both	246	51.6%	214	44.9%	17	3.6%	268	54.7%	206	42.0%	16	3.3%

7 Does it make a difference whether someone has taken ST 311 or not as to whether they got question 10 or 9 correct?

7.1 Table

Below is a frequency table for questions 9, 10 and both that tabulates correct, incorrect and no record responses by whether or not ST 311 was taken. The first two rows are for 2019 and the second two rows are for 2020. These questions are prior to intervention in the spring 2020 semester so we would roughly expect to see the same trends across 2019 and 2020 assuming similar populations of students.

		Q9			Q10			Both
		Correct	Incorrect	No Record	Correct	Incorrect	No Record	Correct	Incorrect	No Record
2019	Not Taken	175	60	13	169	70	9	125	114	9
2019	Took 311	168	54	7	152	69	8	121	100	8
2020	Not Taken	202	39	10	168	73	10	150	91	10
2020	Took 311	176	56	7	152	81	6	118	115	6

7.2 Significant Differences

Using a binomial glm model logodds(BothCorrect) ~ HighestMTH + tookST311 + ST311current did not yield any significant factors.

Marginal binomial models for the log odds of answering each separate question correctly, using whether or not a student has taken ST 311 as the factor of interest indicated no significant association of taking ST 311 and grades for 2019 on correct answers for each question and both combined. The same results were found for 2020 except for question 10 where the model indicates a significant association between taking ST 311 and correct answers at the .032 significane level using a Wald Test. However, the chi-square test does not indicate significance and accounting for the multiple tests, the association is not likely significant.

‘No Record’ responses were excluded from these models.

Below is the summary output for the binomial model coefficients for question 9 in 2019 along with the chi-square association test. The last two rows are the same models for question 9 in 2020. All other tests of interest are similar in that there is no evidence of statistically significant association between taking ST 311 on answer status.

##                      Estimate Std. Error    z value     Pr(>|z|)
## (Intercept)       -1.07044141  0.1496025 -7.1552365 8.352878e-13
## tookST311Took 311 -0.06453852  0.2164527 -0.2981645 7.655776e-01

## Number of cases in table: 477 
## Number of factors: 2 
## Test for independence of all factors:
##  Chisq = 1.5042, df = 2, p-value = 0.4714

##                     Estimate Std. Error   z value     Pr(>|z|)
## (Intercept)       -1.6447061  0.1749043 -9.403462 5.279685e-21
## tookST311Took 311  0.4995737  0.2326595  2.147231 3.177488e-02

## Number of cases in table: 490 
## Number of factors: 2 
## Test for independence of all factors:
##  Chisq = 5.069, df = 2, p-value = 0.0793

8 Analysis in regard to HW 6 questions

Intervention occurred between homework 2 and homework 6. We want to look at any possible impact the intervention may have had. There are a number of questions from homework 6 to consider here. There are binary indicators of correct/incorrect for each and one summary average variable that aggregates across the questions.

For all of the questions, ignoring missing values (students that didn’t complete the question and students that didn’t have a cohort) the first quartile of binary scores is 1. This indicates that 75% of people got an individual question correct. The sample proportion of correct responses for each question is given below as well as the summary stats on the aggregate variable.

means <- full_data %>% group_by(Cohort) %>% select(Cohort, ends_with("bin")) %>% 
  summarize_if(.predicate = function(x) is.numeric(x), .funs = funs(mean="mean"), na.rm = TRUE) 
kable(means[1:2,], col.names = c("Cohort", paste("Q", c(3:10, 15:19)), "Aggregate"), digits = 3) %>% 
  kable_styling(bootstrap_options = "striped",full_width = T)

Cohort	Q 3	Q 4	Q 5	Q 6	Q 7	Q 8	Q 9	Q 10	Q 15	Q 16	Q 17	Q 18	Q 19	Aggregate
Fall2019	0.978	0.978	0.876	0.868	0.868	0.863	0.857	0.854	0.881	0.951	0.911	0.867	0.880	0.900
Spring2020	0.969	0.966	0.921	0.906	0.901	0.864	0.841	0.846	0.890	0.959	0.931	0.927	0.921	0.921

Looking closely at the questions themselves, I’m going to remove question 8, 9, and 10 (Keeping all decimal digits during your calculations and rounding your answer to 3 decimal digits, what is the calculated chi-square value? What is the number for the degrees of freedom? What is the critical value? Round to two decimal places.) as these weren’t things focused on in the intervention.

full_data <- select(full_data, -HW6_Q_8_score_bin, -HW6_Q_9_score_bin, - HW6_Q_10_score_bin)

Conducting a quick comparison of these sample proportions by question using a logistic regression model to get a p-value (assumptions likely not met but still somewhat useful).

full_data <- full_data[!is.na(full_data$Cohort),]

#create indicator of math above 100 level or not
full_data$MTHLevel <- ifelse(full_data$MTHcourse > 200, "200's", "100's")

sum_glm <- function(data, response){ 
  fit <- glm(data[[response]] ~ Cohort, data = data)
  means <- aggregate(data[[response]] ~ Cohort, data = data, FUN = mean)
  resp <- gregexpr(response, pattern = "(Q_\\d+)")
  ret <- c(substring(response, resp[[1]], resp[[1]]+attr(resp[[1]],'match.length')-1), round(c(fit$coefficients, means[,2], means[2,2]-means[1,2], summary(fit)$coefficients[2,4]), 4))
  names(ret) <- c("Response", "Intercept", "Beta1", "2019 mean", "2020 mean", "Difference", "p-value")
  ret
}

bin_names <- c("HW6_Q_3_score_bin", "HW6_Q_4_score_bin", "HW6_Q_5_score_bin",
               "HW6_Q_6_score_bin", "HW6_Q_7_score_bin",  "HW6_Q_15_score_bin",
               "HW6_Q_16_score_bin", "HW6_Q_17_score_bin", "HW6_Q_18_score_bin",
           "HW6_Q_19_score_bin")
lapply(X = bin_names, FUN = sum_glm, data = full_data)

## [[1]]
##   Response  Intercept      Beta1  2019 mean  2020 mean Difference    p-value 
##      "Q_3"   "0.9785"  "-0.0097"   "0.9785"   "0.9688"  "-0.0097"   "0.4166" 
## 
## [[2]]
##   Response  Intercept      Beta1  2019 mean  2020 mean Difference    p-value 
##      "Q_4"   "0.9784"  "-0.0125"   "0.9784"   "0.9659"  "-0.0125"   "0.3053" 
## 
## [[3]]
##   Response  Intercept      Beta1  2019 mean  2020 mean Difference    p-value 
##      "Q_5"    "0.876"   "0.0453"    "0.876"   "0.9213"   "0.0453"   "0.0461" 
## 
## [[4]]
##   Response  Intercept      Beta1  2019 mean  2020 mean Difference    p-value 
##      "Q_6"   "0.8679"   "0.0385"   "0.8679"   "0.9064"   "0.0385"   "0.1058" 
## 
## [[5]]
##   Response  Intercept      Beta1  2019 mean  2020 mean Difference    p-value 
##      "Q_7"   "0.8679"    "0.033"   "0.8679"   "0.9009"    "0.033"   "0.1704" 
## 
## [[6]]
##   Response  Intercept      Beta1  2019 mean  2020 mean Difference    p-value 
##     "Q_15"   "0.8808"   "0.0091"   "0.8808"   "0.8899"   "0.0091"   "0.7037" 
## 
## [[7]]
##   Response  Intercept      Beta1  2019 mean  2020 mean Difference    p-value 
##     "Q_16"   "0.9514"   "0.0081"   "0.9514"   "0.9594"   "0.0081"   "0.6027" 
## 
## [[8]]
##   Response  Intercept      Beta1  2019 mean  2020 mean Difference    p-value 
##     "Q_17"   "0.9111"   "0.0198"   "0.9111"   "0.9308"   "0.0198"   "0.3278" 
## 
## [[9]]
##   Response  Intercept      Beta1  2019 mean  2020 mean Difference    p-value 
##     "Q_18"   "0.8672"   "0.0599"   "0.8672"   "0.9271"   "0.0599"   "0.0088" 
## 
## [[10]]
##   Response  Intercept      Beta1  2019 mean  2020 mean Difference    p-value 
##     "Q_19"   "0.8804"   "0.0408"   "0.8804"   "0.9213"   "0.0408"   "0.0696"

Three of these are significant or marginally signficant and in the direction we’d hope for. That’s a good sign.

We’ll also consider just the students that missed at least one question from the earlier homework assignment. Perhaps they are the ones that will show improvement.

#filter by missing an earlier question or having no record
missed_data <- filter(full_data, bothQscorrect != 1)
lapply(X = bin_names, FUN = sum_glm, data = missed_data)

## [[1]]
##   Response  Intercept      Beta1  2019 mean  2020 mean Difference    p-value 
##      "Q_3"   "0.9665"  "-0.0242"   "0.9665"   "0.9423"  "-0.0242"   "0.2873" 
## 
## [[2]]
##   Response  Intercept      Beta1  2019 mean  2020 mean Difference    p-value 
##      "Q_4"   "0.9719"   "-0.036"   "0.9719"   "0.9359"   "-0.036"   "0.1135" 
## 
## [[3]]
##   Response  Intercept      Beta1  2019 mean  2020 mean Difference    p-value 
##      "Q_5"   "0.8212"   "0.0359"   "0.8212"   "0.8571"   "0.0359"   "0.3834" 
## 
## [[4]]
##   Response  Intercept      Beta1  2019 mean  2020 mean Difference    p-value 
##      "Q_6"   "0.8212"    "7e-04"   "0.8212"   "0.8219"    "7e-04"   "0.9872" 
## 
## [[5]]
##   Response  Intercept      Beta1  2019 mean  2020 mean Difference    p-value 
##      "Q_7"   "0.8156"    "7e-04"   "0.8156"   "0.8163"    "7e-04"   "0.9874" 
## 
## [[6]]
##   Response  Intercept      Beta1  2019 mean  2020 mean Difference    p-value 
##     "Q_15"   "0.8475"   "0.0192"   "0.8475"   "0.8667"   "0.0192"    "0.623" 
## 
## [[7]]
##   Response  Intercept      Beta1  2019 mean  2020 mean Difference    p-value 
##     "Q_16"   "0.9438"  "-0.0034"   "0.9438"   "0.9404"  "-0.0034"   "0.8949" 
## 
## [[8]]
##   Response  Intercept      Beta1  2019 mean  2020 mean Difference    p-value 
##     "Q_17"   "0.8939"   "-0.005"   "0.8939"   "0.8889"   "-0.005"   "0.8851" 
## 
## [[9]]
##   Response  Intercept      Beta1  2019 mean  2020 mean Difference    p-value 
##     "Q_18"   "0.8079"   "0.0847"   "0.8079"   "0.8926"   "0.0847"   "0.0346" 
## 
## [[10]]
##   Response  Intercept      Beta1  2019 mean  2020 mean Difference    p-value 
##     "Q_19"   "0.8239"   "0.0755"   "0.8239"   "0.8993"   "0.0755"    "0.052"

Looking like just the last two questions showed improvement (none went the wrong way) when averaged across things.

9 HW 6 Q’s broken down - all students

To further investigate the effect of the intervention we’ll look at a break down comparing cohorts for correct/incorrect question status by things like:

highest math course taken (>200 or <200) (MTHLevel)
ST 311 status (not taken or taken) (tookST311)
class level (senior, etc.) (NC_LVL_BOT_DESCR)
race (STDNT_RACE_IPEDS)
sex (STUDENT_GENDER_IPEDS)
transfer status (ORIG_ENROLL_STATUS)
rural status(RuralStatus)
first gen status (FirstGenStatus)

First just the means across some combinations.

9.1 By Cohort, Math Level, Transfer, and First Gen

out2 <- lapply(X = bin_names, FUN = q_means, data = full_data, preds = preds[c(1,2,7,9)])

out2e <- lapply(FUN = nice_it, X= out2)

for(x in 1:length(out2e)){
  print(kable(out2e[[x]], digits = 3, col.names = c("MathLevel", "Transfer", "First Gen", "Avg2019", "Avg2020", "n2019", "n2020", "AvgDiff"), caption = paste0("Question ", qs[x], " Summary")) %>% 
          kable_styling(bootstrap_options = "striped",full_width = T) )
}

Question 3 Summary
MathLevel	Transfer	First Gen	Avg2019	Avg2020	n2019	n2020	AvgDiff
100’s	New Student	First Gen	0.909	1.000	11	10	0.091
200’s	New Student	First Gen	1.000	0.976	33	42	-0.024
100’s	New Transfer Student	First Gen	1.000	1.000	9	5	0.000
200’s	New Transfer Student	First Gen	1.000	0.818	8	11	-0.182
100’s	New Student	Not First	0.975	0.984	80	63	0.009
200’s	New Student	Not First	0.979	0.978	190	180	-0.001
100’s	New Transfer Student	Not First	1.000	1.000	11	11	0.000
200’s	New Transfer Student	Not First	0.957	1.000	23	17	0.043
100’s	New Student	Unknown	1.000	0.667	3	3	-0.333
200’s	New Student	Unknown	1.000	1.000	2	3	0.000
100’s	New Transfer Student	Unknown	NA	1.000	NA	3	NA
200’s	New Transfer Student	Unknown	1.000	0.500	2	4	-0.500

Question 4 Summary
MathLevel	Transfer	First Gen	Avg2019	Avg2020	n2019	n2020	AvgDiff
100’s	New Student	First Gen	0.909	1.000	11	10	0.091
200’s	New Student	First Gen	1.000	1.000	33	42	0.000
100’s	New Transfer Student	First Gen	1.000	0.600	9	5	-0.400
200’s	New Transfer Student	First Gen	1.000	0.818	8	11	-0.182
100’s	New Student	Not First	0.962	0.984	79	63	0.022
200’s	New Student	Not First	0.984	0.983	190	179	-0.001
100’s	New Transfer Student	Not First	1.000	1.000	11	11	0.000
200’s	New Transfer Student	Not First	0.957	0.941	23	17	-0.015
100’s	New Student	Unknown	1.000	0.667	3	3	-0.333
200’s	New Student	Unknown	1.000	1.000	2	3	0.000
100’s	New Transfer Student	Unknown	NA	1.000	NA	3	NA
200’s	New Transfer Student	Unknown	1.000	0.500	2	4	-0.500

Question 5 Summary
MathLevel	Transfer	First Gen	Avg2019	Avg2020	n2019	n2020	AvgDiff
100’s	New Student	First Gen	0.636	0.667	11	9	0.030
200’s	New Student	First Gen	0.970	0.927	33	41	-0.043
100’s	New Transfer Student	First Gen	0.778	1.000	9	5	0.222
200’s	New Transfer Student	First Gen	0.750	0.818	8	11	0.068
100’s	New Student	Not First	0.838	0.935	80	62	0.098
200’s	New Student	Not First	0.905	0.926	190	176	0.021
100’s	New Transfer Student	Not First	0.909	1.000	11	10	0.091
200’s	New Transfer Student	Not First	0.818	1.000	22	17	0.182
100’s	New Student	Unknown	0.667	1.000	3	2	0.333
200’s	New Student	Unknown	1.000	1.000	2	3	0.000
100’s	New Transfer Student	Unknown	NA	0.667	NA	3	NA
200’s	New Transfer Student	Unknown	1.000	0.667	2	3	-0.333

Question 6 Summary
MathLevel	Transfer	First Gen	Avg2019	Avg2020	n2019	n2020	AvgDiff
100’s	New Student	First Gen	0.636	0.750	11	8	0.114
200’s	New Student	First Gen	0.970	0.878	33	41	-0.092
100’s	New Transfer Student	First Gen	0.778	0.800	9	5	0.022
200’s	New Transfer Student	First Gen	0.750	0.909	8	11	0.159
100’s	New Student	Not First	0.838	0.903	80	62	0.066
200’s	New Student	Not First	0.889	0.920	190	176	0.031
100’s	New Transfer Student	Not First	0.909	1.000	11	10	0.091
200’s	New Transfer Student	Not First	0.818	0.941	22	17	0.123
100’s	New Student	Unknown	0.667	1.000	3	2	0.333
200’s	New Student	Unknown	1.000	1.000	2	3	0.000
100’s	New Transfer Student	Unknown	NA	0.667	NA	3	NA
200’s	New Transfer Student	Unknown	1.000	0.667	2	3	-0.333

Question 7 Summary
MathLevel	Transfer	First Gen	Avg2019	Avg2020	n2019	n2020	AvgDiff
100’s	New Student	First Gen	0.636	0.556	11	9	-0.081
200’s	New Student	First Gen	0.970	0.878	33	41	-0.092
100’s	New Transfer Student	First Gen	0.778	0.800	9	5	0.022
200’s	New Transfer Student	First Gen	0.750	0.818	8	11	0.068
100’s	New Student	Not First	0.838	0.935	80	62	0.098
200’s	New Student	Not First	0.895	0.915	190	176	0.020
100’s	New Transfer Student	Not First	0.909	1.000	11	10	0.091
200’s	New Transfer Student	Not First	0.818	0.941	22	17	0.123
100’s	New Student	Unknown	0.667	1.000	3	2	0.333
200’s	New Student	Unknown	1.000	1.000	2	3	0.000
100’s	New Transfer Student	Unknown	NA	0.667	NA	3	NA
200’s	New Transfer Student	Unknown	0.500	0.667	2	3	0.167

Question 8 Summary
MathLevel	Transfer	First Gen	Avg2019	Avg2020	n2019	n2020	AvgDiff
100’s	New Student	First Gen	0.727	0.889	11	9	0.162
200’s	New Student	First Gen	0.848	0.929	33	42	0.080
100’s	New Transfer Student	First Gen	1.000	1.000	9	5	0.000
200’s	New Transfer Student	First Gen	0.875	1.000	8	10	0.125
100’s	New Student	Not First	0.886	0.852	79	61	-0.034
200’s	New Student	Not First	0.884	0.876	189	177	-0.008
100’s	New Transfer Student	Not First	0.818	1.000	11	11	0.182
200’s	New Transfer Student	Not First	0.909	0.941	22	17	0.032
100’s	New Student	Unknown	1.000	0.667	3	3	-0.333
200’s	New Student	Unknown	1.000	1.000	2	3	0.000
100’s	New Transfer Student	Unknown	NA	1.000	NA	3	NA
200’s	New Transfer Student	Unknown	1.000	0.667	2	3	-0.333

Question 9 Summary
MathLevel	Transfer	First Gen	Avg2019	Avg2020	n2019	n2020	AvgDiff
100’s	New Student	First Gen	0.909	1.000	11	9	0.091
200’s	New Student	First Gen	0.970	0.952	33	42	-0.017
100’s	New Transfer Student	First Gen	1.000	0.800	9	5	-0.200
200’s	New Transfer Student	First Gen	1.000	0.909	8	11	-0.091
100’s	New Student	Not First	0.975	0.984	80	61	0.009
200’s	New Student	Not First	0.937	0.966	189	177	0.030
100’s	New Transfer Student	Not First	1.000	1.000	11	11	0.000
200’s	New Transfer Student	Not First	0.955	0.941	22	17	-0.013
100’s	New Student	Unknown	0.667	0.500	3	2	-0.167
200’s	New Student	Unknown	1.000	1.000	2	3	0.000
100’s	New Transfer Student	Unknown	NA	0.667	NA	3	NA
200’s	New Transfer Student	Unknown	1.000	1.000	2	3	0.000

Question 10 Summary
MathLevel	Transfer	First Gen	Avg2019	Avg2020	n2019	n2020	AvgDiff
100’s	New Student	First Gen	0.727	0.800	11	10	0.073
200’s	New Student	First Gen	0.970	0.929	33	42	-0.041
100’s	New Transfer Student	First Gen	0.778	1.000	9	5	0.222
200’s	New Transfer Student	First Gen	0.750	0.818	8	11	0.068
100’s	New Student	Not First	0.938	0.933	81	60	-0.005
200’s	New Student	Not First	0.910	0.966	189	178	0.056
100’s	New Transfer Student	Not First	1.000	0.636	11	11	-0.364
200’s	New Transfer Student	Not First	0.864	0.941	22	17	0.078
100’s	New Student	Unknown	1.000	0.667	3	3	-0.333
200’s	New Student	Unknown	1.000	1.000	2	3	0.000
100’s	New Transfer Student	Unknown	NA	0.667	NA	3	NA
200’s	New Transfer Student	Unknown	1.000	1.000	2	3	0.000

Question 15 Summary
MathLevel	Transfer	First Gen	Avg2019	Avg2020	n2019	n2020	AvgDiff
100’s	New Student	First Gen	0.818	0.778	11	9	-0.040
200’s	New Student	First Gen	0.939	0.952	33	42	0.013
100’s	New Transfer Student	First Gen	0.889	0.800	9	5	-0.089
200’s	New Transfer Student	First Gen	0.750	0.900	8	10	0.150
100’s	New Student	Not First	0.888	0.934	80	61	0.047
200’s	New Student	Not First	0.851	0.932	188	176	0.081
100’s	New Transfer Student	Not First	0.909	0.909	11	11	0.000
200’s	New Transfer Student	Not First	0.909	0.941	22	17	0.032
100’s	New Student	Unknown	1.000	1.000	3	2	0.000
200’s	New Student	Unknown	0.500	1.000	2	3	0.500
100’s	New Transfer Student	Unknown	NA	1.000	NA	3	NA
200’s	New Transfer Student	Unknown	0.500	0.667	2	3	0.167

Question 16 Summary
MathLevel	Transfer	First Gen	Avg2019	Avg2020	n2019	n2020	AvgDiff
100’s	New Student	First Gen	0.818	0.778	11	9	-0.040
200’s	New Student	First Gen	0.939	0.929	33	42	-0.011
100’s	New Transfer Student	First Gen	0.889	0.800	9	5	-0.089
200’s	New Transfer Student	First Gen	0.750	0.900	8	10	0.150
100’s	New Student	Not First	0.888	0.902	80	61	0.014
200’s	New Student	Not First	0.872	0.943	188	176	0.071
100’s	New Transfer Student	Not First	0.909	0.909	11	11	0.000
200’s	New Transfer Student	Not First	0.952	0.882	21	17	-0.070
100’s	New Student	Unknown	1.000	1.000	3	2	0.000
200’s	New Student	Unknown	0.500	1.000	2	3	0.500
100’s	New Transfer Student	Unknown	NA	1.000	NA	3	NA
200’s	New Transfer Student	Unknown	0.500	0.667	2	3	0.167

9.2 BY Cohort, Math Level, and Rural status

out3 <- lapply(X = bin_names, FUN = q_means, data = full_data, preds = preds[c(1,2, 8)])

out3e <- lapply(FUN = nice_it, X= out3)

for(x in 1:length(out3e)){
  print(kable(out3e[[x]], digits = 3, col.names = c("MathLevel", "Rural", "Avg2019", "Avg2020", "n2019", "n2020", "AvgDiff"), caption = paste0("Question ", qs[x], " Summary")) %>% 
          kable_styling(bootstrap_options = "striped",full_width = T) )
}

Question 3 Summary
MathLevel	Rural	Avg2019	Avg2020	n2019	n2020	AvgDiff
100’s	OutofState_International	1.000	1.000	19	13	0.000
200’s	OutofState_International	1.000	1.000	31	26	0.000
100’s	Tier1&2	0.946	0.967	56	30	0.020
200’s	Tier1&2	0.987	0.939	79	82	-0.048
100’s	Tier3	1.000	0.981	39	52	-0.019
200’s	Tier3	0.973	0.979	148	146	0.006

Question 4 Summary
MathLevel	Rural	Avg2019	Avg2020	n2019	n2020	AvgDiff
100’s	OutofState_International	0.895	1.000	19	13	0.105
200’s	OutofState_International	1.000	1.000	31	26	0.000
100’s	Tier1&2	0.964	0.967	55	30	0.003
200’s	Tier1&2	1.000	0.963	79	81	-0.037
100’s	Tier3	1.000	0.942	39	52	-0.058
200’s	Tier3	0.973	0.973	148	146	0.000

Question 5 Summary
MathLevel	Rural	Avg2019	Avg2020	n2019	n2020	AvgDiff
100’s	OutofState_International	0.842	1.000	19	13	0.158
200’s	OutofState_International	0.935	0.923	31	26	-0.012
100’s	Tier1&2	0.800	0.893	55	28	0.093
200’s	Tier1&2	0.886	0.924	79	79	0.038
100’s	Tier3	0.825	0.900	40	50	0.075
200’s	Tier3	0.905	0.930	147	143	0.025

Question 6 Summary
MathLevel	Rural	Avg2019	Avg2020	n2019	n2020	AvgDiff
100’s	OutofState_International	0.737	1.000	19	13	0.263
200’s	OutofState_International	0.935	0.923	31	26	-0.012
100’s	Tier1&2	0.818	0.889	55	27	0.071
200’s	Tier1&2	0.873	0.911	79	79	0.038
100’s	Tier3	0.850	0.860	40	50	0.010
200’s	Tier3	0.891	0.916	147	143	0.025

Question 7 Summary
MathLevel	Rural	Avg2019	Avg2020	n2019	n2020	AvgDiff
100’s	OutofState_International	0.737	1.000	19	13	0.263
200’s	OutofState_International	0.935	0.923	31	26	-0.012
100’s	Tier1&2	0.818	0.857	55	28	0.039
200’s	Tier1&2	0.873	0.911	79	79	0.038
100’s	Tier3	0.850	0.880	40	50	0.030
200’s	Tier3	0.891	0.909	147	143	0.018

Question 8 Summary
MathLevel	Rural	Avg2019	Avg2020	n2019	n2020	AvgDiff
100’s	OutofState_International	0.895	1.000	19	13	0.105
200’s	OutofState_International	0.871	0.800	31	25	-0.071
100’s	Tier1&2	0.889	0.862	54	29	-0.027
200’s	Tier1&2	0.873	0.873	79	79	0.000
100’s	Tier3	0.850	0.860	40	50	0.010
200’s	Tier3	0.890	0.917	146	145	0.027

Question 9 Summary
MathLevel	Rural	Avg2019	Avg2020	n2019	n2020	AvgDiff
100’s	OutofState_International	0.895	1.000	19	13	0.105
200’s	OutofState_International	0.903	1.000	31	26	0.097
100’s	Tier1&2	0.982	0.929	55	28	-0.053
200’s	Tier1&2	0.962	0.975	79	80	0.013
100’s	Tier3	0.975	0.960	40	50	-0.015
200’s	Tier3	0.945	0.944	146	144	-0.001

Question 10 Summary
MathLevel	Rural	Avg2019	Avg2020	n2019	n2020	AvgDiff
100’s	OutofState_International	0.947	0.846	19	13	-0.101
200’s	OutofState_International	0.935	0.923	31	26	-0.012
100’s	Tier1&2	0.893	0.833	56	30	-0.060
200’s	Tier1&2	0.899	0.950	79	80	0.051
100’s	Tier3	0.925	0.898	40	49	-0.027
200’s	Tier3	0.911	0.959	146	145	0.048

Question 15 Summary
MathLevel	Rural	Avg2019	Avg2020	n2019	n2020	AvgDiff
100’s	OutofState_International	0.947	0.923	19	13	-0.024
200’s	OutofState_International	0.839	0.923	31	26	0.084
100’s	Tier1&2	0.873	0.964	55	28	0.092
200’s	Tier1&2	0.899	0.937	79	79	0.038
100’s	Tier3	0.875	0.880	40	50	0.005
200’s	Tier3	0.841	0.930	145	143	0.089

Question 16 Summary
MathLevel	Rural	Avg2019	Avg2020	n2019	n2020	AvgDiff
100’s	OutofState_International	0.947	0.923	19	13	-0.024
200’s	OutofState_International	0.871	0.962	31	26	0.091
100’s	Tier1&2	0.873	0.964	55	28	0.092
200’s	Tier1&2	0.910	0.924	78	79	0.014
100’s	Tier3	0.875	0.840	40	50	-0.035
200’s	Tier3	0.862	0.930	145	143	0.068

10 HW 6 Q’s broken down - incorrect HW 2

10.1 By Cohort, Math Level, Transfer, and First Gen

out2 <- lapply(X = bin_names, FUN = q_means, data = missed_data, preds = preds[c(1,2,7,9)])

out2e <- lapply(FUN = nice_it, X= out2)

for(x in 1:length(out2e)){
  print(kable(out2e[[x]], digits = 3, col.names = c("MathLevel", "Transfer", "First Gen", "Avg2019", "Avg2020", "n2019", "n2020", "AvgDiff"), caption = paste0("Question ", qs[x], " Summary")) %>% 
          kable_styling(bootstrap_options = "striped",full_width = T) )
}

Question 3 Summary
MathLevel	Transfer	First Gen	Avg2019	Avg2020	n2019	n2020	AvgDiff
100’s	New Student	First Gen	0.800	1.000	5	9	0.200
200’s	New Student	First Gen	1.000	0.944	19	18	-0.056
100’s	New Transfer Student	First Gen	1.000	1.000	7	4	0.000
200’s	New Transfer Student	First Gen	1.000	0.833	3	6	-0.167
100’s	New Student	Not First	0.935	0.966	31	29	0.030
200’s	New Student	Not First	0.968	0.957	94	69	-0.012
100’s	New Transfer Student	Not First	1.000	1.000	5	7	0.000
200’s	New Transfer Student	Not First	1.000	1.000	9	6	0.000
100’s	New Student	Unknown	1.000	0.667	3	3	-0.333
200’s	New Student	Unknown	1.000	NA	2	NA	NA
100’s	New Transfer Student	Unknown	NA	1.000	NA	1	NA
200’s	New Transfer Student	Unknown	1.000	0.500	1	4	-0.500

Question 4 Summary
MathLevel	Transfer	First Gen	Avg2019	Avg2020	n2019	n2020	AvgDiff
100’s	New Student	First Gen	0.800	1.000	5	9	0.200
200’s	New Student	First Gen	1.000	1.000	19	18	0.000
100’s	New Transfer Student	First Gen	1.000	0.750	7	4	-0.250
200’s	New Transfer Student	First Gen	1.000	0.833	3	6	-0.167
100’s	New Student	Not First	0.933	0.966	30	29	0.032
200’s	New Student	Not First	0.979	0.957	94	69	-0.022
100’s	New Transfer Student	Not First	1.000	1.000	5	7	0.000
200’s	New Transfer Student	Not First	1.000	0.833	9	6	-0.167
100’s	New Student	Unknown	1.000	0.667	3	3	-0.333
200’s	New Student	Unknown	1.000	NA	2	NA	NA
100’s	New Transfer Student	Unknown	NA	1.000	NA	1	NA
200’s	New Transfer Student	Unknown	1.000	0.500	1	4	-0.500

Question 5 Summary
MathLevel	Transfer	First Gen	Avg2019	Avg2020	n2019	n2020	AvgDiff
100’s	New Student	First Gen	0.400	0.625	5	8	0.225
200’s	New Student	First Gen	0.947	0.882	19	17	-0.065
100’s	New Transfer Student	First Gen	0.714	1.000	7	4	0.286
200’s	New Transfer Student	First Gen	0.667	0.833	3	6	0.167
100’s	New Student	Not First	0.774	0.893	31	28	0.119
200’s	New Student	Not First	0.851	0.848	94	66	-0.003
100’s	New Transfer Student	Not First	0.800	1.000	5	6	0.200
200’s	New Transfer Student	Not First	0.778	1.000	9	6	0.222
100’s	New Student	Unknown	0.667	1.000	3	2	0.333
200’s	New Student	Unknown	1.000	NA	2	NA	NA
100’s	New Transfer Student	Unknown	NA	0.000	NA	1	NA
200’s	New Transfer Student	Unknown	1.000	0.667	1	3	-0.333

Question 6 Summary
MathLevel	Transfer	First Gen	Avg2019	Avg2020	n2019	n2020	AvgDiff
100’s	New Student	First Gen	0.400	0.714	5	7	0.314
200’s	New Student	First Gen	0.947	0.765	19	17	-0.183
100’s	New Transfer Student	First Gen	0.714	0.750	7	4	0.036
200’s	New Transfer Student	First Gen	0.667	0.833	3	6	0.167
100’s	New Student	Not First	0.774	0.857	31	28	0.083
200’s	New Student	Not First	0.851	0.833	94	66	-0.018
100’s	New Transfer Student	Not First	0.800	1.000	5	6	0.200
200’s	New Transfer Student	Not First	0.778	0.833	9	6	0.056
100’s	New Student	Unknown	0.667	1.000	3	2	0.333
200’s	New Student	Unknown	1.000	NA	2	NA	NA
100’s	New Transfer Student	Unknown	NA	0.000	NA	1	NA
200’s	New Transfer Student	Unknown	1.000	0.667	1	3	-0.333

Question 7 Summary
MathLevel	Transfer	First Gen	Avg2019	Avg2020	n2019	n2020	AvgDiff
100’s	New Student	First Gen	0.400	0.500	5	8	0.100
200’s	New Student	First Gen	0.947	0.765	19	17	-0.183
100’s	New Transfer Student	First Gen	0.714	0.750	7	4	0.036
200’s	New Transfer Student	First Gen	0.667	0.833	3	6	0.167
100’s	New Student	Not First	0.774	0.893	31	28	0.119
200’s	New Student	Not First	0.840	0.833	94	66	-0.007
100’s	New Transfer Student	Not First	0.800	1.000	5	6	0.200
200’s	New Transfer Student	Not First	0.778	0.833	9	6	0.056
100’s	New Student	Unknown	0.667	1.000	3	2	0.333
200’s	New Student	Unknown	1.000	NA	2	NA	NA
100’s	New Transfer Student	Unknown	NA	0.000	NA	1	NA
200’s	New Transfer Student	Unknown	1.000	0.667	1	3	-0.333

Question 8 Summary
MathLevel	Transfer	First Gen	Avg2019	Avg2020	n2019	n2020	AvgDiff
100’s	New Student	First Gen	0.800	0.875	5	8	0.075
200’s	New Student	First Gen	0.789	0.944	19	18	0.155
100’s	New Transfer Student	First Gen	1.000	1.000	7	4	0.000
200’s	New Transfer Student	First Gen	0.667	1.000	3	5	0.333
100’s	New Student	Not First	0.867	0.815	30	27	-0.052
200’s	New Student	Not First	0.828	0.838	93	68	0.010
100’s	New Transfer Student	Not First	0.800	1.000	5	7	0.200
200’s	New Transfer Student	Not First	1.000	1.000	9	6	0.000
100’s	New Student	Unknown	1.000	0.667	3	3	-0.333
200’s	New Student	Unknown	1.000	NA	2	NA	NA
100’s	New Transfer Student	Unknown	NA	1.000	NA	1	NA
200’s	New Transfer Student	Unknown	1.000	0.667	1	3	-0.333

Question 9 Summary
MathLevel	Transfer	First Gen	Avg2019	Avg2020	n2019	n2020	AvgDiff
100’s	New Student	First Gen	0.800	1.000	5	8	0.200
200’s	New Student	First Gen	0.947	1.000	19	18	0.053
100’s	New Transfer Student	First Gen	1.000	0.750	7	4	-0.250
200’s	New Transfer Student	First Gen	1.000	0.833	3	6	-0.167
100’s	New Student	Not First	1.000	0.964	31	28	-0.036
200’s	New Student	Not First	0.925	0.956	93	68	0.031
100’s	New Transfer Student	Not First	1.000	1.000	5	7	0.000
200’s	New Transfer Student	Not First	1.000	0.833	9	6	-0.167
100’s	New Student	Unknown	0.667	0.500	3	2	-0.167
200’s	New Student	Unknown	1.000	NA	2	NA	NA
100’s	New Transfer Student	Unknown	NA	0.000	NA	1	NA
200’s	New Transfer Student	Unknown	1.000	1.000	1	3	0.000

Question 10 Summary
MathLevel	Transfer	First Gen	Avg2019	Avg2020	n2019	n2020	AvgDiff
100’s	New Student	First Gen	0.400	0.778	5	9	0.378
200’s	New Student	First Gen	0.947	0.833	19	18	-0.114
100’s	New Transfer Student	First Gen	0.857	1.000	7	4	0.143
200’s	New Transfer Student	First Gen	1.000	0.667	3	6	-0.333
100’s	New Student	Not First	0.938	0.963	32	27	0.025
200’s	New Student	Not First	0.882	0.942	93	69	0.060
100’s	New Transfer Student	Not First	1.000	0.571	5	7	-0.429
200’s	New Transfer Student	Not First	0.889	0.833	9	6	-0.056
100’s	New Student	Unknown	1.000	0.667	3	3	-0.333
200’s	New Student	Unknown	1.000	NA	2	NA	NA
100’s	New Transfer Student	Unknown	NA	1.000	NA	1	NA
200’s	New Transfer Student	Unknown	1.000	1.000	1	3	0.000

Question 15 Summary
MathLevel	Transfer	First Gen	Avg2019	Avg2020	n2019	n2020	AvgDiff
100’s	New Student	First Gen	0.600	0.750	5	8	0.150
200’s	New Student	First Gen	0.895	1.000	19	18	0.105
100’s	New Transfer Student	First Gen	0.857	0.750	7	4	-0.107
200’s	New Transfer Student	First Gen	0.667	1.000	3	5	0.333
100’s	New Student	Not First	0.774	0.893	31	28	0.119
200’s	New Student	Not First	0.804	0.896	92	67	0.091
100’s	New Transfer Student	Not First	0.800	0.857	5	7	0.057
200’s	New Transfer Student	Not First	0.889	0.833	9	6	-0.056
100’s	New Student	Unknown	1.000	1.000	3	2	0.000
200’s	New Student	Unknown	0.500	NA	2	NA	NA
100’s	New Transfer Student	Unknown	NA	1.000	NA	1	NA
200’s	New Transfer Student	Unknown	1.000	0.667	1	3	-0.333

Question 16 Summary
MathLevel	Transfer	First Gen	Avg2019	Avg2020	n2019	n2020	AvgDiff
100’s	New Student	First Gen	0.600	0.750	5	8	0.150
200’s	New Student	First Gen	0.895	0.944	19	18	0.050
100’s	New Transfer Student	First Gen	0.857	0.750	7	4	-0.107
200’s	New Transfer Student	First Gen	0.667	1.000	3	5	0.333
100’s	New Student	Not First	0.742	0.893	31	28	0.151
200’s	New Student	Not First	0.837	0.925	92	67	0.088
100’s	New Transfer Student	Not First	0.800	0.857	5	7	0.057
200’s	New Transfer Student	Not First	1.000	0.833	8	6	-0.167
100’s	New Student	Unknown	1.000	1.000	3	2	0.000
200’s	New Student	Unknown	0.500	NA	2	NA	NA
100’s	New Transfer Student	Unknown	NA	1.000	NA	1	NA
200’s	New Transfer Student	Unknown	1.000	0.667	1	3	-0.333

10.2 BY Cohort, Math Level, and Rural status

out3 <- lapply(X = bin_names, FUN = q_means, data = missed_data, preds = preds[c(1,2, 8)])

out3e <- lapply(FUN = nice_it, X= out3)

for(x in 1:length(out3e)){
  print(kable(out3e[[x]], digits = 3, col.names = c("MathLevel", "Rural", "Avg2019", "Avg2020", "n2019", "n2020", "AvgDiff"), caption = paste0("Question ", qs[x], " Summary")) %>% 
          kable_styling(bootstrap_options = "striped",full_width = T) )
}

Question 3 Summary
MathLevel	Rural	Avg2019	Avg2020	n2019	n2020	AvgDiff
100’s	OutofState_International	1.000	1.000	9	6	0.000
200’s	OutofState_International	1.000	1.000	14	12	0.000
100’s	Tier1&2	0.889	0.955	27	22	0.066
200’s	Tier1&2	0.978	0.900	46	40	-0.078
100’s	Tier3	1.000	0.960	15	25	-0.040
200’s	Tier3	0.971	0.959	68	49	-0.011

Question 4 Summary
MathLevel	Rural	Avg2019	Avg2020	n2019	n2020	AvgDiff
100’s	OutofState_International	0.889	1.000	9	6	0.111
200’s	OutofState_International	1.000	1.000	14	12	0.000
100’s	Tier1&2	0.923	0.955	26	22	0.031
200’s	Tier1&2	1.000	0.925	46	40	-0.075
100’s	Tier3	1.000	0.920	15	25	-0.080
200’s	Tier3	0.971	0.939	68	49	-0.032

Question 5 Summary
MathLevel	Rural	Avg2019	Avg2020	n2019	n2020	AvgDiff
100’s	OutofState_International	0.778	1.000	9	6	0.222
200’s	OutofState_International	0.929	0.917	14	12	-0.012
100’s	Tier1&2	0.654	0.850	26	20	0.196
200’s	Tier1&2	0.848	0.868	46	38	0.021
100’s	Tier3	0.812	0.826	16	23	0.014
200’s	Tier3	0.853	0.848	68	46	-0.005

Question 6 Summary
MathLevel	Rural	Avg2019	Avg2020	n2019	n2020	AvgDiff
100’s	OutofState_International	0.667	1.000	9	6	0.333
200’s	OutofState_International	0.929	0.917	14	12	-0.012
100’s	Tier1&2	0.692	0.842	26	19	0.150
200’s	Tier1&2	0.826	0.842	46	38	0.016
100’s	Tier3	0.812	0.783	16	23	-0.030
200’s	Tier3	0.868	0.783	68	46	-0.085

Question 7 Summary
MathLevel	Rural	Avg2019	Avg2020	n2019	n2020	AvgDiff
100’s	OutofState_International	0.667	1.000	9	6	0.333
200’s	OutofState_International	0.929	0.917	14	12	-0.012
100’s	Tier1&2	0.692	0.800	26	20	0.108
200’s	Tier1&2	0.826	0.842	46	38	0.016
100’s	Tier3	0.812	0.783	16	23	-0.030
200’s	Tier3	0.853	0.804	68	46	-0.049

Question 8 Summary
MathLevel	Rural	Avg2019	Avg2020	n2019	n2020	AvgDiff
100’s	OutofState_International	1.000	1.000	9	6	0.000
200’s	OutofState_International	0.857	0.750	14	12	-0.107
100’s	Tier1&2	0.920	0.857	25	21	-0.063
200’s	Tier1&2	0.826	0.868	46	38	0.042
100’s	Tier3	0.750	0.826	16	23	0.076
200’s	Tier3	0.836	0.896	67	48	0.060

Question 9 Summary
MathLevel	Rural	Avg2019	Avg2020	n2019	n2020	AvgDiff
100’s	OutofState_International	0.889	1.000	9	6	0.111
200’s	OutofState_International	0.929	1.000	14	12	0.071
100’s	Tier1&2	0.962	0.900	26	20	-0.062
200’s	Tier1&2	0.957	0.974	46	39	0.018
100’s	Tier3	1.000	0.917	16	24	-0.083
200’s	Tier3	0.925	0.917	67	48	-0.009

Question 10 Summary
MathLevel	Rural	Avg2019	Avg2020	n2019	n2020	AvgDiff
100’s	OutofState_International	0.889	1.000	9	6	0.111
200’s	OutofState_International	0.857	0.833	14	12	-0.024
100’s	Tier1&2	0.889	0.864	27	22	-0.025
200’s	Tier1&2	0.891	0.923	46	39	0.032
100’s	Tier3	0.875	0.826	16	23	-0.049
200’s	Tier3	0.910	0.898	67	49	-0.012

Question 15 Summary
MathLevel	Rural	Avg2019	Avg2020	n2019	n2020	AvgDiff
100’s	OutofState_International	0.889	0.833	9	6	-0.056
200’s	OutofState_International	0.714	0.833	14	12	0.119
100’s	Tier1&2	0.808	0.950	26	20	0.142
200’s	Tier1&2	0.870	0.947	46	38	0.078
100’s	Tier3	0.688	0.792	16	24	0.104
200’s	Tier3	0.803	0.894	66	47	0.091

Question 16 Summary
MathLevel	Rural	Avg2019	Avg2020	n2019	n2020	AvgDiff
100’s	OutofState_International	0.889	0.833	9	6	-0.056
200’s	OutofState_International	0.786	0.917	14	12	0.131
100’s	Tier1&2	0.769	0.950	26	20	0.181
200’s	Tier1&2	0.889	0.921	45	38	0.032
100’s	Tier3	0.688	0.792	16	24	0.104
200’s	Tier3	0.833	0.915	66	47	0.082

11 Logistic Regression with Variable Selection

On the full data I’ll do some automated variable selection just to see what variables pop out as useful.

full_fit <- function(data, response, preds){
  fit <- glm(as.formula(paste0(response, "~", "(", paste(preds, collapse = "*"), ")^2")), data = data, family = binomial)
  mod <- stepAIC(fit, scope = list(lower =~Cohort, upper = fit), trace = FALSE)
  summary(mod)
}


#remove NAs before use...
full_data <- full_data %>% filter(!is.na(FirstGenStatus))
full_data <- full_data %>% filter(!is.na(RuralStatus))

11.1 Cohort, Math Level, and Transfer

lapply(X = bin_names, FUN = full_fit, data = full_data, preds = preds[c(1,2, 7)])

## [[1]]
## 
## Call:
## glm(formula = HW6_Q_3_score_bin ~ Cohort + MTHLevel + ORIG_ENROLL_STATUS + 
##     MTHLevel:ORIG_ENROLL_STATUS, family = binomial, data = data)
## 
## Deviance Residuals: 
##     Min       1Q   Median       3Q      Max  
## -2.8553   0.1850   0.2164   0.2266   0.3903  
## 
## Coefficients:
##                                                       Estimate Std. Error
## (Intercept)                                             3.6496     0.5191
## CohortSpring2020                                       -0.3162     0.4826
## MTHLevel200's                                           0.4097     0.5660
## ORIG_ENROLL_STATUSNew Transfer Student                 15.0798  1042.7900
## MTHLevel200's:ORIG_ENROLL_STATUSNew Transfer Student  -16.2864  1042.7902
##                                                      z value Pr(>|z|)    
## (Intercept)                                            7.030 2.06e-12 ***
## CohortSpring2020                                      -0.655    0.512    
## MTHLevel200's                                          0.724    0.469    
## ORIG_ENROLL_STATUSNew Transfer Student                 0.014    0.988    
## MTHLevel200's:ORIG_ENROLL_STATUSNew Transfer Student  -0.016    0.988    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for binomial family taken to be 1)
## 
##     Null deviance: 168.40  on 720  degrees of freedom
## Residual deviance: 162.67  on 716  degrees of freedom
##   (38 observations deleted due to missingness)
## AIC: 172.67
## 
## Number of Fisher Scoring iterations: 17
## 
## 
## [[2]]
## 
## Call:
## glm(formula = HW6_Q_4_score_bin ~ Cohort + MTHLevel + ORIG_ENROLL_STATUS + 
##     Cohort:ORIG_ENROLL_STATUS + MTHLevel:ORIG_ENROLL_STATUS, 
##     family = binomial, data = data)
## 
## Deviance Residuals: 
##     Min       1Q   Median       3Q      Max  
## -2.9791   0.1542   0.1736   0.2514   0.5541  
## 
## Coefficients:
##                                                         Estimate Std. Error
## (Intercept)                                               3.2016     0.4775
## CohortSpring2020                                          0.2375     0.5932
## MTHLevel200's                                             0.9866     0.5853
## ORIG_ENROLL_STATUSNew Transfer Student                    1.0912     1.2878
## CohortSpring2020:ORIG_ENROLL_STATUSNew Transfer Student  -2.2297     1.2505
## MTHLevel200's:ORIG_ENROLL_STATUSNew Transfer Student     -1.4910     1.0561
##                                                         z value Pr(>|z|)    
## (Intercept)                                               6.705 2.02e-11 ***
## CohortSpring2020                                          0.400   0.6888    
## MTHLevel200's                                             1.686   0.0919 .  
## ORIG_ENROLL_STATUSNew Transfer Student                    0.847   0.3968    
## CohortSpring2020:ORIG_ENROLL_STATUSNew Transfer Student  -1.783   0.0746 .  
## MTHLevel200's:ORIG_ENROLL_STATUSNew Transfer Student     -1.412   0.1580    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for binomial family taken to be 1)
## 
##     Null deviance: 175.56  on 718  degrees of freedom
## Residual deviance: 161.36  on 713  degrees of freedom
##   (40 observations deleted due to missingness)
## AIC: 173.36
## 
## Number of Fisher Scoring iterations: 7
## 
## 
## [[3]]
## 
## Call:
## glm(formula = HW6_Q_5_score_bin ~ Cohort + MTHLevel, family = binomial, 
##     data = data)
## 
## Deviance Residuals: 
##     Min       1Q   Median       3Q      Max  
## -2.3367   0.3673   0.4696   0.4696   0.6069  
## 
## Coefficients:
##                  Estimate Std. Error z value Pr(>|z|)    
## (Intercept)        1.5985     0.2211   7.230 4.84e-13 ***
## CohortSpring2020   0.5131     0.2588   1.983   0.0474 *  
## MTHLevel200's      0.5510     0.2571   2.144   0.0321 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for binomial family taken to be 1)
## 
##     Null deviance: 466.00  on 709  degrees of freedom
## Residual deviance: 457.15  on 707  degrees of freedom
##   (49 observations deleted due to missingness)
## AIC: 463.15
## 
## Number of Fisher Scoring iterations: 5
## 
## 
## [[4]]
## 
## Call:
## glm(formula = HW6_Q_6_score_bin ~ Cohort + MTHLevel, family = binomial, 
##     data = data)
## 
## Deviance Residuals: 
##     Min       1Q   Median       3Q      Max  
## -2.2485   0.4079   0.4912   0.4912   0.6176  
## 
## Coefficients:
##                  Estimate Std. Error z value Pr(>|z|)    
## (Intercept)        1.5600     0.2158   7.229 4.87e-13 ***
## CohortSpring2020   0.3906     0.2438   1.602   0.1091    
## MTHLevel200's      0.4942     0.2469   2.001   0.0454 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for binomial family taken to be 1)
## 
##     Null deviance: 499.71  on 708  degrees of freedom
## Residual deviance: 492.92  on 706  degrees of freedom
##   (50 observations deleted due to missingness)
## AIC: 498.92
## 
## Number of Fisher Scoring iterations: 5
## 
## 
## [[5]]
## 
## Call:
## glm(formula = HW6_Q_7_score_bin ~ Cohort + MTHLevel, family = binomial, 
##     data = data)
## 
## Deviance Residuals: 
##     Min       1Q   Median       3Q      Max  
## -2.2322   0.4158   0.4935   0.4935   0.6131  
## 
## Coefficients:
##                  Estimate Std. Error z value Pr(>|z|)    
## (Intercept)        1.5760     0.2161   7.294 3.02e-13 ***
## CohortSpring2020   0.3608     0.2416   1.493   0.1354    
## MTHLevel200's      0.4680     0.2460   1.903   0.0571 .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for binomial family taken to be 1)
## 
##     Null deviance: 504.06  on 709  degrees of freedom
## Residual deviance: 498.04  on 707  degrees of freedom
##   (49 observations deleted due to missingness)
## AIC: 504.04
## 
## Number of Fisher Scoring iterations: 5
## 
## 
## [[6]]
## 
## Call:
## glm(formula = HW6_Q_15_score_bin ~ Cohort + ORIG_ENROLL_STATUS, 
##     family = binomial, data = data)
## 
## Deviance Residuals: 
##     Min       1Q   Median       3Q      Max  
## -2.3187   0.5020   0.5020   0.5208   0.5208  
## 
## Coefficients:
##                                        Estimate Std. Error z value Pr(>|z|)    
## (Intercept)                             1.92953    0.16522  11.679   <2e-16 ***
## CohortSpring2020                        0.07834    0.23579   0.332    0.740    
## ORIG_ENROLL_STATUSNew Transfer Student  0.60981    0.41103   1.484    0.138    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for binomial family taken to be 1)
## 
##     Null deviance: 508.14  on 709  degrees of freedom
## Residual deviance: 505.50  on 707  degrees of freedom
##   (49 observations deleted due to missingness)
## AIC: 511.5
## 
## Number of Fisher Scoring iterations: 5
## 
## 
## [[7]]
## 
## Call:
## glm(formula = HW6_Q_16_score_bin ~ Cohort + ORIG_ENROLL_STATUS + 
##     Cohort:ORIG_ENROLL_STATUS, family = binomial, data = data)
## 
## Deviance Residuals: 
##     Min       1Q   Median       3Q      Max  
## -2.8111   0.2635   0.2635   0.3315   0.4172  
## 
## Coefficients:
##                                                         Estimate Std. Error
## (Intercept)                                               2.8739     0.2493
## CohortSpring2020                                          0.4690     0.4070
## ORIG_ENROLL_STATUSNew Transfer Student                    1.0579     1.0400
## CohortSpring2020:ORIG_ENROLL_STATUSNew Transfer Student  -2.0029     1.2074
##                                                         z value Pr(>|z|)    
## (Intercept)                                              11.528   <2e-16 ***
## CohortSpring2020                                          1.152   0.2493    
## ORIG_ENROLL_STATUSNew Transfer Student                    1.017   0.3090    
## CohortSpring2020:ORIG_ENROLL_STATUSNew Transfer Student  -1.659   0.0972 .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for binomial family taken to be 1)
## 
##     Null deviance: 261.00  on 710  degrees of freedom
## Residual deviance: 257.28  on 707  degrees of freedom
##   (48 observations deleted due to missingness)
## AIC: 265.28
## 
## Number of Fisher Scoring iterations: 6
## 
## 
## [[8]]
## 
## Call:
## glm(formula = HW6_Q_17_score_bin ~ Cohort + MTHLevel + ORIG_ENROLL_STATUS + 
##     Cohort:MTHLevel, family = binomial, data = data)
## 
## Deviance Residuals: 
##     Min       1Q   Median       3Q      Max  
## -2.5161   0.2936   0.3983   0.4066   0.6972  
## 
## Coefficients:
##                                        Estimate Std. Error z value Pr(>|z|)    
## (Intercept)                             2.53751    0.34561   7.342  2.1e-13 ***
## CohortSpring2020                       -0.42858    0.45641  -0.939   0.3477    
## MTHLevel200's                          -0.08611    0.39948  -0.216   0.8293    
## ORIG_ENROLL_STATUSNew Transfer Student -0.81826    0.32633  -2.507   0.0122 *  
## CohortSpring2020:MTHLevel200's          1.09953    0.58694   1.873   0.0610 .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for binomial family taken to be 1)
## 
##     Null deviance: 397.50  on 713  degrees of freedom
## Residual deviance: 384.64  on 709  degrees of freedom
##   (45 observations deleted due to missingness)
## AIC: 394.64
## 
## Number of Fisher Scoring iterations: 5
## 
## 
## [[9]]
## 
## Call:
## glm(formula = HW6_Q_18_score_bin ~ Cohort, family = binomial, 
##     data = data)
## 
## Deviance Residuals: 
##     Min       1Q   Median       3Q      Max  
## -2.2835   0.3914   0.3914   0.5338   0.5338  
## 
## Coefficients:
##                  Estimate Std. Error z value Pr(>|z|)    
## (Intercept)        1.8765     0.1534  12.232   <2e-16 ***
## CohortSpring2020   0.6540     0.2583   2.532   0.0113 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for binomial family taken to be 1)
## 
##     Null deviance: 474.22  on 707  degrees of freedom
## Residual deviance: 467.51  on 706  degrees of freedom
##   (51 observations deleted due to missingness)
## AIC: 471.51
## 
## Number of Fisher Scoring iterations: 5
## 
## 
## [[10]]
## 
## Call:
## glm(formula = HW6_Q_19_score_bin ~ Cohort, family = binomial, 
##     data = data)
## 
## Deviance Residuals: 
##     Min       1Q   Median       3Q      Max  
## -2.2495   0.4074   0.4074   0.5047   0.5047  
## 
## Coefficients:
##                  Estimate Std. Error z value Pr(>|z|)    
## (Intercept)        1.9966     0.1607  12.427   <2e-16 ***
## CohortSpring2020   0.4506     0.2570   1.753   0.0796 .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for binomial family taken to be 1)
## 
##     Null deviance: 460.98  on 706  degrees of freedom
## Residual deviance: 457.84  on 705  degrees of freedom
##   (52 observations deleted due to missingness)
## AIC: 461.84
## 
## Number of Fisher Scoring iterations: 5

11.2 Cohort, Math Level, and Rural Status

lapply(X = bin_names, FUN = full_fit, data = full_data, preds = preds[c(1,2, 8)])

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## [[1]]
## 
## Call:
## glm(formula = HW6_Q_3_score_bin ~ Cohort + RuralStatus, family = binomial, 
##     data = data)
## 
## Deviance Residuals: 
##     Min       1Q   Median       3Q      Max  
## -2.8435   0.1882   0.2196   0.2667   0.3108  
## 
## Coefficients:
##                     Estimate Std. Error z value Pr(>|z|)
## (Intercept)          19.7119  1138.1521   0.017    0.986
## CohortSpring2020     -0.3123     0.4830  -0.647    0.518
## RuralStatusTier1&2  -16.3937  1138.1521  -0.014    0.989
## RuralStatusTier3    -15.6869  1138.1521  -0.014    0.989
## 
## (Dispersion parameter for binomial family taken to be 1)
## 
##     Null deviance: 168.40  on 720  degrees of freedom
## Residual deviance: 161.12  on 717  degrees of freedom
##   (38 observations deleted due to missingness)
## AIC: 169.12
## 
## Number of Fisher Scoring iterations: 18
## 
## 
## [[2]]
## 
## Call:
## glm(formula = HW6_Q_4_score_bin ~ (Cohort * MTHLevel * RuralStatus)^2, 
##     family = binomial, data = data)
## 
## Deviance Residuals: 
##      Min        1Q    Median        3Q       Max  
## -2.68735   0.00005   0.23571   0.27218   0.47165  
## 
## Coefficients:
##                                                    Estimate Std. Error z value
## (Intercept)                                          2.1401     0.7475   2.863
## CohortSpring2020                                    18.4260  4917.5199   0.004
## MTHLevel200's                                       18.4260  3184.4685   0.006
## RuralStatusTier1&2                                   1.1371     1.0381   1.095
## RuralStatusTier3                                    18.4260  2839.1315   0.006
## CohortSpring2020:MTHLevel200's                     -18.4260  6812.7705  -0.003
## CohortSpring2020:RuralStatusTier1&2                -18.3359  4917.5201  -0.004
## CohortSpring2020:RuralStatusTier3                  -36.1989  5678.2629  -0.006
## MTHLevel200's:RuralStatusTier1&2                    -1.1371  3757.6798   0.000
## MTHLevel200's:RuralStatusTier3                     -35.4086  4266.3225  -0.008
## CohortSpring2020:MTHLevel200's:RuralStatusTier1&2    1.0279  7098.8140   0.000
## CohortSpring2020:MTHLevel200's:RuralStatusTier3     36.1849  7380.6850   0.005
##                                                   Pr(>|z|)   
## (Intercept)                                         0.0042 **
## CohortSpring2020                                    0.9970   
## MTHLevel200's                                       0.9954   
## RuralStatusTier1&2                                  0.2734   
## RuralStatusTier3                                    0.9948   
## CohortSpring2020:MTHLevel200's                      0.9978   
## CohortSpring2020:RuralStatusTier1&2                 0.9970   
## CohortSpring2020:RuralStatusTier3                   0.9949   
## MTHLevel200's:RuralStatusTier1&2                    0.9998   
## MTHLevel200's:RuralStatusTier3                      0.9934   
## CohortSpring2020:MTHLevel200's:RuralStatusTier1&2   0.9999   
## CohortSpring2020:MTHLevel200's:RuralStatusTier3     0.9961   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for binomial family taken to be 1)
## 
##     Null deviance: 175.56  on 718  degrees of freedom
## Residual deviance: 160.79  on 707  degrees of freedom
##   (40 observations deleted due to missingness)
## AIC: 184.79
## 
## Number of Fisher Scoring iterations: 19
## 
## 
## [[3]]
## 
## Call:
## glm(formula = HW6_Q_5_score_bin ~ Cohort + MTHLevel, family = binomial, 
##     data = data)
## 
## Deviance Residuals: 
##     Min       1Q   Median       3Q      Max  
## -2.3367   0.3673   0.4696   0.4696   0.6069  
## 
## Coefficients:
##                  Estimate Std. Error z value Pr(>|z|)    
## (Intercept)        1.5985     0.2211   7.230 4.84e-13 ***
## CohortSpring2020   0.5131     0.2588   1.983   0.0474 *  
## MTHLevel200's      0.5510     0.2571   2.144   0.0321 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for binomial family taken to be 1)
## 
##     Null deviance: 466.00  on 709  degrees of freedom
## Residual deviance: 457.15  on 707  degrees of freedom
##   (49 observations deleted due to missingness)
## AIC: 463.15
## 
## Number of Fisher Scoring iterations: 5
## 
## 
## [[4]]
## 
## Call:
## glm(formula = HW6_Q_6_score_bin ~ Cohort + MTHLevel, family = binomial, 
##     data = data)
## 
## Deviance Residuals: 
##     Min       1Q   Median       3Q      Max  
## -2.2485   0.4079   0.4912   0.4912   0.6176  
## 
## Coefficients:
##                  Estimate Std. Error z value Pr(>|z|)    
## (Intercept)        1.5600     0.2158   7.229 4.87e-13 ***
## CohortSpring2020   0.3906     0.2438   1.602   0.1091    
## MTHLevel200's      0.4942     0.2469   2.001   0.0454 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for binomial family taken to be 1)
## 
##     Null deviance: 499.71  on 708  degrees of freedom
## Residual deviance: 492.92  on 706  degrees of freedom
##   (50 observations deleted due to missingness)
## AIC: 498.92
## 
## Number of Fisher Scoring iterations: 5
## 
## 
## [[5]]
## 
## Call:
## glm(formula = HW6_Q_7_score_bin ~ Cohort + MTHLevel, family = binomial, 
##     data = data)
## 
## Deviance Residuals: 
##     Min       1Q   Median       3Q      Max  
## -2.2322   0.4158   0.4935   0.4935   0.6131  
## 
## Coefficients:
##                  Estimate Std. Error z value Pr(>|z|)    
## (Intercept)        1.5760     0.2161   7.294 3.02e-13 ***
## CohortSpring2020   0.3608     0.2416   1.493   0.1354    
## MTHLevel200's      0.4680     0.2460   1.903   0.0571 .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for binomial family taken to be 1)
## 
##     Null deviance: 504.06  on 709  degrees of freedom
## Residual deviance: 498.04  on 707  degrees of freedom
##   (49 observations deleted due to missingness)
## AIC: 504.04
## 
## Number of Fisher Scoring iterations: 5
## 
## 
## [[6]]
## 
## Call:
## glm(formula = HW6_Q_15_score_bin ~ Cohort, family = binomial, 
##     data = data)
## 
## Deviance Residuals: 
##     Min       1Q   Median       3Q      Max  
## -2.0949   0.4861   0.4861   0.5039   0.5039  
## 
## Coefficients:
##                  Estimate Std. Error z value Pr(>|z|)    
## (Intercept)       1.99964    0.16064  12.448   <2e-16 ***
## CohortSpring2020  0.07651    0.23541   0.325    0.745    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for binomial family taken to be 1)
## 
##     Null deviance: 508.14  on 709  degrees of freedom
## Residual deviance: 508.04  on 708  degrees of freedom
##   (49 observations deleted due to missingness)
## AIC: 512.04
## 
## Number of Fisher Scoring iterations: 4
## 
## 
## [[7]]
## 
## Call:
## glm(formula = HW6_Q_16_score_bin ~ Cohort + RuralStatus + Cohort:RuralStatus, 
##     family = binomial, data = data)
## 
## Deviance Residuals: 
##     Min       1Q   Median       3Q      Max  
## -2.6501   0.2462   0.3150   0.3253   0.4590  
## 
## Coefficients:
##                                      Estimate Std. Error z value Pr(>|z|)    
## (Intercept)                            2.1972     0.4714   4.661 3.15e-06 ***
## CohortSpring2020                      16.3688  1044.4582   0.016   0.9875    
## RuralStatusTier1&2                     1.2840     0.6928   1.853   0.0638 .  
## RuralStatusTier3                       0.7817     0.5822   1.343   0.1794    
## CohortSpring2020:RuralStatusTier1&2  -16.5920  1044.4584  -0.016   0.9873    
## CohortSpring2020:RuralStatusTier3    -16.4354  1044.4583  -0.016   0.9874    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for binomial family taken to be 1)
## 
##     Null deviance: 261.00  on 710  degrees of freedom
## Residual deviance: 253.55  on 705  degrees of freedom
##   (48 observations deleted due to missingness)
## AIC: 265.55
## 
## Number of Fisher Scoring iterations: 17
## 
## 
## [[8]]
## 
## Call:
## glm(formula = HW6_Q_17_score_bin ~ Cohort + MTHLevel + Cohort:MTHLevel, 
##     family = binomial, data = data)
## 
## Deviance Residuals: 
##     Min       1Q   Median       3Q      Max  
## -2.4660   0.3130   0.4265   0.4339   0.5287  
## 
## Coefficients:
##                                Estimate Std. Error z value Pr(>|z|)    
## (Intercept)                     2.35138    0.33094   7.105  1.2e-12 ***
## CohortSpring2020               -0.45426    0.45316  -1.002   0.3161    
## MTHLevel200's                  -0.03583    0.39660  -0.090   0.9280    
## CohortSpring2020:MTHLevel200's  1.13027    0.58364   1.937   0.0528 .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for binomial family taken to be 1)
## 
##     Null deviance: 397.5  on 713  degrees of freedom
## Residual deviance: 390.3  on 710  degrees of freedom
##   (45 observations deleted due to missingness)
## AIC: 398.3
## 
## Number of Fisher Scoring iterations: 5
## 
## 
## [[9]]
## 
## Call:
## glm(formula = HW6_Q_18_score_bin ~ Cohort, family = binomial, 
##     data = data)
## 
## Deviance Residuals: 
##     Min       1Q   Median       3Q      Max  
## -2.2835   0.3914   0.3914   0.5338   0.5338  
## 
## Coefficients:
##                  Estimate Std. Error z value Pr(>|z|)    
## (Intercept)        1.8765     0.1534  12.232   <2e-16 ***
## CohortSpring2020   0.6540     0.2583   2.532   0.0113 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for binomial family taken to be 1)
## 
##     Null deviance: 474.22  on 707  degrees of freedom
## Residual deviance: 467.51  on 706  degrees of freedom
##   (51 observations deleted due to missingness)
## AIC: 471.51
## 
## Number of Fisher Scoring iterations: 5
## 
## 
## [[10]]
## 
## Call:
## glm(formula = HW6_Q_19_score_bin ~ Cohort, family = binomial, 
##     data = data)
## 
## Deviance Residuals: 
##     Min       1Q   Median       3Q      Max  
## -2.2495   0.4074   0.4074   0.5047   0.5047  
## 
## Coefficients:
##                  Estimate Std. Error z value Pr(>|z|)    
## (Intercept)        1.9966     0.1607  12.427   <2e-16 ***
## CohortSpring2020   0.4506     0.2570   1.753   0.0796 .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for binomial family taken to be 1)
## 
##     Null deviance: 460.98  on 706  degrees of freedom
## Residual deviance: 457.84  on 705  degrees of freedom
##   (52 observations deleted due to missingness)
## AIC: 461.84
## 
## Number of Fisher Scoring iterations: 5

11.3 Cohort, Math Level, and First Gen

lapply(X = bin_names, FUN = full_fit, data = full_data, preds = preds[c(1,2, 9)])

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## [[1]]
## 
## Call:
## glm(formula = HW6_Q_3_score_bin ~ Cohort, family = binomial, 
##     data = data)
## 
## Deviance Residuals: 
##     Min       1Q   Median       3Q      Max  
## -2.7711   0.2085   0.2085   0.2411   0.2411  
## 
## Coefficients:
##                  Estimate Std. Error z value Pr(>|z|)    
## (Intercept)        3.8177     0.3574  10.682   <2e-16 ***
## CohortSpring2020  -0.2943     0.4803  -0.613     0.54    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for binomial family taken to be 1)
## 
##     Null deviance: 168.40  on 720  degrees of freedom
## Residual deviance: 168.02  on 719  degrees of freedom
##   (38 observations deleted due to missingness)
## AIC: 172.02
## 
## Number of Fisher Scoring iterations: 6
## 
## 
## [[2]]
## 
## Call:
## glm(formula = HW6_Q_4_score_bin ~ Cohort, family = binomial, 
##     data = data)
## 
## Deviance Residuals: 
##     Min       1Q   Median       3Q      Max  
## -2.7701   0.2088   0.2088   0.2535   0.2535  
## 
## Coefficients:
##                  Estimate Std. Error z value Pr(>|z|)    
## (Intercept)        3.8150     0.3574  10.674   <2e-16 ***
## CohortSpring2020  -0.3928     0.4708  -0.834    0.404    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for binomial family taken to be 1)
## 
##     Null deviance: 175.56  on 718  degrees of freedom
## Residual deviance: 174.86  on 717  degrees of freedom
##   (40 observations deleted due to missingness)
## AIC: 178.86
## 
## Number of Fisher Scoring iterations: 6
## 
## 
## [[3]]
## 
## Call:
## glm(formula = HW6_Q_5_score_bin ~ Cohort + MTHLevel + FirstGenStatus + 
##     MTHLevel:FirstGenStatus, family = binomial, data = data)
## 
## Deviance Residuals: 
##     Min       1Q   Median       3Q      Max  
## -2.3345   0.3682   0.4160   0.4727   0.8658  
## 
## Coefficients:
##                                        Estimate Std. Error z value Pr(>|z|)  
## (Intercept)                             0.82245    0.40172   2.047   0.0406 *
## CohortSpring2020                        0.52192    0.26124   1.998   0.0457 *
## MTHLevel200's                           1.26757    0.53966   2.349   0.0188 *
## FirstGenStatusNot First                 1.05914    0.46454   2.280   0.0226 *
## FirstGenStatusUnknown                  -0.03425    0.91170  -0.038   0.9700  
## MTHLevel200's:FirstGenStatusNot First  -1.01399    0.62066  -1.634   0.1023  
## MTHLevel200's:FirstGenStatusUnknown    14.24292  795.33269   0.018   0.9857  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for binomial family taken to be 1)
## 
##     Null deviance: 466.0  on 709  degrees of freedom
## Residual deviance: 449.9  on 703  degrees of freedom
##   (49 observations deleted due to missingness)
## AIC: 463.9
## 
## Number of Fisher Scoring iterations: 15
## 
## 
## [[4]]
## 
## Call:
## glm(formula = HW6_Q_6_score_bin ~ Cohort + MTHLevel + FirstGenStatus + 
##     MTHLevel:FirstGenStatus, family = binomial, data = data)
## 
## Deviance Residuals: 
##     Min       1Q   Median       3Q      Max  
## -2.2419   0.4111   0.4586   0.4950   0.8489  
## 
## Coefficients:
##                                        Estimate Std. Error z value Pr(>|z|)  
## (Intercept)                             0.83524    0.40159   2.080   0.0375 *
## CohortSpring2020                        0.39087    0.24587   1.590   0.1119  
## MTHLevel200's                           1.18496    0.52760   2.246   0.0247 *
## FirstGenStatusNot First                 0.97330    0.45943   2.119   0.0341 *
## FirstGenStatusUnknown                   0.02796    0.91014   0.031   0.9755  
## MTHLevel200's:FirstGenStatusNot First  -0.95581    0.60253  -1.586   0.1127  
## MTHLevel200's:FirstGenStatusUnknown    14.31313  797.19440   0.018   0.9857  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for binomial family taken to be 1)
## 
##     Null deviance: 499.71  on 708  degrees of freedom
## Residual deviance: 486.29  on 702  degrees of freedom
##   (50 observations deleted due to missingness)
## AIC: 500.29
## 
## Number of Fisher Scoring iterations: 15
## 
## 
## [[5]]
## 
## Call:
## glm(formula = HW6_Q_7_score_bin ~ Cohort + MTHLevel + FirstGenStatus + 
##     MTHLevel:FirstGenStatus, family = binomial, data = data)
## 
## Deviance Residuals: 
##     Min       1Q   Median       3Q      Max  
## -2.2363   0.4138   0.4362   0.4929   0.9384  
## 
## Coefficients:
##                                       Estimate Std. Error z value Pr(>|z|)   
## (Intercept)                             0.5920     0.3794   1.560  0.11868   
## CohortSpring2020                        0.3680     0.2446   1.505  0.13244   
## MTHLevel200's                           1.4392     0.5094   2.825  0.00472 **
## FirstGenStatusNot First                 1.3447     0.4449   3.022  0.00251 **
## FirstGenStatusUnknown                   0.2845     0.8992   0.316  0.75170   
## MTHLevel200's:FirstGenStatusNot First  -1.3290     0.5913  -2.248  0.02460 * 
## MTHLevel200's:FirstGenStatusUnknown    -0.4276     1.4356  -0.298  0.76581   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for binomial family taken to be 1)
## 
##     Null deviance: 504.06  on 709  degrees of freedom
## Residual deviance: 488.88  on 703  degrees of freedom
##   (49 observations deleted due to missingness)
## AIC: 502.88
## 
## Number of Fisher Scoring iterations: 5
## 
## 
## [[6]]
## 
## Call:
## glm(formula = HW6_Q_15_score_bin ~ Cohort + FirstGenStatus + 
##     Cohort:FirstGenStatus, family = binomial, data = data)
## 
## Deviance Residuals: 
##     Min       1Q   Median       3Q      Max  
## -2.3614   0.4972   0.4972   0.5073   0.6335  
## 
## Coefficients:
##                                          Estimate Std. Error z value Pr(>|z|)
## (Intercept)                                1.7540     0.3610   4.858 1.18e-06
## CohortSpring2020                           0.9706     0.6299   1.541    0.123
## FirstGenStatusNot First                    0.2741     0.4033   0.680    0.497
## FirstGenStatusUnknown                     13.8120   550.0887   0.025    0.980
## CohortSpring2020:FirstGenStatusNot First  -1.0134     0.6816  -1.487    0.137
## CohortSpring2020:FirstGenStatusUnknown   -15.0326   550.0895  -0.027    0.978
##                                             
## (Intercept)                              ***
## CohortSpring2020                            
## FirstGenStatusNot First                     
## FirstGenStatusUnknown                       
## CohortSpring2020:FirstGenStatusNot First    
## CohortSpring2020:FirstGenStatusUnknown      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for binomial family taken to be 1)
## 
##     Null deviance: 508.14  on 709  degrees of freedom
## Residual deviance: 503.18  on 704  degrees of freedom
##   (49 observations deleted due to missingness)
## AIC: 515.18
## 
## Number of Fisher Scoring iterations: 14
## 
## 
## [[7]]
## 
## Call:
## glm(formula = HW6_Q_16_score_bin ~ Cohort + MTHLevel + FirstGenStatus + 
##     MTHLevel:FirstGenStatus, family = binomial, data = data)
## 
## Deviance Residuals: 
##     Min       1Q   Median       3Q      Max  
## -2.8774   0.2029   0.2979   0.3366   1.0304  
## 
## Coefficients:
##                                       Estimate Std. Error z value Pr(>|z|)    
## (Intercept)                             2.6761     0.7414   3.609 0.000307 ***
## CohortSpring2020                        0.2503     0.3737   0.670 0.502965    
## MTHLevel200's                           0.2934     0.8922   0.329 0.742290    
## FirstGenStatusNot First                 1.1972     0.9335   1.283 0.199666    
## FirstGenStatusUnknown                  -2.3200     1.0372  -2.237 0.025298 *  
## MTHLevel200's:FirstGenStatusNot First  -1.3244     1.0895  -1.216 0.224128    
## MTHLevel200's:FirstGenStatusUnknown    15.7831   798.9864   0.020 0.984240    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for binomial family taken to be 1)
## 
##     Null deviance: 261.00  on 710  degrees of freedom
## Residual deviance: 247.48  on 704  degrees of freedom
##   (48 observations deleted due to missingness)
## AIC: 261.48
## 
## Number of Fisher Scoring iterations: 15
## 
## 
## [[8]]
## 
## Call:
## glm(formula = HW6_Q_17_score_bin ~ (Cohort * MTHLevel * FirstGenStatus)^2, 
##     family = binomial, data = data)
## 
## Deviance Residuals: 
##     Min       1Q   Median       3Q      Max  
## -2.5776   0.2711   0.3898   0.4463   0.9005  
## 
## Coefficients:
##                                                         Estimate Std. Error
## (Intercept)                                               1.0986     0.5164
## CohortSpring2020                                          0.7732     0.9185
## MTHLevel200's                                             1.4404     0.7914
## FirstGenStatusNot First                                   1.7579     0.6915
## FirstGenStatusUnknown                                    15.4675  1385.3779
## CohortSpring2020:MTHLevel200's                           -1.0715     1.1935
## CohortSpring2020:FirstGenStatusNot First                 -1.5660     1.0936
## CohortSpring2020:FirstGenStatusUnknown                  -16.6461  1385.3784
## MTHLevel200's:FirstGenStatusNot First                    -2.0403     0.9450
## MTHLevel200's:FirstGenStatusUnknown                      -1.4404  1832.6827
## CohortSpring2020:MTHLevel200's:FirstGenStatusNot First    2.8929     1.4072
## CohortSpring2020:MTHLevel200's:FirstGenStatusUnknown     16.9444  2123.7444
##                                                        z value Pr(>|z|)  
## (Intercept)                                              2.127   0.0334 *
## CohortSpring2020                                         0.842   0.3999  
## MTHLevel200's                                            1.820   0.0688 .
## FirstGenStatusNot First                                  2.542   0.0110 *
## FirstGenStatusUnknown                                    0.011   0.9911  
## CohortSpring2020:MTHLevel200's                          -0.898   0.3693  
## CohortSpring2020:FirstGenStatusNot First                -1.432   0.1522  
## CohortSpring2020:FirstGenStatusUnknown                  -0.012   0.9904  
## MTHLevel200's:FirstGenStatusNot First                   -2.159   0.0308 *
## MTHLevel200's:FirstGenStatusUnknown                     -0.001   0.9994  
## CohortSpring2020:MTHLevel200's:FirstGenStatusNot First   2.056   0.0398 *
## CohortSpring2020:MTHLevel200's:FirstGenStatusUnknown     0.008   0.9936  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for binomial family taken to be 1)
## 
##     Null deviance: 397.50  on 713  degrees of freedom
## Residual deviance: 377.68  on 702  degrees of freedom
##   (45 observations deleted due to missingness)
## AIC: 401.68
## 
## Number of Fisher Scoring iterations: 15
## 
## 
## [[9]]
## 
## Call:
## glm(formula = HW6_Q_18_score_bin ~ Cohort + MTHLevel + FirstGenStatus + 
##     MTHLevel:FirstGenStatus, family = binomial, data = data)
## 
## Deviance Residuals: 
##     Min       1Q   Median       3Q      Max  
## -2.4036   0.3617   0.3966   0.5399   1.0334  
## 
## Coefficients:
##                                       Estimate Std. Error z value Pr(>|z|)   
## (Intercept)                             1.3053     0.4601   2.837  0.00456 **
## CohortSpring2020                        0.6508     0.2608   2.496  0.01257 * 
## MTHLevel200's                           0.8753     0.6014   1.456  0.14553   
## FirstGenStatusNot First                 0.7380     0.5283   1.397  0.16245   
## FirstGenStatusUnknown                  14.8882   841.0358   0.018  0.98588   
## MTHLevel200's:FirstGenStatusNot First  -1.0663     0.6793  -1.570  0.11651   
## MTHLevel200's:FirstGenStatusUnknown   -16.7201   841.0362  -0.020  0.98414   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for binomial family taken to be 1)
## 
##     Null deviance: 474.22  on 707  degrees of freedom
## Residual deviance: 459.75  on 701  degrees of freedom
##   (51 observations deleted due to missingness)
## AIC: 473.75
## 
## Number of Fisher Scoring iterations: 15
## 
## 
## [[10]]
## 
## Call:
## glm(formula = HW6_Q_19_score_bin ~ Cohort + MTHLevel + FirstGenStatus + 
##     MTHLevel:FirstGenStatus, family = binomial, data = data)
## 
## Deviance Residuals: 
##     Min       1Q   Median       3Q      Max  
## -2.2992   0.3902   0.4134   0.4821   0.9914  
## 
## Coefficients:
##                                       Estimate Std. Error z value Pr(>|z|)   
## (Intercept)                             1.3731     0.4600   2.985  0.00284 **
## CohortSpring2020                        0.4435     0.2595   1.709  0.08744 . 
## MTHLevel200's                           0.7526     0.5849   1.287  0.19822   
## FirstGenStatusNot First                 0.6003     0.5193   1.156  0.24769   
## FirstGenStatusUnknown                  14.9314   844.9684   0.018  0.98590   
## MTHLevel200's:FirstGenStatusNot First  -0.6323     0.6614  -0.956  0.33913   
## MTHLevel200's:FirstGenStatusUnknown   -16.6024   844.9688  -0.020  0.98432   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for binomial family taken to be 1)
## 
##     Null deviance: 460.98  on 706  degrees of freedom
## Residual deviance: 450.36  on 700  degrees of freedom
##   (52 observations deleted due to missingness)
## AIC: 464.36
## 
## Number of Fisher Scoring iterations: 15

12 Logistic rough conclusions

Cohort is reasonably important in quite a few of the models. We are doing a lot of model fitting and tests so p-values aren’t a great metric here but we are getting some evidence of an improvement by cohort. Math level is also important in a good number of the models. There are some interactions with cohort and the other variables that are significant here or there as well. This would imply that the intervention might help certain groups more. However, again, with all the testing it is hard to say that these are real results - encouraging to some degree though!

GN 311, June 2020