Read S24

S24_Score <- S24 |> select(contains("Score"), Max.Points
)

Read W24

W24_VB <- 
  read.csv("W24_Midterm_Version_Set_Scores/Midterm_Version_B_scores.csv", header = T)

W24_VB <- 
  W24_VB |> select(
    -c(First.Name, Last.Name,SID, Email, Submission.ID, Sections, Status, Status, View.Count, Submission.Time, Lateness..H.M.S., Submission.Count))

W24_VA <- 
  read.csv("W24_Midterm_Version_Set_Scores/Midterm_Version_A_scores.csv", header = T)

W24_VA <- 
  W24_VA |> select(
    -c(First.Name, Last.Name,SID, Email, Submission.ID, Sections, Status, Status, View.Count, Submission.Time, Lateness..H.M.S., Submission.Count))

Rename Features :

library(stringr)

colnames(W24_VA) <- colnames(W24_VA) |>
  str_replace(
    pattern = "X\\d+\\.\\.Question\\.(\\d+)\\.\\.1\\.0\\.pts\\.",
    replacement = "Question.\\1.Score_VA"
  )


colnames(W24_VB) <- colnames(W24_VB) |>
  str_replace(
    pattern = "X\\d+\\.\\.Question\\.(\\d+)\\.\\.1\\.0\\.pts\\.",
    replacement = "Question.\\1.Score_VB"
  )

W24_lst <- list(W24_VA = W24_VA , W24_VB=W24_VB)

Read F23

F23_VA <- 
  read.csv("F23_Midterm_Version_Set_Scores/Midterm_Version_A_scores.csv", header = T) |> select(
    -c(First.Name, Last.Name,SID, Email, Submission.ID, Sections, Status, Status, View.Count, Submission.Time, Lateness..H.M.S., Submission.Count))


F23_VB <- 
  read.csv("F23_Midterm_Version_Set_Scores/Midterm_Version_B_scores.csv", header = T) |> select(
    -c(First.Name, Last.Name,SID, Email, Submission.ID, Sections, Status, Status, View.Count, Submission.Time, Lateness..H.M.S., Submission.Count))

colnames(F23_VA) <- colnames(F23_VA) |>
  str_replace(
    pattern = "X\\d+\\.\\.Question\\.(\\d+)\\.\\.1\\.0\\.pts\\.",
    replacement = "Question.\\1.Score_VA"
  )


colnames(F23_VB) <- colnames(F23_VB) |>
  str_replace(
    pattern = "X\\d+\\.\\.Question\\.(\\d+)\\.\\.1\\.0\\.pts\\.",
    replacement = "Question.\\1.Score_VB"
  )

F23_lst <- list(F23_VA = F23_VA, F23_VB=F23_VB)

Scores_lst <- list(F23_lst=F23_lst, W24_lst=W24_lst, S24_Score=S24_Score)

Generate Box Plots – Total Score as PCT

Generate PCT Total Score

Scores_lst$S24_Score$Total.Score <- Scores_lst$S24_Score$Total.Score |> as.numeric()
Scores_lst$S24_Score$Max.Points <- Scores_lst$S24_Score$Max.Points |> as.numeric()


Scores_lst$S24_Score <- Scores_lst$S24_Score |> mutate(Score_Pct = Total.Score/Max.Points)


library(purrr)
Scores_lst[c("F23_lst", "W24_lst")] <- 
  Scores_lst[c("F23_lst", "W24_lst")] |>
  map(
    ~ map(
      .x,
      ~ .x |>
        dplyr::mutate(
          Total.Score = as.numeric(Total.Score),
          Max.Points  = as.numeric(Max.Points),
          Score_Pct   = Total.Score / Max.Points
        ) 
    )
  )

score_box_df <- bind_rows(
  data.frame(
    Group = "F23_VA",
    Score_Pct = Scores_lst$F23_lst$F23_VA$Score_Pct
  ),
  data.frame(
    Group = "F23_VB",
    Score_Pct = Scores_lst$F23_lst$F23_VB$Score_Pct
  ),
  data.frame(
    Group = "W24_VA",
    Score_Pct = Scores_lst$W24_lst$W24_VA$Score_Pct
  ),
  data.frame(
    Group = "W24_VB",
    Score_Pct = Scores_lst$W24_lst$W24_VB$Score_Pct
  ),
  data.frame(
    Group = "S24",
    Score_Pct = Scores_lst$S24_Score$Score_Pct
  )
) |>
  filter(!is.na(Score_Pct))

boxplot(
  Score_Pct ~ Group,
  data = score_box_df,
  main = "Score Percentage by Quarter/Year",
  xlab = "Quarter/Year",
  ylab = "Score Percentage",
  las = 2
)

Generate pct Per Q

ignore my unclever method of doing this

make_pct_vec <- function(dat){
  pct_df <- dat |>
    select(starts_with("Q")) |>
    summarize(
      across(
        everything(),
        ~ sum(.x, na.rm = TRUE) / n(),
        .names = "pct_{.col}"
      )
    ) |>
    rename_with(~ paste0("Q", seq_along(.x)))
  
  v <- as.numeric(pct_df)
  names(v) <- colnames(pct_df)
  v
}

v_F23_VA <- make_pct_vec(Scores_lst$F23_lst$F23_VA)
print("v_F23_VA")

## [1] "v_F23_VA"

v_F23_VA

##        Q1        Q2        Q3        Q4        Q5        Q6        Q7        Q8 
## 0.5285714 0.5595238 0.3547619 0.6166667 0.4571429 0.6119048 0.6285714 0.5785714 
##        Q9       Q10       Q11       Q12       Q13       Q14       Q15       Q16 
## 0.4095238 0.5333333 0.5333333 0.4547619 0.3333333 0.3666667 0.4714286 0.5833333 
##       Q17       Q18       Q19       Q20       Q21       Q22       Q23       Q24 
## 0.5809524 0.5880952 0.5047619 0.4642857 0.6047619 0.5071429 0.4500000 0.4952381 
##       Q25       Q26       Q27       Q28       Q29       Q30       Q31       Q32 
## 0.5690476 0.4238095 0.5833333 0.3047619 0.6000000 0.5000000 0.5357143 0.4571429 
##       Q33       Q34 
## 0.4976190 0.2761905

v_F23_VB <- make_pct_vec(Scores_lst$F23_lst$F23_VB)
print("v_F23_VB")

## [1] "v_F23_VB"

v_F23_VB

##        Q1        Q2        Q3        Q4        Q5        Q6        Q7        Q8 
## 0.5577889 0.5477387 0.3743719 0.6055276 0.5050251 0.6005025 0.6005025 0.5778894 
##        Q9       Q10       Q11       Q12       Q13       Q14       Q15       Q16 
## 0.4447236 0.4773869 0.5477387 0.3844221 0.4195980 0.3743719 0.5276382 0.5829146 
##       Q17       Q18       Q19       Q20       Q21       Q22       Q23       Q24 
## 0.5778894 0.5804020 0.5226131 0.4497487 0.5829146 0.5150754 0.4246231 0.5125628 
##       Q25       Q26       Q27       Q28       Q29       Q30       Q31       Q32 
## 0.5552764 0.4648241 0.5778894 0.4221106 0.5929648 0.5201005 0.5276382 0.4698492 
##       Q33       Q34 
## 0.5427136 0.3417085

v_W24_VA <- make_pct_vec(Scores_lst$W24_lst$W24_VA)
print("v_W24_VA")

## [1] "v_W24_VA"

v_W24_VA

##        Q1        Q2        Q3        Q4        Q5        Q6        Q7        Q8 
## 0.4309211 0.4539474 0.4013158 0.2532895 0.2631579 0.2532895 0.4835526 0.3980263 
##        Q9       Q10       Q11       Q12       Q13       Q14       Q15       Q16 
## 0.4835526 0.2960526 0.4967105 0.4506579 0.4375000 0.3980263 0.3848684 0.4605263 
##       Q17       Q18       Q19       Q20       Q21       Q22       Q23       Q24 
## 0.4309211 0.4144737 0.4210526 0.5000000 0.3125000 0.2203947 0.3026316 0.2631579 
##       Q25       Q26       Q27       Q28       Q29       Q30       Q31       Q32 
## 0.4638158 0.4671053 0.4703947 0.3848684 0.3289474 0.4539474 0.3750000 0.3190789 
##       Q33 
## 0.4013158

v_W24_VB <- make_pct_vec(Scores_lst$W24_lst$W24_VB)
print("v_W24_VB")

## [1] "v_W24_VB"

v_W24_VB

##        Q1        Q2        Q3        Q4        Q5        Q6        Q7        Q8 
## 0.3921569 0.4215686 0.3660131 0.2058824 0.2516340 0.2254902 0.4281046 0.3660131 
##        Q9       Q10       Q11       Q12       Q13       Q14       Q15       Q16 
## 0.4281046 0.2712418 0.4444444 0.4084967 0.3823529 0.3856209 0.3692810 0.3954248 
##       Q17       Q18       Q19       Q20       Q21       Q22       Q23       Q24 
## 0.3823529 0.3758170 0.4019608 0.4150327 0.2875817 0.1960784 0.2745098 0.2385621 
##       Q25       Q26       Q27       Q28       Q29       Q30       Q31       Q32 
## 0.4117647 0.4052288 0.3856209 0.3888889 0.3235294 0.4084967 0.3790850 0.3594771 
##       Q33 
## 0.3725490

v_S24    <- make_pct_vec(Scores_lst$S24_Score)
print("v_S24")

## [1] "v_S24"

v_S24

##        Q1        Q2        Q3        Q4        Q5        Q6        Q7        Q8 
## 0.9161290 0.9225806 0.8967742 0.4451613 0.4000000 0.5935484 0.9483871 0.6967742 
##        Q9       Q10       Q11       Q12       Q13       Q14       Q15       Q16 
## 0.9354839 0.5741935 0.9354839 0.8322581 0.8774194 0.8193548 0.8322581 0.8838710 
##       Q17       Q18       Q19       Q20       Q21       Q22       Q23       Q24 
## 0.9032258 0.7741935 0.8322581 0.9290323 0.7354839 0.2903226 0.6838710 0.5870968 
##       Q25       Q26       Q27       Q28       Q29       Q30       Q31       Q32 
## 0.8451613 0.8580645 0.7935484 0.7935484 0.6129032 0.8709677 0.7161290 0.6709677 
##       Q33       Q34 
## 0.4645161 0.4387097

pct_Q_lst <- grep("^v", ls(), value=T) |> mget()

Generate BarPlots Per Q

barplot(v_F23_VA, main = "F23 VA", ylim = c(0, 1))

barplot(v_F23_VB, main = "F23 VB", ylim = c(0, 1))

barplot(v_W24_VA, main = "W24 VA", ylim = c(0, 1))

barplot(v_W24_VB, main = "W24 VB", ylim = c(0, 1))

barplot(v_S24,    main = "S24",    ylim = c(0, 1))

Analyze Correlations (tetrachoric cuz its binary)

library(psych)

get_tetra <- function(dat) {
  dat |>
    select(starts_with("Q")) |>
    tetrachoric()
}

tet_F23_VA <- get_tetra(Scores_lst$F23_lst$F23_VA)

## Warning in cor.smooth(mat): Matrix was not positive definite, smoothing was
## done

tet_F23_VB <- get_tetra(Scores_lst$F23_lst$F23_VB)

## Warning in cor.smooth(mat): Matrix was not positive definite, smoothing was
## done

tet_W24_VA <- get_tetra(Scores_lst$W24_lst$W24_VA)

## Warning in cor.smooth(mat): Matrix was not positive definite, smoothing was
## done

tet_W24_VB <- get_tetra(Scores_lst$W24_lst$W24_VB)

## Warning in cor.smooth(mat): Matrix was not positive definite, smoothing was
## done

tet_S24    <- get_tetra(Scores_lst$S24_Score)

## Warning in cor.smooth(mat): Matrix was not positive definite, smoothing was
## done

tet_F23_VA_cor <- tet_F23_VA$rho
tet_F23_VB_cor <- tet_F23_VB$rho
tet_W24_VA_cor <- tet_W24_VA$rho
tet_W24_VB_cor <- tet_W24_VB$rho
tet_S24_cor <- tet_S24$rho

cor.plot(tet_F23_VA_cor, main = "F23 VA")

cor.plot(tet_F23_VB_cor, main = "F23 VB")

cor.plot(tet_W24_VA_cor, main = "W24 VA")

cor.plot(tet_W24_VB_cor, main = "W24 VB")

cor.plot(tet_S24_cor,    main = "S24")

Per Question Correlation on total score:

\[ \text{For each question } Q_j,\text{ compute the rest score:} \qquad \mathrm{Rest}_j = \mathrm{Total.Score} - Q_j \]

\[ \text{Then correlate } Q_j \text{ with } \mathrm{Rest}_j. \]

High Correlation : item discriminates well. Students who got that question right also tended to score high on the rest of the test.
Low Correlation : item has weak discrimination. Getting it right was only weakly related to doing well overall.
Zero Correlation : item does not distinguish stronger from weaker students much at all
Negative Correlation : a warning sign. Higher-performing students were less likely to get it right, which may suggest a miskeyed item, ambiguous wording, or unusual item behavior.

get_corrected_item_total <- function(dat) {
  
  qdat <- dat |> select(starts_with("Q")) |> mutate(across(everything(), as.numeric))
  
  out <- sapply(seq_along(qdat), function(j) {
    qj <- qdat[[j]]
    rest_score <- rowSums(qdat[, -j, drop = FALSE], na.rm = TRUE)
    cor(qj, rest_score, use = "complete.obs")
  })
  
  data.frame(
    Question = names(qdat),
    Corrected_Item_Total_Cor = out
  ) |> arrange(desc(Corrected_Item_Total_Cor))
}

get_corrected_item_total(Scores_lst$F23_lst$F23_VA)

get_corrected_item_total(Scores_lst$F23_lst$F23_VB)

get_corrected_item_total(Scores_lst$W24_lst$W24_VA)

get_corrected_item_total(Scores_lst$W24_lst$W24_VB)

get_corrected_item_total(Scores_lst$S24_Score)

Generate IRT Model

Generate Bayesian Model

Notes

Purpose : Be able to generate correlation coefficient
Sample from the overall mean
See how the correlation coefficient simplifies
- Estimate the Variability
- When a small number of students get it wrong, check how the variability changes
- Estimate the variability
Put this into a bayesian framework
What happens when everyone gets the question right, all wrong
Prior and data weighting
Add 20 artificiallly genrated observation where there is no correlation
Sample from binomial dist.

Spring 2024 Midterm Q Types :

Side Note:

correct responses are underlined when appropriate.

Guiding Principles :

ALWAYS put every problem in the context of real-world application.
Always provide R-outputs for graphics and calculations. Students must be able to interpret R-Outputs. For example, where do we find \(r^2_{xy}\) in a regression output?

Per Q Problem Types :

Problem Type: Classify a variable as categorical or numerical variable
Template: A real-world variable is described. Decide whether it should be treated as categorical or numerical.
Problem Type: Choose the correct plot for one categorical variable
Template: A real-world categorical variable is given. Choose the most appropriate display for its distribution.
Answer Choices: Box Plot, Bar Plot, Scatter Plot
Problem Type: Choose the correct plot for association between two numerical variables
Template: Two real-world numerical variables are given. Choose the most appropriate display for their relationship.
Answer Choices: Box Plots, Histograms, Scatter Plot
Problem Type: Decide whether empirical rule applies when mean and standard deviation is provided and NOT shape
Template: Provide mean and SD but DONT provide shape – empirical rule does NOT APPLY
Problem Type: Compare two distributions using z-scores to decide which outcome is more likely – understanding the effect of SD in the calculation of z-score.
Template: Two options are described with different means and standard deviations. Compare which option is more likely based on z-score.
Problem Type: Estimate the correlation from a scatterplot with a non-linear pattern
Template: A scatterplot is shown. Decide what value of the correlation would be most reasonable–student must understand correlation as a linear measure.
Problem Type: Compute the mean from a small raw dataset
Template: A small real-world dataset ({x1, x2, x3}) is given. Compute the average value.
Problem Type: Compute the standard deviation from a small raw dataset : {x1, x2, x3}
Template: Compute the standard deviation.
Problem Type: Compute the median from a small raw dataset : {x1, x2, x3}
Template: A small real-world dataset is given. Compute the median.
Problem Type: Interpret the skew of a distribution from a boxplot
Template: A boxplot is shown. Identify what it suggests about skewness – right-skew or left-skew or symmetric.
Problem Type: Two-way contingency table
Template: Conditional Probability problem P(A|B)
Problem Type: Two-way contingency table
Template: Conditional Probability problem P(B|A)
Problem Type: Decide whether two categorical variables are associated or independent – independent events
Template: Is P(A|B) = P(A)? If so, its likely an independent event.
Problem Type: Identify whether a study is an observational study or a controlled experiment
Template: A study description is given. Decide whether researchers RANDOMLY assigned the treatment or only observed what happened.
Problem Type: Identify treatment variable, response variable, and whether the study is observational or experimental
Template: A study description is given. Identify the explanatory variable, the outcome variable, and the type of study. Decide whether researchers RANDOMLY assigned the treatment or only observed what happened.
Problem Type: Use a regression line to make a prediction
Template: A regression equation and an x-value are given. Use the line to predict the corresponding estimated y-value.
Problem Type: Interpret the coefficient of determination \((r^2)\) in context
Template: A regression model and its \(r^2\) are given. Interpret what percent of variation in the response is explained by the explanatory variable.
Problem Type: Interpret the intercept of a regression line in context
Template: A regression equation is given. Interpret the intercept as the predicted response when \(x=0\), and decide whether that interpretation makes sense in context. Note that the intercept doesnt always have a relevant interpretation.
Problem Type: Interpret the slope of a regression line in context
Template: A regression equation is given. Interpret the slope as the average change in the response for a one-unit increase in the explanatory variable.
Problem Type: Find the correlation from \(r^2\) and the direction of the slope
Template: A regression model gives \(r^2\) and the line’s direction. Use that information to determine the correlation.
Problem Type: Decide whether changing units affects correlation – it doesnt – correlation is a unit-less measure
Template: One variable is converted to different units. Determine correlation stays the same.
Problem Type: Choose the best regression model for the research goal
Template: Several candidate regression models are shown – Routputs. Choose the one that best matches the actual research question, not just the one with the largest \(r^2\). Focus is on the research question.
Problem Type: Identify the number of observations in a dataset
Template: A dataset is described in context. Determine how many observations it contains.
Problem Type: Infer the shape of a distribution from its mean, standard deviation, and context of a count variable.
Template: A variable counts how many items are sold per day, so values cannot go below 0. The mean is relatively small, and the standard deviation is large compared with the mean. Decide whether the histogram is most likely symmetric, left-skewed, right-skewed, or could be any shape
Problem Type: Determine which histogram bin contains the median
Template: A histogram is shown. Use cumulative frequency to locate the 50th percentile.
Problem Type: Estimate the proportion in a histogram above or below a cutoff
Template: A histogram is shown. Estimate the proportion of observations that are above or below a specified value.
Problem Type: Match boxplots to histograms for two groups
Template: Histograms and boxplots for two groups are shown separately (R-Output). Match them by comparing center, spread, skew, and outliers.
Problem Type: Decide whether data support causation – data is from observational study.
Template: An observed group difference is described. Data is from observational study but causal claim is made. Focus : Study type (Observational vs. Experiment)
Problem Type: Estimate the standard deviation from a histogram and center
Template: A histogram (R-ouput) is shown along with the mean or median. Use the spread of the data to judge a plausible standard deviation.
Problem Type: Interpret the strength and direction of a linear association from a correlation value
Template: A correlation coefficient is given. Describe the direction and strength of the linear association. Is it positive/negative, and weak/moderate/strong?
Problem Type: Compute correlation from paired z-scores
Template: Generate a table of z-scores for variables. Compute the correlation by multiplying the paired z-scores and averaging.
Problem Type: Infer where the mean lies using skewness and median location.
Template: Provide left/right skew, 50% of data lies below X (Median). 10% score above/below Y. Where might the mean b? Key Point : Mean is in the direction of skew, mean is affected by outliers.
Problem Type: Determine whether z-score is above or below zero.
Template: Provide left/right skew. State median as value. Key Point : z-score is \(z=\frac{x-\bar{x}}{\text{SD}}\) so if \(x>\bar{x}\) then its negative and if \(x<\bar{x}\) its positive. So when skew is present we know \(\text{Median}_{x}<\bar{x} \text{ or, }\text{Median}_{x}>\bar{x}\) depending on the direction of skew.

Saving Data Objects :

v_S24_df <- tibble(
  category = names(v_S24),
  prop_correct = as.numeric(v_S24)
) |> arrange(prop_correct)

v_S24

##        Q1        Q2        Q3        Q4        Q5        Q6        Q7        Q8 
## 0.9161290 0.9225806 0.8967742 0.4451613 0.4000000 0.5935484 0.9483871 0.6967742 
##        Q9       Q10       Q11       Q12       Q13       Q14       Q15       Q16 
## 0.9354839 0.5741935 0.9354839 0.8322581 0.8774194 0.8193548 0.8322581 0.8838710 
##       Q17       Q18       Q19       Q20       Q21       Q22       Q23       Q24 
## 0.9032258 0.7741935 0.8322581 0.9290323 0.7354839 0.2903226 0.6838710 0.5870968 
##       Q25       Q26       Q27       Q28       Q29       Q30       Q31       Q32 
## 0.8451613 0.8580645 0.7935484 0.7935484 0.6129032 0.8709677 0.7161290 0.6709677 
##       Q33       Q34 
## 0.4645161 0.4387097

tet_S24

## Call: tetrachoric(x = select(dat, starts_with("Q")))
## tetrachoric correlation 
##                   Q.1.S Q.2.S Q.3.S Q.4.S Q.5.S Q.6.S Q.7.S Q.8.S Q.9.S Q.10.
## Question.1.Score   1.00                                                      
## Question.2.Score   0.50  1.00                                                
## Question.3.Score   0.20  0.52  1.00                                          
## Question.4.Score   0.15 -0.05  0.02  1.00                                    
## Question.5.Score   0.03  0.27  0.16 -0.10  1.00                              
## Question.6.Score  -0.08  0.11  0.39 -0.12  0.31  1.00                        
## Question.7.Score   0.52  0.31  0.24  0.00  0.19  0.36  1.00                  
## Question.8.Score   0.21  0.23  0.28  0.26  0.20  0.03  0.23  1.00            
## Question.9.Score   0.18  0.42  0.30  0.16  0.18  0.15  0.36  0.28  1.00      
## Question.10.Score  0.35  0.50  0.52  0.36  0.25  0.12  0.11  0.40  0.48  1.00
## Question.11.Score  0.12  0.19  0.14  0.03  0.30  0.09  0.36  0.43  0.49  0.27
## Question.12.Score  0.19  0.30  0.16  0.22  0.17  0.23  0.15  0.34  0.39  0.42
## Question.13.Score -0.04 -0.01  0.33  0.47  0.07  0.39  0.13  0.26  0.09  0.19
## Question.14.Score  0.01  0.25  0.27  0.02  0.25  0.18  0.12  0.23  0.35  0.05
## Question.15.Score  0.02 -0.09  0.05  0.05  0.02  0.24  0.33 -0.05 -0.01 -0.15
## Question.16.Score  0.20  0.15 -0.09  0.15  0.05  0.06  0.18  0.20  0.53  0.24
## Question.17.Score  0.24  0.30  0.09  0.40 -0.12 -0.03  0.17  0.31  0.14  0.29
## Question.18.Score -0.04 -0.03  0.37  0.35  0.26  0.22  0.03  0.37  0.27  0.36
## Question.19.Score  0.19 -0.08  0.22  0.31  0.30  0.23  0.13  0.29  0.18  0.25
## Question.20.Score  0.14  0.14  0.29  0.27  0.43  0.23  0.31  0.53  0.49  0.49
## Question.21.Score -0.12  0.13  0.21  0.29  0.48  0.12 -0.07  0.11  0.06  0.25
## Question.22.Score  0.05  0.32  0.02  0.01  0.09 -0.13  0.11  0.08  0.07  0.00
## Question.23.Score  0.13  0.07  0.34  0.26  0.30  0.42 -0.09  0.19  0.00  0.34
## Question.24.Score  0.32  0.17  0.21 -0.28  0.15  0.02  0.09 -0.12  0.10 -0.01
## Question.25.Score  0.04 -0.06  0.27  0.10  0.22  0.41  0.36  0.32  0.22  0.22
## Question.26.Score -0.12  0.15  0.15 -0.14  0.46  0.33  0.14  0.16  0.23  0.17
## Question.27.Score -0.04  0.24  0.44  0.15  0.44  0.63  0.31  0.31  0.53  0.50
## Question.28.Score  0.30  0.23  0.32  0.29  0.18  0.02  0.01  0.06  0.16  0.45
## Question.29.Score -0.07  0.16  0.25  0.18  0.06  0.46  0.13  0.05  0.36  0.32
## Question.30.Score  0.32  0.52  0.36  0.22  0.08  0.12  0.16  0.31  0.27  0.47
## Question.31.Score  0.30  0.31  0.32  0.07  0.38  0.31  0.23  0.54  0.23  0.39
## Question.32.Score  0.31  0.22 -0.12  0.05  0.09  0.20  0.18  0.04 -0.04  0.25
## Question.33.Score  0.18  0.29  0.07  0.17  0.35  0.35  0.05  0.03  0.18  0.34
## Question.34.Score  0.05  0.28  0.20  0.23  0.23  0.21 -0.01  0.22  0.01  0.37
##                   Q.11.
## Question.1.Score       
## Question.2.Score       
## Question.3.Score       
## Question.4.Score       
## Question.5.Score       
## Question.6.Score       
## Question.7.Score       
## Question.8.Score       
## Question.9.Score       
## Question.10.Score      
## Question.11.Score  1.00
## Question.12.Score  0.40
## Question.13.Score  0.23
## Question.14.Score  0.33
## Question.15.Score -0.06
## Question.16.Score  0.47
## Question.17.Score  0.09
## Question.18.Score  0.26
## Question.19.Score  0.19
## Question.20.Score  0.48
## Question.21.Score  0.24
## Question.22.Score -0.14
## Question.23.Score -0.02
## Question.24.Score  0.14
## Question.25.Score  0.18
## Question.26.Score  0.42
## Question.27.Score  0.15
## Question.28.Score -0.09
## Question.29.Score  0.14
## Question.30.Score  0.03
## Question.31.Score  0.07
## Question.32.Score -0.06
## Question.33.Score -0.16
## Question.34.Score  0.20
##                   Q.12. Q.13. Q.14. Q.15. Q.16. Q.17. Q.18. Q.19. Q.20. Q.21.
## Question.12.Score  1.00                                                      
## Question.13.Score  0.45  1.00                                                
## Question.14.Score  0.16  0.13  1.00                                          
## Question.15.Score  0.13  0.25  0.33  1.00                                    
## Question.16.Score  0.47  0.21  0.08  0.05  1.00                              
## Question.17.Score  0.41 -0.07  0.12 -0.03 -0.08  1.00                        
## Question.18.Score  0.28  0.38 -0.05  0.07  0.36  0.04  1.00                  
## Question.19.Score  0.36  0.43 -0.01 -0.08  0.41  0.13  0.66  1.00            
## Question.20.Score  0.51  0.49  0.06 -0.07  0.48  0.10  0.65  0.73  1.00      
## Question.21.Score  0.34  0.34  0.22  0.04  0.27  0.01  0.39  0.27  0.21  1.00
## Question.22.Score  0.35 -0.02  0.20  0.08  0.20  0.26 -0.19  0.09  0.11  0.15
## Question.23.Score  0.31  0.43  0.34  0.13  0.14  0.03  0.34  0.36  0.32  0.43
## Question.24.Score -0.06 -0.22  0.27  0.05  0.22 -0.21  0.02  0.04  0.01  0.12
## Question.25.Score  0.30  0.38  0.13  0.13  0.11  0.04  0.38  0.48  0.56  0.09
## Question.26.Score  0.01  0.12 -0.05 -0.18  0.31 -0.17  0.22  0.26  0.40  0.04
## Question.27.Score  0.23  0.31  0.29  0.14  0.13  0.08  0.45  0.33  0.46  0.20
## Question.28.Score -0.07 -0.02  0.08  0.07  0.24 -0.06  0.42  0.32  0.08  0.23
## Question.29.Score  0.44  0.16  0.23  0.13  0.27  0.22  0.06  0.06  0.06  0.27
## Question.30.Score  0.16 -0.19  0.21 -0.25 -0.03  0.63  0.20  0.17  0.02  0.17
## Question.31.Score  0.32  0.17  0.09  0.07  0.30 -0.02  0.37  0.25  0.38  0.33
## Question.32.Score  0.24  0.10  0.03  0.22  0.27  0.20  0.07  0.22  0.12 -0.02
## Question.33.Score  0.35  0.25  0.05  0.33  0.27  0.21  0.31  0.40  0.30  0.20
## Question.34.Score  0.44  0.20  0.06  0.07  0.05  0.39  0.34  0.16  0.28  0.27
##                   Q.22.
## Question.12.Score      
## Question.13.Score      
## Question.14.Score      
## Question.15.Score      
## Question.16.Score      
## Question.17.Score      
## Question.18.Score      
## Question.19.Score      
## Question.20.Score      
## Question.21.Score      
## Question.22.Score  1.00
## Question.23.Score  0.01
## Question.24.Score  0.02
## Question.25.Score  0.01
## Question.26.Score -0.04
## Question.27.Score -0.11
## Question.28.Score  0.11
## Question.29.Score  0.17
## Question.30.Score  0.14
## Question.31.Score  0.02
## Question.32.Score  0.08
## Question.33.Score  0.14
## Question.34.Score -0.09
##                   Q.23. Q.24. Q.25. Q.26. Q.27. Q.28. Q.29. Q.30. Q.31. Q.32.
## Question.23.Score  1.00                                                      
## Question.24.Score  0.03  1.00                                                
## Question.25.Score  0.24 -0.15  1.00                                          
## Question.26.Score  0.04 -0.10  0.19  1.00                                    
## Question.27.Score  0.34 -0.20  0.38  0.33  1.00                              
## Question.28.Score  0.19  0.18  0.01  0.13  0.33  1.00                        
## Question.29.Score  0.29 -0.18  0.46  0.26  0.36  0.15  1.00                  
## Question.30.Score  0.14 -0.12  0.05 -0.08  0.45  0.44  0.27  1.00            
## Question.31.Score  0.42  0.04  0.30  0.25  0.54  0.26  0.31  0.30  1.00      
## Question.32.Score  0.30 -0.28  0.23  0.11  0.33  0.24  0.21  0.32  0.30  1.00
## Question.33.Score  0.38 -0.09  0.37  0.18  0.36  0.30  0.30  0.16  0.24  0.58
## Question.34.Score  0.11  0.00  0.30  0.19  0.27  0.05  0.32  0.25  0.41  0.30
##                   Q.33.
## Question.23.Score      
## Question.24.Score      
## Question.25.Score      
## Question.26.Score      
## Question.27.Score      
## Question.28.Score      
## Question.29.Score      
## Question.30.Score      
## Question.31.Score      
## Question.32.Score      
## Question.33.Score  1.00
## Question.34.Score  0.32
## [1]  1.00
## 
##  with tau of 
##  Question.1.Score  Question.2.Score  Question.3.Score  Question.4.Score 
##            -1.675            -1.748            -1.498             0.093 
##  Question.5.Score  Question.6.Score  Question.7.Score  Question.8.Score 
##             0.212            -0.299            -2.214            -0.597 
##  Question.9.Score Question.10.Score Question.11.Score Question.12.Score 
##            -1.929            -0.246            -1.929            -1.107 
## Question.13.Score Question.14.Score Question.15.Score Question.16.Score 
##            -1.358            -1.047            -1.107            -1.401 
## Question.17.Score Question.18.Score Question.19.Score Question.20.Score 
##            -1.551            -0.861            -1.107            -1.831 
## Question.21.Score Question.22.Score Question.23.Score Question.24.Score 
##            -0.723             0.519            -0.558            -0.281 
## Question.25.Score Question.26.Score Question.27.Score Question.28.Score 
##            -1.171            -1.241            -0.937            -0.937 
## Question.29.Score Question.30.Score Question.31.Score Question.32.Score 
##            -0.352            -1.317            -0.659            -0.519 
## Question.33.Score Question.34.Score 
##             0.042             0.110

v_S24_df

get_corrected_item_total_func <- get_corrected_item_total
correlation_total_vs_wout_problem <- get_corrected_item_total(Scores_lst$S24_Score)

Brief Midterm Analysis

Isaiah C. Mireles

2026-04-15

Read S24

Read W24

Rename Features :

Read F23

Generate Box Plots – Total Score as PCT

Generate PCT Total Score

Generate pct Per Q

Generate BarPlots Per Q

Analyze Correlations (tetrachoric cuz its binary)

Per Question Correlation on total score:

Generate IRT Model

Generate Bayesian Model

Spring 2024 Midterm Q Types :

Side Note:

Guiding Principles :

Per Q Problem Types :

Saving Data Objects :