GR5243-Homework 1 Solved

The data were recorded in the following files:

Prior Knowledge: ../Data/Prior Courses.csv

Digital System, Prior to the Midterm Examination: ../Data/Knowledge Check – Level 2.csv

Digital System, Prior to the Final Examination: ../Data/Knowledge Check – Level 5.csv

Scores on the Homework, Exams, and Overall: ../Data/Grades.csv

Delimiter: Each column of each file is separated with a comma , delimiter.

All of the data files include an identifier column Student ID so that the information from different files can be linked. These identifiers also link to the names of the student and other private information about them, which have been separately stored in a secure location.

In some places, the data may contain unusual values. Any value that does not match up with reasonable expectations for the measure should be converted to a missing value for the purpose of the analysis.

Completing the Assignment
Use the information in the files to answer the questions below. To receive full credit, you must provide the output along with the full set of code used to generate it.

This assignment includes a relatively small amount of information. It would be possible to open all of the files in spreadsheet programs, perform visual inspections, or even answer the questions using other tools. However, you must fully complete this assignment using R.

Tips: We recommend familiarizing yourself with the data.table package in R. This will enable you to work with large amounts of data. Many of the questions can be answered with a relatively small amount of code by making use of data.table’s functionality. We also recommend organizing your code. Within a folder (e.g. Homework 1 for this class), create separate subfolders for the Data and the Analysis. Store this file in the Analysis folder. Then you can use relative directories to read in the data. The template for this assignment includes variables defined in the constant code chunk that refer to the names of all of the files.

Question 1: Preliminaries
One way to read data files is using the fread function. Read in the data and answer these questions:

Question 1a) Dimensions
How many rows and columns are there in each file? Use the dim command to display the dimensions.

Prior Knowledge
Knowledge Check 1
Knowledge Check 2
Grades
Question 1b) Subjects
How many unique students were in the class? Make sure this calculation includes information from all of the files.

Question 2: Multiple Records
Which files (if any) contain more than 1 row per student? Display the records from these files for any students with multiple rows. Write a function called display.multiple.records that will perform this work on each table of data. Use the datatable function in the DT package to display an HTML table of these results in sorted order of Student ID. (In spite of the similarity in their names, the datatable function in the DT library for displaying tables in HTML should not be confused with the data.table package for data processing.) If there are no students with multiple records in a given table, display an empty table as the result.

Prior Knowledge
Knowledge Check 1
Knowledge Check 2
Grades
Question 3: Reduction to a Single Record
To handle the students with multiple records, we decided to summarize their prior knowledge as follows:

·         For each student, the highest score in a prior class will be used. If no numeric record is included, an NA value should be used. For reference, we have provided a function called max.with.na that can perform this calculation for a single student.

·         We will also create an overall score called Prior Knowledge Level. For each student, this will be defined as the average of the student’s highest score in Trigonometry and the student’s highest score in Calculus. For students who did not take both of these classes, the overall score will be based on the measured values.

Based on these criteria, we will answer the following questions.

Question 3a) Summary Before the Reduction
Starting with the original table of Prior Knowledge scores, compute the following for each class: the number of measured records, the number of unique students with a measured record, the average score among all of the measured records, and the standard deviation of the scores among all of the measured records. Round all of the numeric values to 2 decimal places. Write a function called summarize.pk.class that will display the name of the prior class along with these figures using the datatable method from the DT package.

Trigonometry
Calculus
Question 3b) Reduction of Information
Now create a new table called pk.reduced that will contain 1 record per student according to the criteria specified above. For the students with multiple records in the original file, display their records in the pk.reduced table using the datatable function in the DT package.

Question 3c) Summary After the Reduction
Now, using the pk.reduced table, compute the following for each class and the Prior Knowledge Level: the number of measured records, the number of unique students with a measured record, the average score among all of the measured records, and the standard deviation of the scores among all of the measured records. Round all of the numeric values to 2 decimal places.

Trigonometry
Calculus
Prior Knowledge Level
Question 4: Combining the Tables
Now we want to create one comprehensive table called dat. It should be constructed according to the following criteria:

·         Each student has 1 row of information (1 record).

·         The Student IDs are sorted in increasing order (1, 2, 3, etc.)

·         The columns first include the Prior Knowledge, then the Knowledge Check 1, then the Knowledge Check 2, and then the Grades.

·         Every column has a unique and meaningful name.

After creating this table, display it using the datatable function in the DT package. Round all of the numeric measures to 2 decimal places.

Hints: There are a number of ways to combine multiple tables. The data.table(a, b, c, …) function will bind the columns of multiple objects. The merge(x, y, by, all.x, all.y) function will combine (join) two tables x and y according to a character vector of column names by (or alternatively by.x* and by.y). Specifying all.x** and all.y as TRUE or FALSE (in different combinations) will give different options for combining tables with different records or elements. By comparison, data.table and merge have different advantages and drawbacks. Using data.table is more straightforward, but it assumes more about the structure of the tables. Using merge is more flexible in terms of the ordering and differences in the tables, but it requires more code and complexity for joining more than two tables together. Meanwhile, combining the tables based on the Student ID can encounter ordering problems as a character vector. It may be easier to extract a numeric version of the Student ID for sorting purposes. However, the final version of the table should only include the original identifier.

Question 5: Knowledge Check 1
How did the students do on the first knowledge check? Create a table with the following columns:

·         Topic

·         Number of Students (with measured scores)

·         Mean Score

·         Standard Deviation of Scores

·         Percentage Reaching Threshold 2 or Higher (on a scale from 0 to 100).

·         Mean Minutes

·         Standard Deviation of Minutes

The table should have one row for each topic in the first Knowledge Check. Round all numeric values to 2 decimal places.

Question 6: Knowledge Check 2
How did the students do on the second knowledge check? Create a table with the following columns:

·         Topic

·         Number of Students (with measured scores)

·         Mean Score

·         Standard Deviation of Scores

·         Percentage Reaching Threshold 2.0 or Higher (on a scale from 0 to 100).

·         Mean Minutes

·         Standard Deviation of Minutes

The table should have one row for each topic in the first Knowledge Check. Round all numeric values to 2 decimal places.

Question 7: Is Time Spent Time Well Used?
For each knowledge check topic at each level, compute the correlation between the students’ scores and their minutes spent using the digital system. Display the results using the datatable function in the DT package. Round the numeric values to 2 decimal places.

Then comment on the findings. Do you think spending more time on the digital system is beneficial? Is your notion confirmed by the data? Whatever you believe, why might the opposite be true?

Hint: Reshaping the data to place all of the knowledge check scores in one column and all of the time spent in another may simplify the calculation. To do this, consider using the melt or melt.data.table function.

Question 8: Summary of Scores
For each homework assignment, the student’s average homework score across all assignments, the midterm exam, the final exam, and the overall score, compute the following quantities:

·         The number of students with a measured value.

·         The mean score.

·         The standard deviation of the score.

Display these results using the datatable function in the DT package. Round all of the numeric values to 2 decimal places.

Question 9: Correlations with Outcomes
For the purpose of evaluating the class, consider the following outcomes:

Homework Average
Midterm Score
Final Exam Score
Total Score
For each of these outcomes, compute their correlation with each of the following predictors:

The Prior Knowledge Level
Total Minutes spent on the knowledge check activities.
The average score on the Level 2 knowledge checks (with a 5 threshold).
For the purpose of the time calculations, consider any missing value as a zero in computing each student’s total minutes using the system.

Display the results using the datatable function in the DT package. Round all of the numeric values to 2 decimal places.

Question 10: Qualitative and Quantitative Conclusions
Based on the results that you have seen, what can you conclude about the digital system that the students used? Does spending more time on the system seem to help improve the scores on the homwork, midterm, final exam, and overall grade? How do higher scores on the system impact these outcomes? And how does this compare to the impact of the Prior Knowledge Level? Write a few sentences to outline your conclusions and recommendations.