DAM4_Assignment_Fall2024

Author

Hoffman

Purpose of the Data-Analytic Memo

We again continue analyses on behalf of the 3rd-grade teachers at Lindquist Elementary School in Hometown, USA. Ms. Affolter, Mr. Miller-Lane, and Ms. Weston plan their instruction together often.

The first quarter of instruction has ended now, and they have asked us to help them with two big jobs that require your expertise:

  1. Construct scales to convey each student’s performance on spelling and math for this first quarter.
  2. Calculate the reliability of the end-of-term math exam.

They’ve provided you with a Google Sheet with the data, similar to what they’ve sent in the past. The data are contained in the DAM4_Data_Fall2024 Google Sheet:

https://docs.google.com/spreadsheets/d/1C_n2y24R3N8k4JIJz6K9FTkcuNxDOElbfsHpSARIOq0/edit?usp=sharing

Boys were assigned as 1; girls were assigned as 2. However, she left three of the students’ gender blank, as Morgan, Paige, and River are to be categorized as nonbinary.

The three classrooms are labeled 1 for Ms. Affolter’s class, 2 for Mr. Miller-Lane’s class, and 3 for Ms. Weston’s class.

Remember that this assignment is all about collaborative learning. It is an opportunity to try out your skills as a coder and your understanding of educational testing. Please ensure that you engage in a full, fair, and mutually-agreeable collaboration with your partner(s). Do not simply divide the work. Discuss and plan your analyses together; debate what you have found with each other; collaborate on the writing.

After working through this assignment, turn in a .qmd file – with your names on it – to Canvas by Wednesday, November 6.

Task 1 - Data Import and Cleaning

  • “library” the packages you will use in this analysis, including tidyverse, googlesheets4, and kableExtra.

  • Read in the data provided by the teachers.

  • Clean the data set by producing suitable labels for assigned classroom and student gender.

  • Print the full data set of all students with labels for classroom and gender.

  • In one paragraph, describe your efforts to clean the data.

Task 2 - Spelling Exam Descriptive Statistics

  • Produce a histogram of the spelling scores for all students.

  • Write a paragraph describing the distribution of the first quarter spelling exam scores, including the shape, center, and spread of the distribution. Be sure to include code required to calculate the center and spread of spelling scores.

Task 3 - Calculate z-scores for the Spelling Exam

  • Mutate a column in the data set that calculates the Sample Standard Scores (z-scores) for the first quarter spelling exam.

  • Print Name, Classroom, Spelling_1q, and the calculated z-scores for all students.

  • Explain briefly how this was obtained.

Task 4 - Construct a Scale for the Spelling Exam

The teachers want to convey each student’s performance on the Spelling Exam. They want to have three “bins” of performance – Excellent, Satisfactory, and Needs Improvement. They are asking that you create this scale, putting all of the students with z-scores of 1.0 or higher in the Excellent category, all of the students with z-scores between -1.0 and 1.0 in the Satisfactory category, and all of the students with z-scores of -1.0 or lower in the Needs Improvement category.

  • Create a new column in the data set that assigns each student to one of the three categories.

  • Print the Name, Classroom, Spelling_1q, and the assigned category for all students using the kableExtra package, so that it looks nice.

Task 5 - Advice about the Spelling Exam Scale

Write a paragraph to the teachers explaining whether you think that this scale is a good way to convey student performance on the spelling exam. Be sure to include a discussion of the advantages and disadvantages of this scale.

Math Exam Data

The teachers have been thinking about estimating the reliability of their tests. (They seem to have been auditing our class by reviewing the slides!) They decided to administer an end-of-the-quarter math test, using published teacher materials for the 3rd-grade math curriculum for the first 9 weeks of the year.

Their strategy is as follows:

  • Construct a math test called Math1 using the even problems (20 items in all) from the teacher materials.

  • Construct a second math test called Math2 using the odd problems (again 20 items) from the teacher materials.

  • Administer the Math1 test during the half-hour directly before lunch.

  • Administer the Math2 test during the half-hour after lunch.

  • Send the scores to the EDST0213 students for analysis.

Task 6 - Math Exams descriptive statistics

  • Produce a histogram of the Math1 exam of even problems.

  • Write a paragraph describing the distribution of the even math exam scores, including the shape, center, and spread of the distributions. Be sure to include code required to calculate the center and spread of the math scores.

  • Produce a histogram of the math exam of the odd problems.

  • Write a paragraph describing the distribution of the odd math exam scores, including the shape, center, and spread of the distributions. Be sure include code required to calculate the center and spread of the math scores.

Task 7 - Scatterplot of Math1 and Math2

  • Produce a scatterplot of the Math1 and Math2 exam scores. Jitter this plot to see the overlapping points. And display this plot as a “square” plot.

  • Write a paragraph describing the relationship between the Math1 and Math2 exam scores.

Task 8 - Calculate the Reliability of the Math Exam

  • Calculate the correlation between Math1 and Math2 exam scores.

  • Calculate the average standard deviation of the Math1 and Math2 exam scores.

  • Calculate the reliability of the Math exam.

  • Write a paragraph explaining how you calculated the reliability of the Math exam and what your professional advice is about their scheme for splitting the test into two sections.

Task 9 - Construct a Scale for the Math Exam

Similar to Task 4, they want to have three “bins” of performance – Excellent, Satisfactory, and Needs Improvement. They are asking that you create this scale, putting all of the students with z-scores of 1.0 or higher in the Excellent category, all of the students with z-scores between -1.0 and 1.0 in the Satisfactory category, and all of the students with z-scores of -1.0 or lower in the Needs Improvement category.

  • Mutate a new column for the Math test combining Math1 & Math2

  • Mutate a new column in the data set that assigns each student to one of the three categories, based on the total on the two math tests.

  • Print the Name, Classroom, Math1, Math2, their total combined math exam score, and the assigned category for all students using the kableExtra package, so that it looks nice.

Task 10 - Advice about the Math Exam Scale

Write a paragraph to the teachers explaining whether you think that this scale is a good way to convey student performance on the math tests. Be sure to include a discussion of the advantages and disadvantages of this scale.