Learning About Analysis - Quantitative Data

Quantitative data is any type of data that takes a numerical form and can be measured. If one gives an assessment that requires students to choose between four answers (multiple-choice), one can number the four answers, 1, 2, 3 and 4. If they are labeled A, B, C and D, these too can be turned into the numbers 1, 2, 3, and 4 through the process of coding them.

Coding

Coding is the process of assigning a number to an answer, a statement or an event. Coding is also the process of equating a number with a word so that a quantitative analysis can be performed. Even qualitative statements can be coded into numbers, providing that one can systematically code the statements one receives. The advantage to quantitative data is that it can be easily summarized, counted, averaged and described to others. The disadvantage is that every piece of data has to fit into the number scheme. The reason why coding is so important is that it helps to convey the outcomes of the assessments into easily digestible statistics represented in tables and graphs.

Recording Quantitative Data

Next, these numbers, the student-chosen answers to the assessments, can be entered into a database. A database is nothing more than a spreadsheet with a grid whereby the student name appears on the left of the grid, and across the top are the numbers of the questions given on the assessment. To fill in a grid, go to the student’s name and fill in, horizontally, the student answers for each of the questions. The answers should be in numbers for a quantitative analysis.

Cross-Tabulation

From here, a grid of numbers can be developed that is as long down the left-hand side as the number of students that one has data for, and as long across the top-side as one has questions on the assessment. For a class of 20 children and 20 assessment questions, the grid has 400 numbers. Then the first set of analyses by cross-tabulating the data can be performed.

Cross-tabulation is a powerful way to analyze data. It involves taking student data and counting down and across the data. When building a database in a spreadsheet, or grid, or table for cross-tabulation, it takes the form of student names crossed with their answers to the questions. For the purposes of simplicity reduce the data to be displayed into a chart, or table, such as the one below:

Cross Tabulation—Table 1

Student ID

Score on a scale from 1-4

001

2.5

002

3.4

003

3.2

When one performs a “cross tab,” or cross-tabulation analysis, one counts down and across the tables to gain the first analytical look at the data, such as in the table below. The first analysis to perform is to see if arranging the data differently would help in the analysis. For example, the table could be reorganized to show the data of student scores in descending order:

Cross Tabulation—Table 2

Student ID

Scores in descending order

002

3.4

003

3.2

001

2.5

If the cutoff score is 3 and above, the analysis of what one now knows is that two students met or exceeded the standard of attaining a “3” on the assessment, and one student did not.

Scores Over Time

Cross tabulations can be organized in a variety of ways to help analyze the information needed. For a more powerful analysis of student learning, create a table that collects assessment scores over time. For example, a group of students can be followed by sampling their knowledge on assessments that are given in a pre-, mid- and post- time frame, like the cross-tabs below:

Cross Tabulation—Table 3

Student ID

Pre-

Mid-

Post-

001

2.5

2.6

3.1

002

3.2

3.0

2.9

003

3.4

3.3

3.5

This is one of the most powerful ways to track student learning because it allows one to analyze student learning over time! Now student progress can be followed and it can be seen, in the table above for example, that student 001 is steadily improving, student 002 is declining and student 003 is holding steady. This is just the beginning of the analytical power that can be harnessed through cross-tabulation of data.

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