Observations, Variables and Data Matrices By Farrokh Alemi, Ph.D. This lecture is organized by Dr. Alemi and narrated by Yara Alemi. The lecture is based on the OpenIntro Statistics book.

Data Matrix Is Rows are cases Columns are variable A data matrix is a table in which rows are cases and columns are variables. This is a common way to organize data for analysis.

Data Matrix Is Here is an example. This matrix shows rows 1, 2, 3, and 50 of a data set concerning 50 emails received during early 2012. Each row in the table represents a single email or case. The columns represent characteristics, called variables, for each of the emails. For example, the 1st row represents email 1, which is a not spam, contains 21,705 characters, 551 line breaks, is written in HTML format, and contains only small numbers.

Data Matrix Is The description of each variable should also accompany a data matrix. It is always important to make sure that one understands the exact definition of each variable.

Variables Are: Variables are either numerical or categorical. A numerical variable can take a wide range of numerical values, and it is sensible to add, subtract, or take averages with those values. An example is dollar amount of expenses. A categorical variable is a number but it cannot be added, averaged or summed. A telephone area code is a number but it cannot be averaged, summed, and the difference of two area codes has no clear meaning.

Variables Are: Expenses Count of hospitalized patients There are two types of numerical values. A discrete variable can only take whole non-negative numbers (0, 1, 2, and so on). It is said to be discrete since it can only take numerical values with jumps. Count of patients who are hospitalized is a discrete variable. On the other hand, spending variable is said to be continuous because it can assume fractions of whole values. Expenses Count of hospitalized patients

Variables Are: International Classification of Disease There are also two types of categorical variables. In ordinal categorical variables, the numbers assigned reflect the rank order of something. For example, numbers given to international classification of disease are a “regular categorical” variable. They are just numerical names for the disease. In contrast, severity scores are ordinal variables. They typically show that one disease has worst prognosis than the other but not how much more. International Classification of Disease Severity of Illness

Take Home Message This section defined data matrix and types of variables

Do One: Data were collected about students in a statistics course. Three variables were recorded for each student: number of siblings, student height, and whether the student had previously taken a statistics course. Classify each of the variables as continuous numerical, discrete numerical, or categorical. Let us test your knowledge of definitions just presented. See if you can answer this question.