Foundations
Module 1.2: Types of Data
All materials can be found at alexcardazzi.github.io.
Data, Data, Data
Nowadays, data is (are?) everywhere. Data has become a buzzword for those in business, policy, government, industry, science, etc. Understanding how to work with data, therefore, is becoming an increasingly valuable and marketable skill. Employers want to hire people who can use data.
However, everyone “knows” Excel. Everyone “knows” what a correlation is. So, how can you differentiate yourself from others? Put differently, how can you send a credible signal to employers that you really know data? This course will (re-)introduce you to statistics and econometrics while exposing you to important, marketable tools like R and Claude Code.
First, let’s review some rudimentary definitions and concepts in statistics.
Types of Statistics
A statistic is a measurement that comes from some data. Broadly, there are two ways to classify the purpose of statistics:
Descriptive statistics are meant to organize, summarize, and present data in ways that helps people understand key facts about the data.
Inferential statistics are descriptive statistics that are used to estimate properties of a population based on a sample.
Samples
Before taking a measurement, one needs to collect data. Those data can be collected either as a population or as a sample of a population.
The entire possible group of observations. For example, the population of students in the college of business.
Any subset of students from the population. For example, Economics majors or business school juniors.
In this example, economics majors are a sample from the population that is business school students. However, business school students can also be thought of as a sample of University students.
Suppose I want to know the average height of ODU students. Asking all 20,000+ students how tall they are would be very expensive (in terms of time, financial cost, and effort), so I need to do something else. One thing I could do relatively easily is collect the heights of all student athletes since they are posted online (most team rosters include heights). Alternatively, I could ask everyone in this course how tall they are.
For example, perhaps the average height of the men’s basketball team is 6’5”. This is an interesting descriptive statistic, but a poor inferential statistic since basketball players are notoriously taller than average. On the other hand, the average height of the individuals in this course would be a much better inferential statistic. However, it could be that people enrolled in ECON 311 are more likely to be male (or female), which would once again make the average a poor representation of the average ODU student.
To get a legitimately random sample, one needs to either use true randomization (picking names from a hat) or use something that is sufficiently independent of what one is studying. For example, sampling individuals who have a 6 as the third digit from the right in their phone number. Phone numbers (and University IDs) are given out randomly, or at least not in terms of anything to do with height.
Qualitative vs Quantitative
Next, one needs to consider whether the statistic they have “measured” from their sample (or population) is either qualitative or quantitative.
Statistics that fall under this category are meant to describe characteristics or traits of something that are not naturally quantifiable. Examples include eye color, nationality, etc.
Quantitative statistics are numerical properties of some data. Examples include height, income, etc.
Types of Measurement
These two broad categories of statistics can be broken down a bit further depending on the scale on which they are measured. These scales are as follows:
Nominal: Nominal data are represented by labels or names. In addition, there is no natural order to these data. An example would be “language spoken”, and responses might be “english”, “spanish”, “japanese”, “italian”, etc. Nominal data are therefore always qualitative.
Ordinal: Ordinal data are recorded in reference to some relative ranking. These data do indeed contain an order to them, unlike nominal data, but the numbers representing the order do not have any other meaning. For example: a list of the fastest 100 meter dash times. The difference between #1 and #2 is not the same as the difference between #8 and #9.
Interval: For interval data, the distance between the numbers is indeed meaningful, and there must be units that accompany the measurements. However, zero is usually meaningless insofar that it does not indicate an absence of the value being measured. For example: Fahrenheit or dress sizes. In both cases, the difference between any two numbers is the same and meaningful. At the same time, zero degrees Fahrenheit or a size zero dress does not mean an absence of temperature or fabric.
Ratio: Ratio measurements are interval measurements, except zero has a natural meaning. When zero has a natural meaning, the ratio of two measurements also has meaning. For example, consider income and Fahrenheit. Someone with $50 has twice as much as someone with $25 but 50 degrees Fahrenheit is not twice as hot as 25 degrees. In addition, having $0 means you have no money (and therefore negatives mean something too).
Discrete vs Continuous
When measurement is quantitative, the measurement can be either discrete or continuous.
Discrete: Discrete measurements do not allow for fractions or decimals. Only things that can be measured as integers (1, 2, 3, …) qualify as discrete. For example, the number of followers you have on social media is discrete because you cannot have half of a follower.
Continuous: Continuous data can be sub divided into non-whole numbers. For example: time is a continuous measurement because you can have 15.623941004 seconds. Income can be considered continuous even though dollars only go to two decimal places – it is close enough that people would consider it continuous.
Structuring Data
In reality, data sets come with rows and columns. Often, each column will contain a different type of measurement, whether it be qualitative or quantitative. In general, there are three main ways to organize data. Usually, we will have datasets with columns for units (states, firms, individuals, etc.) and time (year, month, quarter, day).
- Cross Section: data collected for many units at the same (or similar) time.
- Time Series: data collected for one unit over many time periods.
- Panel: data collected for many units over many time periods.
- When all units are observed for each time period (50 states over 20 years), the panel is said to be balanced.
- When some units are observed more often than others, this is an unbalanced panel.
- Sometimes, people observe totally different, unique units each time period. For example, observing the students in Econ 311 over time. This is called a pooled cross section. Essentially, the data contains many cross sections all pooled together into something that looks like a panel.
Again, most of the time, we will work with panel data. It will be structured such that each row represents a specific unit at an instance of time. For example, each row will represent a state (e.g., Virginia, New York) in a single year (e.g., 2005, 2006).