There are two ways to think about statistics:

1. Descriptive statistics are methods for describing information.

Ex: 66% of eligible voters voted in the 2020 presidential election (the highest turnout since 1900!).

1. Inferential statistics are methods for drawing inference (making decisions about something we are uncertain about).

Ex: A poll suggests that 75% of voters will select a Candidate A. We reasonably conclude that Candidate A will win the election.

Data is factual information. We collect data from a population, the collection of all individuals or items a researcher is interested in.

• Collecting data from an entire population is called a census.
  • This is complicated and expensive!
• We can also take a sample, a subset of the population we get data from.

Data are often organized in what we call a data matrix. If you’ve ever seen data in a spreadsheet, that’s a data matrix!

• Each row represents one observation (also called cases or subjects). These are the individuals or items in the sample.

• Each column represents a variable, the characteristic or thing being measured.

There are two types of variable:

1. Numeric or quantitative variables take numeric values AND it is sensible to do math with those values.
1. Discrete numeric variables take numeric values with jumps. Typically, this means they can only take whole number values. These are often counts of something.
2. Continuous numeric variables take values “between the jumps”. Typically, this means they can take decimal values.
2. Categorical or qualitative variables take values that are categories.

• If you’re unsure whether a variable is discrete or continuous, pick a number with some decimal place and ask yourself if that value makes sense. If it doesn’t, it’s probably discrete.
• Sometimes, categories can be represented by numbers. Ask yourself if it makes sense to do math with those numbers. If it doesn’t make sense, it’s probably a categorical variable.

Checkpoint: The following table shows part of the data matrix from a Stat 1 course survey.

1. What does each row of the data matrix represent?

2. What does each column of the data matrix represent?

Checkpoint: The following table shows part of the data matrix from a Stat 1 course survey.

1. Indicate whether each variable is discrete numeric, continuous numeric, or categorical.