Hello Data

Lending Club Loans

• Random sample of 50 loans made through Lending Club platform
• A sample is a subset of a larger group (the population)
• The sample consists of the 50 loans. The population is all loans made through the platform

• Data organized in a table called a data frame

• Each row represents a single case or observational unit

• Each column represents a variable, corresponding to a loan characteristic. E.g.,

  • loan_amount (amount of loan in USD)
  • term (number of months of the loan)
  • grade (related to likelihood of being repaid)

Summary Statistics

• A summary statistic is a single number that summarizes data from a sample
• Mean loan amount ($17,083.00) is a summary statistic
• Summary statistics can be organized in tables

Association

• If there is a relationship between two variables, we say that the variables are associated
• Interest rate and loan grade appear to be associated
• If there is no relationship between two variables, we say the variables are independent

Variable Types

• A numerical variable takes on values that are described using numbers that make sense to add, subtract, average, etc
• A categorical variable takes on values that indicate different levels or categories

Loan data variable types:

• Numerical variables can be further broken down into

  • discrete: takes on discrete values (with jumps between consecutive values)
  • continuous: can take on any value within a range

• Categorical variables can be further broken down into

  • ordinal: levels have a natural ordering
  • nominal: levels do not have a natural ordering

Variable types. From IMS2 Fig. 1.1.

Loan data variable types:

Scatterplots

• The relationship between two numerical variables can be visualized using a scatterplot

Scatterplot showing loan amount vs. income.

Direction of association

• Two numerical variables are said to have a positive association if the values of one variable tend to be higher when the values of the other variable are higher
• Two numerical variables are said to have a negative association if the values of one variable tend to be lower when the values of the other variable are higher
• Loan amount and total income appear to be positively associated

Stents for Treating Strokes

• Researchers designed a study to study the effectiveness of stents in preventing strokes
• 451 at-risk patients randomly assigned to receive stent (treatment) or not (control)
• Outcome (“stroke” or “no event”) recorded after 365 days

• What are the cases?
• What are the variables?
• What are the variable types?

• The proportion that had a stroke in the control group was 28/227 = 0.12
• The proportion that had a stroke in the treatment group was 45/224 = 0.20
• Does there appear to be an association between group and outcome?

Variable Roles

• In some cases we may think that one variable affects the other variable
• We say that the explanatory variable affects the response variable
• In the stent study, the group (treatment or control) is the explanatory variable, and the outcome is the response variable

Experiment vs. Observational Study

• An experiment is a study in which researchers manipulate or assign the values of the explanatory variable
• The stent study is an experiment, because the researchers assign patients to the treatment or control group
• When cases are randomly assigned to groups, the study is called a randomized experiment
• An observational study is a study without such manipulation. The cases are observed as they are
• The Lending Club data are from an observational study