Class 24: Statistical Arguments

Thesis Statement

You have certainly heard of a thesis statement, but may struggle to formally define what it is. A thesis statement:

offers a concise summary of the main point or claim of the essay, research paper

A hypothesis, which is not the same concept, is:

a supposition or proposed explanation made on the basis of limited evidence as a starting point for further investigation

That is, a hypothesis is a fixed explanation of something. A thesis is a particular rhetorical element that exists within a document or speech and is intended for a particular audience. If you are designing an experiment or collecting data, you will have a hypothesis. When you are writing a paper or giving a presentation you will have a thesis (and that thesis may help to confirm or contradict a prior hypothesis).

Types of Argumentation

Within logical arguments, there are two subtypes that have a place in making arguments from data. These are:

  • deductive reasoning
  • inductive reasoning

In deductive reasoning we start with general assumptions and show that certain conclusions logically follow from them. A classic example is:

Socrates is a man. All men are mortal. Therefore, Socrates is mortal.

If the assumptions of this statement (first two sentences) are true, the conclusions must be true.

Inductive reasoning, in contrast, builds a conclusion by inferring based on patterns seen in particular examples. For instance:

I have taught a total of 700 students over the past 5 years. I enjoyed teaching all 700 of them. Therefore, I enjoy teaching all students.

While the data provides strong evidence for the conclusion, it does not guarantee its validity even if the assumptions and logic is infallible.

Data-Driven Logical Arguments

Deductive reasoning occurs in statistics when some of our facts (assumptions) are derived from an analysis of a dataset. Generally this occurs when we are drawing data from a particular population. For example, say we are looking at election results from every county in the United States. The following is a deductive argument:

A presidential candidate that has more than 270 electoral votes wins the election (assumption). Candidate A had 300 elector votes in 2020 (assumption derived from data). Therefore, candidate A won the election.

Notice that often not all facts are derived from data, but often some of them are. Inductive reasoning usually occurs in statistics when sampling from a larger population or observing a random process. For example:

Only 1 of the 1000 patients injected with the vaccine had serious side-effects. Therefore, the vaccine is safe for distribution.

While inductive reasoning is more traditionally associated with statistics, the deductive case is quite common in both industry and academia.

Examples

If you would like some good examples of data-driven arguments, check out some of these articles:

Practice

Today, will continue to work with the Chicago Crime data: lab24.Rmd

Today you will be working in small groups.