# 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.