Lecture 1: Syllabus

  • Please look over the syllabus as it has all the details of the class and how it will run.

Lecture 1: Who am I?

  • Bill Perry
  • Office is in SSB 13
  • Phone 218-726-8145
  • Email is wlperry_at_d.umn.edu

Lecture 1: My goals

  • How do we make observations and hypotheses?
  • How do we design an experiment
  • How do we collect data?
  • How do we organize, clean, summarize, and view the data?
  • How do we use statistics to test our hypotheses
    • what tests to use
    • what are the assumptions
    • what are the interpretations

Lecture 1: My expectations

  • Communication
  • Practice
  • Failure
  • Learn to correct and troubleshoot

Lecture 1: Science

  • Way to acquire knowledge, organize it and apply it back to the real world
  • Make predictions and testing these predictions using a falsifiable approach - statistics
  • Explanations that cannot be falsified are not science

What is Statistics?

Zar (1999) - “analysis and interpretation of data with view towards objective evaluation of conclusions based on the data”

Lecture 1: Inductive reasoning (Specific → General)

Inductive Reasoning (Specific → General)

Inductive reasoning involves observing specific cases and using them to form a general conclusion.

Example:

  1. Measure 10 pine needles from a tree - average length is 75 mm.
  2. Measure 10 more needles from the same tree and gets similar results.
  3. Measures needles from second tree - average length is 120 mm .
  4. You generalize pine needles from different trees vary in length, but each tree tends to have a characteristic range.

Conclusion (Induction): “Pine needle length varies by tree, but each tree seems to have a typical range of lengths.

Potential Issue: Conclusion is not guaranteed to be true - based on patterns observed in a sample, and there could be exceptions.

Lecture 1: Deductive reasoning (General → Specific)

Deductive Reasoning (General → Specific)

Deductive reasoning starts with a general principle and applies it to a specific case.

Example:

  1. General Principle: Pine needles from a species of pine tree have a predictable length range (e.g., 70–80 mm).
  2. Specific Case: Collect sample of pine needles and measure them.
  3. Prediction: Since its the species the needle lengths should fall within 70–80 mm.
  4. Measurement: Check the data and confirm needles fall within this expected range.

Conclusion (Deduction): “This tree belongs the species with a needle length range of 70–80 mm, we expect its needle lengths to fall in this range.”

Stronger than induction because it’s based on a general rule—but if the assumption (length range) is incorrect, conclusion could still be wrong.

Lecture 1: Reality of reasoning

In reality we are doing both of these processes

How do we test hypotheses

Statistics

  • Design good experiments
  • Design good tests
  • Summarize patterns/data
  • Use to make probabilistic determinations to see if differences are “real”

Data Types

  • Continuous
    • numeric
  • Discrete
    • integer or numerical
  • Categorical
    • nominal – up, down, right, left…
    • ordinal – order - a, b, c, d or morning, afternoon, evening

Measurements

Data is obtained through measurement

The world is a messy place and how you measure matters

Our measures depend on

  • accuracy - how close we are to the real value
  • precision - how close all our measurements are but may not be precise