KINE303 Study Notes: Statistics and Research Methods (Transcript Comprehensive)

Teaching Philosophy

  • This class is for YOU, not for me! My job is to help you learn and develop skills you will use throughout your career.

  • I believe we learn by doing and practical experience, so I will try to engage students and have activities more than simple lecturing.

  • As a student, I ask that you attend class regularly and participate in all class activities and projects!

  • Assignments aren’t (technically) weighted – the course totals to ~500 points. Refer to the syllabus for point breakdowns!

Syllabus

  • View On Course Canvas Home

About This Class

  • What does it mean to "understand" the world scientifically?

  • Scientific Method

About This Class: Understanding Scientifically and the Scientific Method

  • What does it mean to understand the world “scientifically?”

  • We can think of science as constructing MODELS of our bodies, the world, and the universe around us.

  • Scientific Method: “A method of solving problems that uses the following steps: defining and delimiting the problem, forming a hypothesis, gathering data, analyzing data, and interpreting the results.” (Thomas et al, 2015)

What kinds of information can be considered strong "research" evidence?

  • Research studies must be peer-reviewed.

  • Predictions must be quantifiable and testable.

  • MANY studies are required for scientific conclusions.

  • Research studies must be well-designed.

How can we use quantitative evidence to make scientific decisions?

  • Describing and comparing NUMBERS

  • Seeking PATTERNS in the numbers that MAY be MEANINGFUL (like one group > another)

  • CENTRAL QUESTION: IF we DO find potentially important patterns in our measurements, how do we know if the patterns are meaningful? Could patterns have happened simply by CHANCE?

  • CENTRAL QUESTION: WHO decides which scientific MODEL best represents the meaningful (non-chance) patterns that we observe?

How do we know if patterns in our measurements are meaningful, or could have happened simply by CHANCE?

  • Statistics helps us decide if patterns in numbers are NOT just by chance and COULD be meaningful.

  • WHO decides which scientific model best represents the meaningful (non- chance) patterns we observe?

  • Quantitative research helps us ASK QUESTIONS in such a way that NATURE, not us, decides the answers.

Quantitative evidence, thus, is used to make scientific decisions by:

  • Describing and comparing numbers

  • Using REASONING to “explain” and support conclusions

Topics

  • Spreadsheets

  • Probability & Conditional Probability

  • Cognitive Biases

  • Sampling/Resampling

  • Reasoning

  • Measurements

  • Organizing Data

  • Sampling Distribution

  • Cumulative Distribution

  • Scientific Models

  • Statistical Hypotheses

  • Normal Distribution

  • Confidence Intervals

  • Parametric Statistics

  • Chi Square Tests

  • Correlation & Regression

  • Multivariate Analyses

  • Logical Fallacies

This class is more than just learning content – we will also be learning and developing SKILLS!

  • Using computers to solve problems

  • Working with datasets with lots of numbers

  • Creating models of our own

  • Scientific thinking

  • Making CONNECTIONS between new information, information we already know, and/or other things we are learning

Why Statistics?

  • Why study research methods and statistics?

  • “Because science is hard, and the truth is sometimes cunningly hidden in the nooks and crannies of complicated data.” (Navarro & Foxcroft, 2025)

Why Statistics? (Continued)

  • Statistics is often used as a way to form scientific explanations and draw conclusions. Sometimes these conclusions sound like common sense. So why don’t scientists use common sense?

  • “Using ‘common sense’ to evaluate evidence means trusting gut instincts, relying on verbal arguments and on using the raw power of human reason to come up with the right answer. Most scientists don’t think this approach is likely to work.” (Navarro & Foxcroft, 2025)

Why Statistics? Note

  • CORRELATION DOES NOT IMPLIED CAUSATION

Basics of Statistics

  • Statistics helps us decide if patterns in numbers are NOT just by chance and COULD be meaningful.

  • This is helpful when conducting research!

  • What is research? A means of problem solving that includes the following characteristics: systematic, logical, empirical, reductive, replicable (Tuckman, 1978)

Scientific Method

  • 1. Defining the problem

  • 2. Forming a hypothesis

  • 3. Gathering the data

  • 4. Analyzing the data

  • 5. Interpreting the data

  • When is statistics used?

Basics of Statistics: Statistical Use

  • Statistics is used in part 3, 4, and 5 of the scientific method!

Hypothesis

  • Hypothesis – the expected outcome of a study or experiment

  • AKA what YOU think will happen

Probability (Part 1)

Probability

  • Probability is the chance of something happening expressed as a value between 0 and 1, with 0 being no chance of it happening and 1 being a guarantee that it happens.

  • One way to demonstrate this is through population:- How many students are in this class? How many males and how many females?

    • Let’s pretend – 40 students, 23 girls and 17 boys

    • If I were to randomly select a student, what is the probability that I select a male?

    • Probability = 1740=0.425=42.5% chance of selecting a male\frac{17}{40} = 0.425 = 42.5\%\text{ chance of selecting a male}

Probability: Coin Flip Heads

  • What is the probability of flipping a coin and it landing on heads?

  • (selected outcome) / (total outcome)

  • (Heads = 1) / (Heads or Tails = 2), therefore probability = 12\frac{1}{2} or 0.5

  • What are the odds of flipping a coin and it landing on heads?

  • 1:1

Definitions of Probability

  • Empirical: derived from observation or experiments

  • Frequentist: estimating the probability of future events based on observed (empirical) or predicted (theoretical) frequencies

  • Boolean: a variable that can have two values (0 or 1, true or false)

Coin Flips Year-by-Year (Dataset)

  • Coin Flips Year Table (1967–2025 SB coin toss results) includes sequential Heads/Tails data with occasional fan-in-box comments like “GO BIRDS.”

  • Summary at the end:- Total = 59

    • # of Heads = 28

    • # of Tails = 31

Coin Flips Dataset (Continued)

  • Total = 59; # of Heads = 28; Super Bowl 60 Heads or Tails? (Heads = 28, Tails = 31)

  • Question posed: What is the probability that the coin flip of Super Bowl LXI (60) lands on heads?

Probability Calculation for SB LXI (60)

  • What is the probability that the coin flip of Super Bowl LXI (60) lands on heads?

  • Heads = 28, therefore (28/59) = 0.475

  • Is it 47.5%?

Frequentist vs Empirical (Clarification)

  • This is using frequentist probability when we should be using empirical probability

  • Probability of heads = 12=0.5=50%\frac{1}{2} = 0.5 = 50\%

Key Concepts and Formulas (Summary)

  • Probability is the chance of an event and is expressed as a value between 0 and 1:- 0≤p≤10 \le p \le 1

  • For a finite population, probability of selecting a category can be computed as a ratio of favorable outcomes to total outcomes, e.g.,- P(male)=number of malestotal=1740=0.425P(\text{male}) = \frac{\text{number of males}}{\text{total}} = \frac{17}{40} = 0.425

    • P(heads)=12=0.5P(\text{heads}) = \frac{1}{2} = 0.5 (for a fair coin)

  • Odds and probability distinction:- Odds of heads = 1:1

  • Empirical probability is derived from observed data; Frequentist probability uses observed or predicted frequencies to estimate future probabilities; Boolean variable is binary (0 or 1)

Quick Reference: Key Terms

  • Model: A simplified representation used to explain or predict phenomena.

  • Hypothesis: The expected outcome of a study or experiment; what you think will happen.

  • Scientific Method: Steps: Define problem, Form hypothesis, Gather data, Analyze data, Interpret results.

  • Descriptive Statistics: Describing numbers; looking for meaningful patterns beyond chance.

  • Inferential Statistics: Using data to make inferences about a population.

  • Normal Distribution, Confidence Intervals, Parametric Statistics, Chi-Square Tests, Correlation & Regression, Multivariate Analyses: listed topics in this course.

  • Cognitive Biases, Sampling/Resampling, Logical Fallacies: common issues in reasoning and data interpretation.

Note on Citations

  • Thomas et al, 2015 for the Scientific Method definition.

  • Navarro & Foxcroft, 2025 for quotes on science, statistics, and common sense.

  • Tuckman, 1978 for the problem-solving characteristics of research.

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