Inferential Statistics Lecture Notes

Introduction to Inferential Statistics

• Analogy: Compared to being a lawyer - making an argument that something is correct.
• Definition: Making predictions or inferences about a population based on a sample.

Sampling and Sample Distributions

• Sampling: Process of selecting a subset of the population to estimate characteristics of the whole population.
  • Example: Select 100 people from each U.S. state to make statements about the general U.S. population.
• Sample Distribution: Used to provide insight into the viability of estimates by repeatedly drawing samples and calculating mean scores.

Confidence Intervals

• Definition: A range of values to make a statement about a parameter with a certain level of confidence.
  • Example: Estimating average height within a room, confident between 5’3" and 6’1".
• Importance: Indicates how confident we are in our estimate.
• Standard Percentages: 90%, 95%, 98%, 99% due to historical reasons.

Hypothesis Testing

• Definition: Statistical method to make decisions about a population based on sample data.
• Hypothesis: A claim about something, which can be true or false.
  • Example: "Bigfoot exists in Pennsylvania."
• P-values: Probability values used in hypothesis testing to indicate the strength of evidence against the null hypothesis.

Z-tests and T-tests

• Z-test: Uses normal distribution.
• T-test: Uses t-distribution (also called Student t-distribution).
  • Origin: Named after "A Student of Statistics" from the Guinness brewery story.

ANOVA

• Definition: Used to compare the means of three or more groups to identify differences.

Recap on Key Concepts

• Inferential Statistics: Making predictions based on sample data.
• Confidence Intervals: Indicate the range and level of confidence for estimates.
• Hypothesis Testing: Testing claims about a population.
• Z-tests/T-tests: Tools used in hypothesis testing.
• ANOVA: Examines differences among three or more group means.

Next Steps

• Upcoming session will involve practical examples and hypothesis testing with actual data sets.