Inferential Statistics Notes

Inferential Statistics

General Overview

  • Inferential Statistics: Techniques that allow generalizations from a sample to a population.

Key Concepts in Inferential Statistics

  • Null Hypothesis Statistical Testing (NHST):

    • A method used to determine if sample data provides enough evidence to conclude that a pattern observed in the sample applies to the entire population.

    • If findings are "statistically significant", then the pattern is unlikely to have occurred by chance.

Hypotheses in Research

Types of Hypotheses

  • Null Hypothesis (H0): States that there is no effect or no difference in the population (e.g., A = B).

  • Alternative Hypothesis (H1): Contradicts the null; indicates an effect or difference (e.g., A ≠ B).

    • If H0 is found to be false, then H1 is accepted.

Non-Directional vs. Directional Hypotheses

  • Non-Directional:

    • H0: No effect (B1=A=B)

    • H1: An effect exists (A≠B)

  • Directional:

    • H0: No effect, with specific direction (H0: A≤B)

    • H1: Effect is larger/smaller (H1: A>B or H1: A<B)

Examples of Hypotheses

  1. Age is a significant predictor of income.

    • D. Directional, Alternative

  2. Gay males and heterosexual males have similar mental health scores.

    • C. Non-directional, Alternative

  3. Children are more creative than adults.

    • D. Directional, Alternative

  4. Psychologists have lower mental health scores than the general population.

    • D. Directional, Alternative

  5. Boys and girls have a different number of imaginary friends.

    • C. Non-directional, Alternative

  6. Females do not earn lower salaries than males.

    • A. Non-directional, Null

The Logic of Hypothesis Testing

  1. State the hypotheses:

    • H0: People vote at least as frequently as they claim.

    • H1: People vote less frequently than they claim.

  2. Predict the data assuming H0 is true:

    • e.g., If 70% claim they vote, then from 200 people, expect 140 to vote.

  3. Collect data: Obtain a representative sample (perform polling).

  4. Compare observed data with predictions:

    • Determine the probability of obtaining the observed result if H0 is true.

    • Outcomes:

      • If probability ≥ 5%: RETAIN H0 (no statistically significant effect).

      • If probability <5%: REJECT H0 (statistically significant effect).

      • Example: H0 predicted 140 votes vs. observed 118: <0.1% likelihood means H0 rejected.

The Importance of Sample Size

  • Increasing sample size improves the precision of estimates (confidence intervals become smaller) and makes it easier to reject H0.

  • Avoid confusion of statistical significance with the strength or size of effects.

Combining Approaches

  • Use hypothesis testing to check if enough evidence indicates any effect followed by estimating the size or strength of that effect.

Summary

  • Inferential statistics often rely on NHST to determine significance levels of observed data, followed by further analysis of effect sizes.