Inferential Statistics and Hypothesis Testing

Overview

• Transitioning from descriptive to inferential statistics.
• Inferential statistics involves drawing conclusions and making inferences from sample data to the population.
• Introduction to hypothesis testing, including definitions and terminology.

Importance of Understanding Concepts

• Emphasis on understanding concepts over calculations initially.
• Concepts will be revisited in future modules for practical applications.
• Encouragement to use additional resources and revisit material if unclear initially.

Hypothesis Testing Framework

• Hypothesis Testing: A process to test assumptions or claims about data or phenomena.
• Sampling Distribution: Basis for making inferences and decisions in hypothesis tests.
• Statistical Significance: Determining if observed effects are likely due to chance or real effects.

Formulating Hypotheses

• Statistical Hypothesis: Claims about population parameters.
  • Null Hypothesis (H₀): No effect or difference (statement of equality).
  • Alternate Hypothesis (Hₐ): Opposite of the null, suggests an effect or difference (statement of inequality).
• Hypotheses must be complementary and opposing.

Types of Hypothesis Tests

• Left-Tail, Right-Tail, and Two-Tail Tests:
  • Left-Tail Test: Tests for decreases.
  • Right-Tail Test: Tests for increases.
  • Two-Tail Test: Non-directional; tests for changes in either direction.
• Two-Tailed Tests:
  • Focus of the course, deemed more practical and statistically sound.
  • Easier to achieve significant results in one-tailed tests, thus less preferred.

Hypothesis Testing Process

• Null Hypothesis: Assumes no effect.
• Statistical Decisions:
  • Reject Null Hypothesis: If data shows a statistically significant effect.
  • Accept Null Hypothesis: If data lacks sufficient evidence to show an effect.
• Terminology:
  • Use "significant" only for statistical significance, not to denote magnitude or substantiality.

Practical Applications

• Use of sampling distributions starting with the assumption of the null hypothesis being true.
• Decisions based on sample data lead to conclusions about population-level effects.