Ch. 7 PBSI 301 SP24

Chapter 7: Hypotheses

Overview

• Focuses on the following chapters:

  • Chapter 7: Hypotheses

  • Chapter 8: Normal Curve, Probability, Z-Scores

  • Chapter 9: Significance Testing

  • Chapter 10: One Sample Z Test

Probability vs. Statistics

Concepts

• Probability involves predicting how often different kinds of events occur.

• Statistics analyzes known data to draw conclusions or make inferences.

The Monty Hall Problem

Scenario Explanation

• Game show with 3 doors: 1 has a car (prize), 2 have goats.

• You choose Door No. 1. The host opens Door No. 3, revealing a goat.

• Question: Should you stick with Door No. 1 or switch to Door No. 2 for a better chance of winning?

Probability Theory

Definition and Applications

• Defined as "the doctrine of chances".

• A mathematical branch that assesses event occurrence.

• Predictions for repeated experiments (e.g., Monty Hall problem).

Statistics vs. Probability

Key Differences

• Probability deals with predicting unknown outcomes from known facts.

• Statistics focuses on interpreting data where the outcome is known but data can’t provide definitive truth.

  • Example Questions:

    • Coin toss outcomes.

    • Lottery results.

Key Issues: Probabilistic Judgments

• Statistics and probability are distinct yet interconnected fields.

• Hypothesis testing emerges as a tool for navigating uncertainty.

Hypothesis Testing

Purpose in Research

• Essential in psychological research to assess treatment effectiveness or behavioral responses.

  • Examples:

    • Evaluating therapy's impact on depression.

    • Assessing video game effects on aggression.

Null Hypothesis Significance Testing (NHST)

Framework

• Involves using sample data to make inferences about a larger population.

• Steps in NHST:

  1. Establish a Null Hypothesis (H0) and one or more hypotheses.

  2. Analyze if sample data sufficiently convince to reject H0.

The Null Hypothesis (H0)

Definition

• States there is no significant effect or relationship.

  • Examples:

    • No effect of Pill X on depression.

    • No difference in aggression between genders.

Nature of NHST

Conservative Approach

• Assume H0 is true until evidence indicates otherwise.

  • Parallels legal principles: Innocent until proven guilty.

• Benchmarks determine when to reject H0:

  • Legal standard: Beyond reasonable doubt.

  • Statistical standard: Confidence that observed differences are not due to chance.

Statistically Significant

Definition

• Indicates unlikely occurrence of observed results if H0 is true.

• Identifies significant differences between groups.

The Research Hypothesis (H1)

Characteristics

• Framed at the sample level, directly linked to methodologies.

• Contrasts with H0 by proposing potential differences.

  • Examples:

    • Different depression levels between pill takers and non-takers.

    • Gender differences in aggression.

Research Hypothesis Types

Non-directional Hypothesis

• Indicates difference without specifying direction.

  • Example: Mean aggression varies by gender.

  • Symbol: H1: x_a ≠ x_b

Directional Hypothesis

• Specifies direction of difference.

  • Example: Men score higher in aggression.

  • Symbol: H1: x_a > x_b

Importance of Null Hypothesis

Reasons for Null Hypothesis

• Functions as a benchmark for decision-making (reject or fail to reject H0).

• Easier to disprove a null hypothesis than to prove a research hypothesis.

NHST Process

Steps

• Assess likelihood of observed data assuming H0 is true.

• Rejection of H0 implies statistically meaningful difference.

• No proof of hypotheses—only rejection or failure to reject H0.

Null Hypothesis Acceptance

Clarification

• One does not "accept" H0; rather, one fails to reject it based on data.

Crafting a Good Research Hypothesis

Characteristics

1. Declarative Statement:

   • E.g., "Women report more aggressive behaviors than men."

2. Specific:

   • Clearly defined rather than vague statements.

Other Qualities

• Based on existing scientific literature.

• Concise and focused.

• Testable through empirical data.

In-Class Practice Scenarios

Examples for Hypothesis Formulation

1. Food supplements and cognitive functioning in older adults.

   • Null Hypothesis: No effect on cognitive tasks.

   • Research Hypothesis: Supplements improve cognitive performance.

2. Participation in social activities and self-esteem in children.

   • Null Hypothesis: No effect of social activity on self-esteem.

   • Research Hypothesis: Increased social activity leads to higher self-esteem.

3. Music listening while studying impacting test performance.

   • Null Hypothesis: Studying with music has no effect.

   • Research Hypothesis: Studying in silence improves performance.

4. Social intelligence predicting academic performance in college.

   • Null Hypothesis: No relationship between social intelligence and grades.

   • Research Hypothesis: Higher social intelligence correlates with better grades.

Sampling Overview

Need for Samples

• Studying entire populations is impractical; we utilize samples for research.

Sampling Error

Understanding Sampling Error

• Refers to the difference between sample statistics and population parameters.

• Minimizing sampling error is crucial; random sampling helps reduce it.

Significance of Sampling Error

Consequences of Poor Sampling

• Example: Conducting a math ability study with an unrepresentative sample could yield misleading conclusions.

• Highlighting the adage "Garbage in, garbage out" in research validity.

Sampling Bias

Examples of Bias

• Scenario illustrating bias in survey responses leading to skewed results.

• Importance of ensuring diverse sample responses to enhance validity.

The Population vs. The Sample

Definitions

• Population: All individuals of interest.

• Sample: Selected individuals who participate in the study.

• The aim is to generalize results from the sample back to the population.