Hypothesis Testing and Sampling Notes

Introduction to Hypothesis Testing and Sampling

  • Lecture Overview

    • Presented by Genevieve Kwek.

    • Focus on:

    • Understanding hypothesis

    • Performing hypothesis testing

    • Introduction to statistical principles

    • Sample characteristics

What is a Hypothesis?

  • Definition: An educated guess grounded in prediction.

    • Example: "I predict it will rain by 4 p.m. today."

  • Hypothesis in Research:

    • A precise, testable statement regarding the relationship between an independent variable (IV) and a dependent variable (DV).

    • Example: "I predict that drug A will significantly improve participants' headache pain."

  • Characteristics of Hypotheses:

    • Must be stated before data collection.

    • Hypotheses are evaluated through testing against measurable outcomes.

    • Null Hypothesis ($H_0$): Assumes no effect or difference.

    • Alternative Hypothesis ($H_1$): Represents the effect or difference predicted.

Null and Alternative Hypothesis

  • Null Hypothesis ($H_0$):

    • Default assumption. It states that there is no effect or difference.

    • Example: "Drug A has no effect on headache pain."

  • Alternative Hypothesis ($H_1$):

    • Contrary to the null. Represents a claim of an effect.

    • Example: "Drug A improves headache pain."

  • Testing Hypotheses:

    • Hypothesis testing aims to collect evidence to reject the null hypothesis.

    • Importance of being specific: Define both IV and DV explicitly.

Formulating Hypothesis Statements

  • Structure: Use 'if-then' statements to articulate hypotheses.

    • Example: "If I give you drug A (IV), then your headache pain will improve (DV)."

  • Basis for Hypotheses: Findings should stem from prior research, literature, or observations, avoiding random assertions.

P-Value and Statistical Significance

  • P-Value:

    • Represents the probability of obtaining observed results assuming the null hypothesis is true.

    • Smaller P-values indicate stronger evidence against the null hypothesis.

  • Significance Level:

    • Commonly set at 0.05, indicating a 5% risk of identifying a false positive (Type I error).

    • If $P < 0.05$, results are considered statistically significant.

  • Errors in Hypothesis Testing:

    • Type I Error: Rejecting the null hypothesis when it's actually true.

    • Type II Error: Failing to reject the null hypothesis when it is false (not detailed in this section).

Understanding Samples

  • Sample vs. Population:

    • Population: The entire group of interest (e.g., people over 55).

    • Sample: A subset of the population used for testing due to practicality.

Importance of Representative Sampling

  • Sampling must reflect the population to generalize research findings effectively.

  • Sample characteristics should be considered to ensure conclusions are valid for the entire population.

  • Sampling Bias:

    • Sample should not be skewed; methods of selection matter.

    • E.g., recruiting solely from one demographic leads to skewness (e.g., only from premium fitness clubs for over 55s).

Sample Size Considerations

  • Larger samples yield more representative and reliable estimates of population parameters.

  • Typical minimal size cited in research: 25 to 30 participants, depending on desired effect size.

  • Larger effect sizes require smaller samples to detect significant results; conversely, smaller effects require larger samples.

  • Ethical Considerations:

    • Samples that are too large waste resources; too small may not yield significant results.

Sampling Methods

Probability Sampling

  • Definition: Every individual has a known chance of being selected.

    • Allows for randomness and counteracts bias.

  1. Simple Random Sampling:

    • Each participant has an equal chance; can use random number generators.

  2. Systematic Sampling:

    • Choose a starting point and select every k-th individual from a list.

  3. Stratified Random Sampling:

    • Population divided into subgroups; random samples taken from each subgroup.

  4. Cluster Sampling:

    • Randomly select entire clusters from a population.

Non-Probability Sampling

  • Definition: Individuals are selected based on accessibility and willingness, often leading to bias.

    • Common in real-world research due to difficulty accessing complete populations.

  1. Convenience Sampling: Participants who are easy to reach.

  2. Quota Sampling: Setting quotas and selectively sampling based on characteristics.

Conclusion and Self-Assessment

  • Reflect on your understanding of concepts discussed. - Consider how sampling methods used in a study could impact results.

  • Reach out with further questions regarding hypothesis testing or correlation topics.