Inferential Statistics with NHST

Lecture 2.9: Inferential Statistics with Null Hypothesis Testing

Learning Goals

  • Understand the process of Null Hypothesis Significance Testing (NHST).

  • Comprehend the use of p-values for making inferences.

  • Define what an alpha criterion is in statistical testing.

Key Concepts in Statistics

  • Population: Refers to the entire set of subjects or items you want to study (e.g., all college students).

  • Sample: A subset of the population used for analysis (e.g., a group of 52 Duke students).

  • Descriptive Statistics: Techniques for organizing and summarizing data from a sample, including measures of central tendency and variability.

  • Inferential Statistics: Techniques that use sample data to make inferences about the population parameters, which are often unknown.

Null Hypothesis Testing (NHST)

  • Defining Hypotheses: When testing hypotheses, we start with two main hypotheses:

    • Null Hypothesis (H0): Assumes no relationship (e.g., ρ = 0).

    • Alternative Hypothesis (HA): Suggests a relationship exists (e.g., ρ > 0).

  • Probabilities in NHST: NHST assesses the probability of observing your data if the null hypothesis were true. If we find that the result is statistically significant, we reject the null hypothesis.

P-values and Alpha Criterion

  • P-value: Indicates the probability of obtaining your observed data under the null hypothesis. A common threshold for significance is p < 0.05, meaning there's a less than 5% chance of your result occurring if the null hypothesis is true.

  • Alpha Criterion: The threshold for determining statistical significance—spread across different values:

    • If p > 0.05, we do not reject the null hypothesis.

    • If p < 0.05, we reject the null hypothesis and accept the alternative hypothesis.

  • Remember, while p < 0.05 is a common threshold, it is not universally defined and should be adjusted depending on the context.

Types of Errors in NHST

  • Type I Error: Rejecting the null hypothesis when it is actually true (false positive).

  • Type II Error: Failing to reject the null hypothesis when it is false (false negative).

Correlation Analysis

  • Pearson Correlation (r): Measures the strength of a linear relationship between two variables. The range of r can indicate weak (r close to 0), moderate, or strong relationships (r close to 1 or -1).

  • Interpreting Results: When reporting statistical results, provide clarity by stating the correlation's value, significance, and sample size. For example, “No significant relationship between sleep duration and homework performance (p > .05); however, there was a significant negative relationship between sleep variability and homework performance (r(45) = -.39, p < .01).”

Practical Application

  • When conducting research, ensure proper analysis methods are applied, including adjustments for multiple comparisons. Reference significant results with adequate statistics, such as adjusted Pearson coefficients, and specify your significance levels clearly.

Conclusion

  • Familiarize yourself with NHST, p-values, and correlation coefficients to strengthen your understanding of inferential statistics. Consider the importance of proper hypothesis formulation, significance testing, and reporting outcomes accurately to effectively interpret statistical results in real-world scenarios.