PSYU2248 week 1 notes

Research Process, Design, and Data Analysis Steps

Key considerations before analysis:

Research Question/Hypothesis: Determine what to analyze (e.g., does more practice lead to better performance?).

Sample vs. Population: Define your broader population and specific sample (e.g., all stats students vs. 2022 PSYU2248 students).

Unit of Measurement: Identify how constructs are measured (e.g., practice measured by quizzes completed).

    ◦    First variable: Number of quizzes (numerical measurement).

    ◦    Second variable: Final exam grade (scaled from 0 to 100).

Conducting Inferential Statistics: Inferential statistics allow conclusions about a population based on sample data through hypothesis testing:

    ◦    Null Hypothesis (H0): No effect or difference

    ◦    Alternate Hypothesis (H1): Some effect or difference

    ◦    Alpha Level (α): Threshold for significance; commonly set at 0.05

    ◦    Test Statistic & p-value: May be derived from analysis; p-value indicates the likelihood results are due to chance.

    •    Post-analysis, results must be contextualized:

    ◦    Interpret results in light of the original research question/hypothesis.

Analysis Types

Single Variable Analyses:

    ◦    One-sample z-test (known population mean and SD)

    ◦    One-sample t-test (known mean, unknown SD)

    ◦    Chi-square goodness of fit test (categorical)

Two Variable Analyses:

    ◦    Pearson’s correlation (two numeric)

    ◦    Simple linear regression (predictive)

    ◦    t-tests (independent and paired)

    ◦    Chi-square tests (independence & McNemar's test)

Statistical Significance vs. Effect Size

Hypothesis Testing: Determine whether to reject H0 by analyzing test statistics, degrees of freedom, and p-values.

    ◦    Null hypothesis: Assumes no effect or relationship exists.

    ◦    Alternative hypothesis: Indicates some effect or relationship may exist.

    ◦    Aim is to determine if there is enough evidence to reject the null hypothesis.

Importance of Null Hypothesis

    •    Null hypothesis is a critical concept as it reflects a cautious approach to research, especially in fields like medicine.

    •    Research must avoid prematurely announcing effects without sufficient evidence.

Understanding P-Values

    •    P-value: A probability value indicating the likelihood of observing data patterns that would occur if the null hypothesis were true.

    •    A small p-value (e.g., < 0.001) suggests strong evidence against the null hypothesis, leading to its rejection.

    ◦    If p-value is < 0.05, reject the null hypothesis confidently.

Type I and Type II Errors

    •    Type I Error: Rejecting the null hypothesis when it is true.

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

    •    Balancing these errors is crucial for statistical analysis

Key Statistical Concepts

Statistical Significance vs. Effect Size:

    ◦    Statistical significance indicates if results likely reflect true findings, while effect size measures the practical significance of those findings.

    ◦   Effect Size: Measures practical significance or magnitude of an effect, independent from sample size.

95% Confidence Interval: Describes likely range of population parameters; if sampled repeatedly, 95% intervals include true value.

Point Estimates vs. Interval Estimates:

    ◦    Point estimates are single-value estimates (e.g., mean).

    ◦    Interval estimates provide a range (e.g., my cat wakes up between 3-5am).

Power Analysis

    •    Power is the probability of detecting a true effect (1 - β).

Factors affecting power include:

    ◦    Alpha level (increased alpha increases power).

    ◦    Size of the effect (bigger effect increases power).

    ◦    Variance and sample size (larger samples reduce variance and increase power).

    ◦    Choice of design and analysis methods (within-subjects designs are often more powerful).

Implications of Power Analysis

    •    Underpowered Studies: Small sample sizes may lead to undetected effects.

    •    Importance of conducting power calculations to ensure studies are adequately powered (targeting 80% power).