Statistics: T-tests and Research Designs

T-tests

• Determine the likelihood of an observed difference between conditions if the null hypothesis is true.
• Assess whether the variance between conditions is larger than the variance within conditions.
• Calculate t-value by dividing the variance explained by the independent variable (IV) by the unexplained variance.

Within-subjects Design

• All participants participate in all conditions.
• Example: Comparing scores in a real-world situation versus a simulated environment; comparing essay grades before and after a workshop.
• Advantages: Accounts for individual differences, more powerful, fewer participants needed, often preferred for longitudinal studies.
• Disadvantages: Potential order effects (practice or fatigue), participant dropout.

Matched-Pairs Design

• Participants are matched on relevant characteristics (e.g., IQ, gender, age).
• One participant from each pair is assigned to each condition.
• Advantages: Combines benefits of within and between-subjects designs, eliminates order effects, accounts for individual differences.
• Disadvantages: Time-consuming and difficult to match participants perfectly.

Paired Samples T-test

• Compares means of two conditions in within-subjects or matched-pairs designs.
• Calculates the probability of obtaining a mean difference as large or larger by chance.
• Assumes interval or ratio data, a sample size of at least 12, normally distributed differences.

Assumptions and Testing

• Interval or ratio data for the dependent variable.
• Sample size of at least 12 participants.
• Differences between conditions are normally distributed.
• Verify normality of differences using the Shapiro-Wilk test (non-significant p-value > 0.05 indicates normality).

Non-parametric Alternatives

• If assumptions are not met, use non-parametric tests.
• Wilcoxon signed-ranks test for related samples: Alternative to the paired samples t-test if data violates assumptions.

Expected Frequencies (Chance Levels)

• Probabilities vary depending on the context (e.g., coin flip = 50%, dice roll = 16.67%).

Binomial Test

• Determines if an observed proportion differs significantly from an expected proportion by chance.
• Assumes nominal data, a single dichotomy, random sampling, independent scores, known expected distribution, and normality.

Chi-square Test of Independence

• Compares proportions between two groups with nominal data.
• Assumes nominal data, random sampling, independent scores, and expected frequencies of 5 or more in each category.
• Calculates expected frequency using marginal totals and sample size.

Fisher's Exact Test

• Non-parametric alternative to the chi-square test of independence, useful when assumptions of chi-square aren't met.

One-tailed vs. Two-tailed Hypotheses

• One-tailed: Predicts a difference in a specific direction.
• Two-tailed: Predicts a difference without specifying direction.

Chi-square Goodness-of-Fit Test

• Compares observed proportions to expected proportions with nominal data and multiple levels.
• Assumes nominal data, random sampling, independent scores, and expected frequencies of 5 or more in each category.

Reporting p-values

• Report p-values to three decimal places, use lower case italicized p and the exact value, e.g p=0.041, not p < 0.05.

This quiz covers T-tests, including their application in determining variance and assessing differences under the null hypothesis. It also explores within-subjects and matched-pairs designs, highlighting their advantages and disadvantages in research. Perfect for those studying statistics and research methodologies.