Between-Subjects vs. Within-Subjects Designs: A Breakdown

Between-Subjects Design:

• Description: Participants are randomly assigned to different groups, each representing a single condition of the independent variable.
• Independent Variable: Manipulated by the researcher, with different levels assigned to different groups.
• Dependent Variable: Measured in all groups, reflecting the outcome of interest.
• Advantages: Easier to control extraneous variables, avoids order effects (learning or fatigue influencing results within a single participant).
• Disadvantages: Individual differences between participants can influence the results (requires larger sample sizes to account for this).

Within-Subjects Design:

• Description: All participants experience all levels of the independent variable.
• Independent Variable: Manipulated within each participant across multiple trials or measurements.
• Dependent Variable: Measured repeatedly for each participant at each level of the independent variable.
• Advantages: More powerful statistically (needs a smaller sample size), controls for individual differences.
• Disadvantages: Susceptible to order effects (learning or fatigue influencing results across trials).

Choosing the Right Statistic: Variables, Levels, and Design

Here’s what to consider when selecting an appropriate statistic:

• Variables: Identify the independent and dependent variables.
• Levels: Determine the number of levels for each variable (e.g., two types of music, three age groups).
• Design: Recognize if it’s a between-subjects or within-subjects design.

Example: Coffee and Focus

Research Question: Does coffee improve focus?

Independent Variable: Coffee intake (Level 1: No coffee, Level 2: One cup of coffee)

• Level of Measurement: Nominal (categorical) Dependent Variable: Test scores on a focus task
• Level of Measurement: Ratio (continuous)

Hypotheses:

• H1 (Directional): Participants who drink coffee will score higher on the focus task compared to those who don’t drink coffee.
• H2 (Non-Directional): There will be a difference in focus task scores between participants who drink coffee and those who don’t.

Statistics:

• Between-Subjects Design: We could use an independent samples t-test (if only two levels of coffee intake) or one-way ANOVA (if more than two levels) to compare the average focus scores between the coffee and no-coffee groups.
• Within-Subjects Design: A paired-samples t-test would be used to compare the focus scores of each participant before and after coffee consumption.

Choosing a Statistic for Ethnic Groups and Math Achievement

Scenario: You want to see if there’s a difference in math achievement scores among three ethnic groups (African American, Hispanic, Caucasian).

Variables:

• Independent Variable: Ethnicity (Level 1: African American, Level 2: Hispanic, Level 3: Caucasian)
• Level of Measurement: Nominal (categorical)
• Dependent Variable: Math achievement scores
• Level of Measurement: Ratio (continuous)

Statistic:

In this case, you would use a one-way ANOVA (Analysis of Variance). This test is appropriate because:

• It’s designed for between-subjects designs with a single categorical independent variable (ethnicity) with multiple levels (three ethnic groups).
• It allows you to compare the means of the math achievement scores across the three ethnic groups to see if there’s a statistically significant difference.

By comparing the means and the F-statistic from the ANOVA, you can determine if there’s evidence to suggest that ethnicity is associated with differences in math achievement scores in this population. It’s important to follow up with post-hoc tests (if the ANOVA is significant) to identify which specific groups differ from each other.