Question

An experiment is conducted on the effect of age (5 yr, 10 yr and 15 yr) and treatment condition (experimental versus control) on reading speed. Which statistical term (main effect, simple effect, interaction, specific comparison) applies to each of the descriptions of effects. a. The effect of the treatment was larger for 15 -year olds than it was for 5 - or 10-year olds. b. Overall, subjects in the treatment condition performed faster than subjects in the control condition. c. The age effect was significant under the treatment condition. d. The difference between the 15 - year olds and the average of the 5 - and 10 year olds was significant. e. As they grow older, children read faster.

Short answer

a. Interaction, b. Main effect, c. Simple effect, d. Specific comparison, e. Main effect.

Step-by-step solution

Understanding the Experiment Setup

The experiment examines the effect of two factors: age (with levels 5, 10, and 15 years) and treatment condition (experimental vs. control) on reading speed. You need to identify different statistical terms based on how each factor and their possible interactions affect the reading speed.

Analyzing Effect Descriptions

We need to determine what kind of statistical effect each description corresponds to: - Main effect: The overall influence of one independent variable. - Simple effect: The effect of one independent variable at a particular level of another variable. - Interaction: How the effect of one variable changes across the levels of another variable. - Specific comparison: A comparison between specific group means.

Classify Description a

"The effect of the treatment was larger for 15-year-olds than it was for 5- or 10-year-olds." This indicates an interaction effect between age and treatment, as the effect of treatment is not consistent across all age groups.

Classify Description b

"Overall, subjects in the treatment condition performed faster than subjects in the control condition." This is a main effect of the treatment condition, showing a consistent difference regardless of age.

Classify Description c

"The age effect was significant under the treatment condition." This corresponds to a simple effect, where the impact of age is examined within the treatment condition.

Classify Description d

"The difference between the 15-year-olds and the average of the 5- and 10-year-olds was significant." This is a specific comparison, as it focuses on the difference between specific group averages.

Classify Description e

"As they grow older, children read faster." This describes the main effect of age, indicating a general trend across all conditions.

Key concepts

Main Effect

A statistical analysis often involves determining the main effect of one or more independent variables, such as age or treatment condition. The **main effect** is the overarching influence an independent variable has on the dependent variable. In the context of the reading speed experiment:

• The main effect of the treatment condition indicates how it impacts reading speed across all ages. Even if age differs, this effect remains consistent.
• Similarly, the main effect of age would display the overall trend of reading speed as children grow older.

For example, statement (b) states, "Overall, subjects in the treatment condition performed faster than subjects in the control condition." This is a typical main effect of the treatment condition, reflecting performance differences regardless of age level. Similarly, statement (e) mentions, "As they grow older, children read faster," emphasizing the main effect of age in boosting reading speed.

Simple Effect

The **simple effect** focuses on an independent variable's impact while holding another variable constant. It helps in the nuanced understanding of individual factor influences within specific contexts. Referring to the experiment:

• Statement (c) mentions, "The age effect was significant under the treatment condition." Here, we look specifically at how age influences reading speed only within the group receiving the treatment, not in the control group.

Examining simple effects is vital when dissecting the role of single variables in specific scenarios. It illuminates details that might stay hidden in broader analyses, making it very insightful for targeted interventions.

Interaction

An **interaction** effect is where two or more independent variables simultaneously influence the dependent variable in unique ways. This effect can often reveal complex dynamics among variables. For example:

• Statement (a) notes, "The effect of the treatment was larger for 15-year-olds than it was for 5- or 10-year-olds."

Here, the interaction effect between age and treatment condition is clear. As the treatment's impact varies significantly across different age levels, this suggests a nuanced interdependence.
Interactions help uncover these multi-layered relationships, often guiding deeper experiments and revisions in hypotheses that can explain why such variations occur.

Specific Comparison

A **specific comparison** often brings the focus down to a precise examination of particular group means or conditions. It narrows down broader statistical observations into single unit comparisons. In the experiment:

• Statement (d) considers a specific comparison: "The difference between the 15-year-olds and the average of the 5- and 10-year-olds was significant." Here, the spotlight is on assessing specific group differences within age categories.

Specific comparisons are pivotal for highlighting particular differences that broader aggregations might overlook. They offer insights into how individual groups stand in relation to each other, which can aid in understanding targeted intervention outcomes and tailoring strategies accordingly.