Analysis of Variance: ANOVA Designs

Types of Experimental Designs Analyzed by ANOVA

  • Various types of experimental designs can be analyzed using Analysis of Variance, commonly known as ANOVA.

  • This guide discusses ANOVA designs and defines key terms utilized in the analysis.

Key Terms and Definitions

  • Independent Variable:

    • A variable manipulated by the experimenter.

    • Example: In the smiles and leniency case study, the effect of four types of smiles (neutral, false, felt, miserable) on leniency shown to a person was investigated.

    • In this context, the type of smile is the independent variable.

  • Factor:

    • Used synonymously with the independent variable in ANOVA design.

    • In the smiles and leniency case study, the type of smile is also termed a factor.

  • Levels of a Factor:

    • The number of different states or conditions of the factor being studied.

    • In this case, there are four levels as there are four types of smiles compared.

Types of ANOVA

  • One-Way ANOVA:

    • Conducted when there is only one factor, as demonstrated in the smiles and leniency case study.

  • Two-Way ANOVA:

    • Conducted on experiments that involve two factors.

    • Example: The obesity and bias case study examines the influence of two factors:

      • The weight of the woman sitting next to the applicant.

      • The relationship between the applicant and the woman on job qualification ratings.

Between Subjects vs. Within Subjects Factors

  • Between Subjects Factor:

    • When different subjects are assigned to different levels of a factor.

    • Comparison is made between different groups of subjects.

    • Example: In the smiles and leniency study, four levels of the factor (type of smile) were represented by four distinct groups of subjects.

  • Within Subjects Factor:

    • When the same subjects are tested under each level of the factor.

    • This implies that comparisons are made within the same group of subjects, typically in repeated measures format.

    • Example: In the ADHD treatment study, subjects received each of four dosage levels (0.15, 0.30, 0.60 mg per kilogram).

    • Thus, there was only one group of subjects, with comparisons made across conditions within this single subject group.

Complex Experimental Designs

  • Often, studies may involve more than one factor.

    • Example: A hypothetical study examining the effects of age and gender on reading speed testing boys and girls aged 8, 10, and 12.

    • This results in six distinct groups as combinations of age and gender are tested.

    • The analysis in such scenarios would also utilize Two-Way ANOVA.

  • Factorial Design:

    • When all combinations of the different levels of factors are included in the study.

    • The design in the age and gender study can be described concisely as an “Age 3 by Gender 2 factorial design.”

    • Here, ‘3’ represents the three levels of age and ‘2’ reflects the two levels of gender.

  • Complex designs can contain multiple factors and may integrate both between and within subjects variables.