Name: factorial analysis in anova
Uploaded: 2020-02-12T11:07:40.000Z
Duration: 2 min 1 s
Channel: JoVE

K12 Standards

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Biology

BIO.1

BIO.1.b

Factorial Design

If a researcher is curious about a topic, such as people&rsquo;s food preferences, they may consider a factorial analysis design&mdash;an experimental approach used when examining the effects of more than one factor, at least two independent variables, on one dependent variable.

For example, they can decide to manipulate two independent variables: food category and food temperature. Each factor consists of two levels: the ice cream and soup are served hot or cold. This case is referred to as a 2x2 factorial design, with favorability ratings operating as the single dependent variable.

As a result, the researcher can test two types of hypotheses. One type predicts the main effects, which assess the influence of conditions across each factor separately. For instance, to examine the main effect for food category, the favorability ratings of ice cream would be compared against soup.

Similarly, observing participants&rsquo; preferences between these foods when served warm versus cold relates to the main effect for temperature.

The other type of hypothesis&mdash;which is a major advantage of the approach&mdash;involves the assessment of interaction effects. These are observed when the effect of a factor is dependent o

factorial design

Factorial Analysis is an experimental design that applies Analysis of Variance (ANOVA) statistical procedures to examine a change in a dependent variable due to more than one independent variable, also known as factors. Changes in worker productivity can be reasoned, for example, to be influenced by salary and other conditions, such as skill level. One way to test this hypothesis is by categorizing salary into three levels (low, moderate, and high) and skills sets into two levels (entry level vs. experienced).

Naming 

This scientific approach is designated a label that either underscores the number of factors or the number of conditions tested for each independent variable. The example experiment above would be described as a two-way factorial ANOVA, because it involves two independent variables. In respect to&nbsp;the number of levels considered for salary (low, moderate, and high) and skill sets (entry level and&nbsp;experienced), this same experiment is also designated as a 3 by 2 design, formally written as a 3 x 2 Factorial ANOVA. Of note, computing the product of 3 and 2 signifies that there is a total of 6 combinations of experimental conditions observed.

Investigative Advantages 

Observing the effects of at least two independent variables is a more practical and economical approach. This averts the need to expend time and resources for separate experiments. Furthermore, collecting data for different combinations of conditions enables researchers to make a variety of assessments, including main and interaction effects.

Certain research questions may require understanding know how each factor may independently impact a dependent variable. For example, observed changes in worker productivity scores due to salary are separated from those due to skill level, to help determine the main effects for each. Results could potentially reveal that high productivity found in entry level employees may or may not apply to those who are more experienced. Likewise, low productivity that may be found in low salaried employees may or may not be evident with increased wages. The ability to recognize if results can be generalized to different circumstances or group features thus serves as another advantage for this type of design.

An interaction effect occurs when the influence of an independent variable on a given dependent variable depends on the level of other factors being examined. It might be found, for instance, that the impact of salary on worker productivity may be more pronounced for entry level as opposed to experienced employees. This type of analysis allows researchers to gain a deeper view of patterns that may emerge in the data set.

Implications of Factorial Analysis 

Due to its flexibility and practicality, factorial analysis continues to be one of the most common experimental designs used across all disciplines. A recent study, for instance, investigated whether consumer behavior may depend on whether the product is utilitarian or hedonic. In addition to product type, researchers also included product image (close-up vs. wide shot) as a potential factor that influenced purchase decisions. These researchers further examined if type of persuasive technique, such as rational or emotional appeal would have an impact (Kim, Lee, &amp; Choi, 2019). Hedonic products tended to gain more favorable attitudes when a wide shot image was accompanied by emotion inducing advertisements. Inverse findings were observed for utilitarian products in this 2 x 2 x 2 Factorial ANOVA,&nbsp;otherwise known as a three-way ANOVA.

Factorial Analysis is an experimental design that applies Analysis of Variance (ANOVA) statistical procedures to examine a change in a dependent variable ...

Education

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Social Psychology

Foundations of Social Psychology

Research Methods

KEY TERMS AND CONCEPTS

factorial analysis in anova

Factorial analysis is a research design that uses ANOVA, or analysis of variance, to test how more than one independent variable affects a dependent variable. The independent variables are also called factors. A worker productivity study can show how salary and skill level may each influence the result.

In this example, salary can be grouped into three levels: low, moderate, and high. Skill level can be grouped into two levels: entry level and experienced. The study would be called a two-way factorial ANOVA because it includes two independent variables. It can also be described as a 3 x 2 design. That label shows the number of levels for each factor. It also shows that there are six total combinations of conditions.

Factorial analysis is practical because it lets researchers study two or more factors in one experiment. This can save time and resources compared with running separate studies. It also makes it possible to compare results across different combinations of conditions.

The design helps researchers examine main effects and interaction effects. A main effect shows the separate impact of one factor on the dependent variable. In the worker example, researchers can compare productivity changes from salary alone or skill level alone. This helps show whether patterns found in one group, such as entry level workers, also apply to another group, such as experienced workers.

An interaction effect appears when the effect of one independent variable depends on the level of another factor. For example, the effect of salary on productivity may be stronger for entry level employees than for experienced employees. Factorial analysis is useful because it helps researchers see these patterns more clearly and judge whether results generalize across different conditions.

Because it is flexible and efficient, factorial analysis is used often across many fields. One study examined consumer behavior using product type, product image, and persuasive technique as factors. Product type was either utilitarian or hedonic. Product image was close-up or wide shot. Persuasive technique was rational or emotional. The study found that hedonic products got more favorable attitudes when a wide shot image was paired with emotion-inducing ads. The opposite pattern was seen for utilitarian products in this 2 x 2 x 2 factorial ANOVA, also called a three-way ANOVA.

Factorial Analysis in ANOVA

the scientific method

Research Questions and Falsifiable Hypotheses

Research questions and falsifiable hypotheses help scientists separate facts from opinions. Facts are observable realities. Opinions are personal judgments, conclusions, or attitudes that may or may not be accurate. In science, facts are established with evidence from empirical research, which means research based on observation and experience. Scientific knowledge grows through the scientific method, a process that connects ideas with real-world evidence. Researchers test theories and...

case studies

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surveys

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archival research

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longitudinal research

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cross-sectional research

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Factorial analysis is a research design that uses ANOVA, or analysis of variance, to test how more than one independent variable affects a dependent variable. The independent variables are also called factors. A worker productivity study can show how salary and skill level may each influence the result. In this example, salary can be grouped into three levels: low, moderate, and high. Skill level can be grouped into two levels: entry level and experienced. The study would be called a two-way...

the placebo effect

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blind procedures

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correlations

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Correlation can be misleading when two variables move together for a different reason. A confounding variable, or hidden factor, may be causing the pattern instead of one variable directly affecting the other. The ice cream and crime example shows this clearly. When temperatures rise, more people go outside, buy ice cream, and may also have more chances for conflict. A correlation does not prove causation. Even when a relationship looks strong, we should not assume that one variable causes the...

reliability and validity

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regression toward the mean

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measures of central tendency

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variation: normal distribution, range, and standard deviation

variation-normal-distribution-range-and-standard-deviation

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statistical significance

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key terms and concepts

Explore factorial analysis, ANOVA, main effects, and interaction effects using clear high school examples like salary, skill level, and consumer behavior.

Factorial Analysis in ANOVA | JoVE K12

JoVE Core Social Psychology offers a comprehensive learning experience on the principles of social behavior through concise, animated video lessons. The series explores key topics such as self-concept, social cognition, group dynamics, stereotypes, and relationships. It provides a structured foundation for understanding human behavior in social situations. Students gain insights into how individuals think, feel, and behave in social contexts while examining the psychological processes that influence interactions and judgments. By integrating theory with real-world applications, these lessons offer a clear and engaging approach to mastering essential concepts in social psychology.

social psychology

Chemistry

CH.1

CH.1.b

Texas Essential Knowledge and Skills

High School

CHEM.4

CHEM.4.B

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BIO.1.d

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BIO.1.f

Factorial Analysis in ANOVA

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