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A One-Way ANOVA

Topic 1 of 5

Learning Objective:

Interpret the results from a one-way ANOVA.

Before You Begin

Before reading this Skill Builder, be sure to review the following concepts:

• Steps in hypotheses testing

  Steps in hypotheses testing

• Null and alternative hypothesis

  Null and alternative hypothesis

• Alpha level

  Alpha level

• Type I and Type II Errors

  Type I and Type II Errors

• t-test for two independent groups

  t-test for two independent groups

• Definitions of categorical vs. continuous variables

  Definitions of categorical vs. continuous variables

Introduction

When researchers conduct a one-way ANOVA, the goal is to examine whether there are mean differences among two or more groups. The one-way ANOVA is a useful statistical analysis for research designs that involve only one independent grouping variable (called a factor in an experimental design) and a single continuous dependent variable. 

Criteria for a One-Way ANOVA

That is, a one-way ANOVA is appropriate in scenarios that meet the following criteria:

• There is one independent variable

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  There is one independent variable

• There is one dependent variable

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  There is one dependent variable

• The independent variable has two or more levels

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  The independent variable has two or more levels

• The dependent variable can be considered to be continuous

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  The dependent variable can be considered to be continuous

In an ANOVA, just like in a t-test, a “level" is a group or category.

Example: IAT Research Scenario

In our IAT research scenario below, for example, there are four levels: American Indians, inner-city, suburban, and undocumented.

Imagine you want to see if cultural groups have different attitudes toward old people and decide to use the Implicit Association Test (IAT), which is a computerized procedure for measuring attribute discrimination (Greenwald, 2012).  Using latency of responses to different kinds of stimuli, the test has been used to study attitudes towards age, race, skin-tone, religion sexuality, and weight, among other attributes (Lane, Banaji, Nosek, & Greewald, 2007).

You might develop an IAT that measures attitudes toward old people and use it to compare four cultural groups: American Indians living on a reservation, inner-city legal residents, suburban legal residents, and undocumented residents. Your interest in comparing four different groups will lead you to consider the one-way ANOVA. In your one-way ANOVA, you would test the following null hypothesis:

HO  :  μAmerican Indians =  μinner-city = μsuburban = μundocumented

The alternative hypothesis would be:

HA : not  HO

The null states that all four populations have the same mean for the IAT test: that is, that all four populations have the same attitudes, on average, toward old people. The alternative states that one or more of the population mean differs from the others: that is, that the four populations are not equivalent in their attitudes, on average, toward old people.

Note: You can participate in a study using the IAT approach at https://implicit.harvard.edu/implicit/.

• Note that although we can use a one-way ANOVA if we have just two levels, a t-test is probably the simpler approach in this case. One-way ANOVAs are typically used when there are more than two levels.  

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  Note that although we can use a one-way ANOVA if we have just two levels, a t-test is probably the simpler approach in this case. One-way ANOVAs are typically used when there are more than two levels.  

• Also note that, although the independent variable in an ANOVA can technically be either categorical or continuous, researchers typically use an ANOVA in cases in which there are not an excessive number of levels. When there are too many levels, there may be very few participants in each level (in each group)  and there will likely not be enough statistical power to discern any differences between the groups. 

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  Also note that, although the independent variable in an ANOVA can technically be either categorical or continuous, researchers typically use an ANOVA in cases in which there are not an excessive number of levels. When there are too many levels, there may be very few participants in each level (in each group)  and there will likely not be enough statistical power to discern any differences between the groups. 

Hence, the one-way ANOVA is usually applied when the independent variable has relatively few levels, and most of the time, the independent variable in a one-way ANOVA is categorical.

For each proposed research study, indicate whether the one-way ANOVA is an appropriate or not appropriate choice for analyzing the data.

Hint: Think about whether the independent variable has two or more levels (two or more groups) and whether the dependent variable can be considered to be continuous.

A true experiment is conducted, and there are two independent variables (factors). The first has three levels, and the second has two levels. The researcher randomly assigns each of 60 participants to one of the six cells (3 x 2) in the experiment. Each participant is assigned to one level of the first factor and one level of the second factor.

Appropriate

Not appropriate

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A researcher wants to see if IQ and sound decision-making are related. The data will consist of an IQ score for each participant along with a score that is obtained by evaluating each participant’s decisions using a scale of 1 to 10 for a set of 10 decisions.

Appropriate

Not appropriate

SUBMIT Incorrect TAKE AGAIN

A food producer wishes to compare profitability of sales of fresh vegetables using three sales methods: big-box grocery chains, specialty grocery stores, and home delivery. The producer randomly samples 10 facilities of each type and calculates profitability (total sales costs) for one month for each facility.

Appropriate

Not appropriate

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A group of high school teachers wants to predict which students will pass their final exam and which students will fail the exam. In order to make this prediction, they ask their students how many hours they spend studying during a typical week.

Appropriate

Not appropriate

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