Three-way ANOVA in SPSS StatisticsThe three-way ANOVA is used to determine if there is mixed model anova spss youtube interaction effect between three independent variables on a continuous dependent variable i. As such, it extends the two-way ANOVAwhich is used to determine if such an interaction exists between just two independent variables i. It is quite common for the independent variables to be called "factors" or "between-subjects factors", but we will continue to refer to them youtubw independent variables in this guide. For example, you might be interested deca eq test e cycle the effect of two different types of exercise programme i. However, you are concerned that the effect that each ykutube of exercise programme has on marathon running performance might epss mixed model anova spss youtube for males and females i. Indeed, you suspect that the effect of the type of exercise programme on marathon running performance will depend on both your gender and body composition.
The three-way ANOVA is used to determine if there is an interaction effect between three independent variables on a continuous dependent variable i. As such, it extends the two-way ANOVA , which is used to determine if such an interaction exists between just two independent variables i.
It is quite common for the independent variables to be called "factors" or "between-subjects factors", but we will continue to refer to them as independent variables in this guide. For example, you might be interested in the effect of two different types of exercise programme i. However, you are concerned that the effect that each type of exercise programme has on marathon running performance might be different for males and females i.
Indeed, you suspect that the effect of the type of exercise programme on marathon running performance will depend on both your gender and body composition. As such, you want to determine if a three-way interaction effect exists between type of exercise programme, gender and body composition i.
However, before we introduce you to this procedure, you need to understand the different assumptions that your data must meet in order for a three-way ANOVA to give you a valid result.
We discuss these assumptions next. When you choose to analyse your data using a three-way ANOVA, part of the process involves checking to make sure that the data you want to analyse can actually be analysed using a three-way ANOVA. In practice, checking for these six assumptions means that you have a few more procedures to run through in SPSS Statistics when performing your analysis, as well as spend a little bit more time thinking about your data, but it is not a difficult task.
Before we introduce you to these six assumptions, do not be surprised if, when analysing your own data using SPSS Statistics, one or more of these assumptions is violated i. This is not uncommon when working with real-world data rather than textbook examples, which often only show you how to carry out a three-way ANOVA when everything goes well! Even when your data fails certain assumptions, there is often a solution to overcome this. Just remember that if you do not run the statistical tests on these assumptions correctly, the results you get when running a three-way ANOVA might not be valid.
This is why we dedicate a number of sections of our enhanced three-way ANOVA guide to help you get this right. You can find out about our enhanced content as a whole here , or more specifically, learn how we help with testing assumptions here.
A researcher wanted to examine a new class of drug that has the potential to lower cholesterol levels and thus help against heart attack. Due to the specific molecular mechanisms by which this new class of drugs work, the researcher hypothesized that the new class of drug might affect males and females differently, as well as those those already at risk of a heart attack. There were three different types of drug within this new class of drug, but the researcher was unsure which would be more successful.
Therefore, the researcher recruited 72 participants split evenly between males and females. Males and females were further equally subdivided into whether they were at low or high risk of heart attack. Each of these subgroups then received one of the three different drugs.
After one month on the different drugs, cholesterol concentration was measured. The researcher wants to understand how each factor i. Participants' cholesterol concentration was recorded in the variable cholesterol , their gender in gender , their risk of heart attack in risk and the drug they took in the variable drug.
In variable terms, the researcher wants to know if there is an interaction between gender , risk and drug on cholesterol.
In this example, there are four variables: The file setup in the Data View window is shown below:. At the end of these six steps, we show you how to interpret the results from this test. If you are looking for help to make sure your data meets assumptions 4, 5 and 6, which are required when using a three-way ANOVA and can be tested using SPSS Statistics, you can learn more in our enhanced guides here.
Transfer the dependent variable, cholesterol , into the D ependent Variable: You will end up with a screen similar to the one below:. Click the button and you will be presented with the Univariate: Options dialogue box, as shown below:. Then select the D escriptive statistics and H omogeneity tests options in the —Display— area. You will end up with the screen shown below:. Click the button and you will be returned to the Univariate dialogue box.
This will generate the output. The primary goal of running a three-way ANOVA is to determine whether there is a three-way interaction between your three independent variables i. You can see that the statistical significance level of the three-way interaction term is. This value is less than. We show you at every stage how to run these tests, interpret and report them and how to write up all your results.
Check out our low prices, which give you access to all our enhanced guides: Your dependent variable should be measured at the continuous level i.
Examples of continuous variables include revision time measured in hours , intelligence measured using IQ score , exam performance measured from 0 to , weight measured in kg , and so forth.
You can learn more about interval and ratio variables in our article: Your three independent variables should each consist of two or more categorical , independent groups.
Example independent variables that meet this criterion include gender two groups: Caucasian, African American and Hispanic , profession five groups: You should have independence of observations , which means that there is no relationship between the observations in each group or between the groups themselves.
For example, there must be different participants in each group with no participant being in more than one group. This is more of a study design issue than something you would test for, but it is an important assumption of the three-way ANOVA. If your study fails this assumption, you will need to use another statistical test instead of the three-way ANOVA e. If you are unsure whether your study meets this assumption, you can use our Statistical Test Selector , which is part of our enhanced guides.
There should be no significant outliers. Outliers are data points within your data that do not follow the usual pattern e. The problem with outliers is that they can have a negative effect on the three-way ANOVA, reducing the accuracy of your results. Your dependent variable should be approximately normally distributed for each combination of the groups of the three independent variables.
Also, when we talk about the three-way ANOVA only requiring approximately normal data, this is because it is quite "robust" to violations of normality, meaning the assumption can be a little violated and still provide valid results. In addition to showing you how to do this in our enhanced three-way ANOVA guide, we also explain what you can do if your data fails this assumption i. There needs to be homogeneity of variances for each combination of the groups of the three independent variables.
SPSS Statistics Example A researcher wanted to examine a new class of drug that has the potential to lower cholesterol levels and thus help against heart attack. The file setup in the Data View window is shown below: Join the 10,s of students, academics and professionals who rely on Laerd Statistics.