One-way ANOVA and SPSS Statistics (2023)

Introduction

One-way analysis of variance (ANOVA) is used to determine if there are statistically significant differences between the means of two or more independent (unrelated) groups (although you tend to see it used only when there are a minimum of three, rather than two groups). . For example, you can use a one-way ANOVA to understand whether test performance differs based on students' anxiety levels by dividing students into three independent groups (for example, low-, medium-, and high-stress students). Also, it is important to realize that one-way ANOVA is abustest statistics and cannot tell which specific groups were statistically significantly different from each other; it only reports that at least two groups were different. Since you may have three, four, five or more groups in your study design, it is important to determine which of these groups differ from each other. You can do this using a post hoc test (N.B., we'll discuss post hoc testing later in this guide).

Observation:If your study design involves not only a dependent variable and an independent variable, but also a third variable (known as a "covariate") that you want to "control for statistically," you may need to perform an ANCOVA (analysis of covariance), which can be considered as an extension of the one-way ANOVA. For more information, see our SPSS Statistics guide atANCOVA. Alternatively, if your dependent variable is the time until an event occurs, you may need to run aKaplan Meieranalysis.

This "quick start" guide shows you how to perform a one-way ANOVA with SPSS Statistics, as well as how to interpret and report the results of this test. Since the one-way ANOVA is often followed by a post hoc test, we also show how to perform a post hoc test with SPSS Statistics. However, before introducing this procedure, you should understand the different assumptions that your data must meet in order for a one-way ANOVA to provide a valid result. We discuss these assumptions below.

SPSS Statistics

Facilities

When you choose to analyze your data using a one-way ANOVA, part of the process is checking that the data you want to analyze can actually be analyzed using a one-way ANOVA. You should do this because it is only appropriate to use a one-way ANOVA if your data "passes through" the six assumptions required for a one-way ANOVA to provide a valid result. In practice, checking these six assumptions just adds a little more time to your analysis, requiring you to click a few more buttons in SPSS Statistics when performing your analysis, as well as thinking a little more about your data, but it's not. A homework. difficult.

Before introducing these six assumptions, don't be surprised if, when analyzing your own data with SPSS Statistics, one or more of these assumptions is violated (ie, not true). This is not uncommon when working with real world data rather than textbook examples, which often only show how to perform a one-way ANOVA when all goes well. Don't worry though. Even when your data fails certain assumptions, there is often a workaround to overcome this. First, let's take a look at these six assumptions:

• Assumption #1:They aredependent variablemust be measured inintervaloratio level(i.e. they arecontinuo). Examples of variables that meet this criteria include review time (measured in hours), intelligence (measured by IQ score), exam performance (measured from 0 to 100), weight (measured in kg ), etc. You can learn more about interval and ratio variables in our article:variable types.
• Assumption #2:They areindependent variablemust consist oftwo or more categories,independent groups. Typically, a one-way ANOVA is used when you havethree or morecategorical and independent groups, but can be used for only two groups (but an independent samples t-test is more commonly used for two groups). Examples of independent variables that meet this criteria include ethnicity (eg, 3 groups: Caucasian, African-American, and Hispanic), level of physical activity (eg, 4 groups: sedentary, low, moderate, and high), occupation (for example, 5 groups: surgeon, doctor, nurse, dentist, therapist) and so on.
• Assumption #3:You shouldindependence of observations, which means that there is no relationship between the observations in each group or between the groups themselves. For example, there should be different participants in each group, with no participant belonging to more than one group. This is more of a study design issue than something you can test, but it is an important assumption of one-way ANOVA. If your study does not meet this assumption, you will need to use another statistical test instead of a one-way ANOVA (for example, a repeated measures design). If you are not sure whether your study meets this assumption, you can use ourStatistical test selector, which is part of our enhanced guides.
• Assumption #4:there must beno significant outliers. Outliers are simply single data points within your data that do not follow the usual pattern (for example, in a study of IQ scores of 100 students, where the average score was 108 with only slight variation between students, one student scored 156, which is highly unusual and might even put her in the top 1% of IQ scores globally). The problem with outliers is that they can have a negative effect on the one-way ANOVA, reducing the validity of the results. Fortunately, by using SPSS Statistics to run a one-way ANOVA on your data, you can easily spot potential outliers. In our improved one-way ANOVA guide, we: (a) show how to detect outliers using SPSS Statistics; and (b) discuss some of the options you have for dealing with outliers. You can learn more about our improved one-way ANOVA guidance in ourFeatures: One-way ANOVApage.
• Assumption No. 5:They aredependent variableshould beapproximately normal distribution for each category of the independent variable. We are talking about a one-way ANOVA that requires onlyaboutnormal data because it is quite "robust" to violations of normality, which means that this assumption can be violated a bit and still give valid results. You can test for normality with the Shapiro-Wilk normality test, which is easily tested with SPSS Statistics. In addition to showing you how to do this in our improved one-way ANOVA guide, we also explain what you can do if your data doesn't meet this assumption (that is, if it misses more than a little). Again, you can get more information on ourFeatures: One-way ANOVApage.
• Assumption No. 6:there must behomogeneity of variances. You can test this assumption in SPSS Statistics using Levene's test for homogeneity of variances. If your data does not meet this assumption, you should not only perform a Welch's ANOVA instead of a one-way ANOVA, which can be performed with SPSS Statistics, but also use a different post hoc test. In our improved one-way ANOVA guide, we (a) show you how to perform Levene's test for homogeneity of variances in SPSS Statistics, (b) explain some of the things you'll need to keep in mind when interpreting your data, and (c) present possible ways to continue your analysis if your data do not meet this assumption, including running a Welch's ANOVA in SPSS Statistics instead of a one-way ANOVA and a Games-Howell test instead of a post hoc Tukey test (learn more). information in ourFeatures: One-way ANOVApage).

You can verify assumptions #4, #5, and #6 with SPSS Statistics. Before you do this, make sure your data meets Assumptions #1, #2, and #3, although you don't need SPSS Statistics to do this. Note that if you do not correctly run the statistical tests on these assumptions, the results you get when you run a one-way ANOVA may not be valid. That's why we've devoted several sections of our improved One-Way ANOVA guide to helping you get it right. You can learn more about our improved one-way ANOVA guidance in ourFeatures: One-way ANOVApage, or more generally, our enhanced content as a whole on ourResources: summarypage.

In the section,Test Procedure in SPSS Statistics, we illustrate the SPSS Statistics procedure for performing a one-way ANOVA assuming no assumptions are violated. First, we define the example that we use to explain the one-way ANOVA procedure in SPSS Statistics.

SPSS Statistics

Example

A manager wants to increase his company's productivity by increasing the speed at which his employees can use a particular spreadsheet program. Since he doesn't have the in-house skills, he employs an outside agency that provides training in this spreadsheet program. They offer 3 courses: beginner, intermediate and advanced. He isn't sure which course is needed for the type of work his company does, so he sends 10 employees to the beginner course, 10 to the intermediate course, and 10 to the advanced course. When everyone returns from training, he gives them a problem to solve using the spreadsheet program and calculates how long it takes them to solve the problem. He then compares the three courses (Beginning, Intermediate, Advanced) to see if there is any difference in the average time it took to complete the problem.

SPSS Statistics

Configuration in SPSS Statistics

In SPSS Statistics, we separate the groups for analysis by creating a grouping variable calledCourse(i.e., the independent variable), and gave the beginner course a value of "1", the intermediate course a value of "2", and the advanced course a value of "3". The time to complete the defined problem has been entered in the variable nameTempo(ie, the dependent variable). In our Enhanced One-Way ANOVA guide, we show you how to correctly enter data into SPSS Statistics to perform a One-Way ANOVA (see ourFeatures: One-way ANOVApage). You can find out about our improved data configuration content in general in ourFeatures: data settings. Alternatively, check out our generic "quick start" guide:Entering data in SPSS Statistics.