# One-way ANOVA and SPSS Statistics (2023)

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## 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.

## 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.

(Video) Oneway ANOVA - SPSS (part 1)

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.

## 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.

## 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.

## Test Procedure in SPSS Statistics

The eight steps below show you how to analyze your data using a one-way ANOVA in SPSS Statistics when the six assumptions in the previous section,FacilitiesThey were not raped. At the end of these eight steps, we show you how to interpret the results of this test. If you're looking for help making sure your data meets Assumptions #4, #5, and #6, which are required when using a one-way ANOVA and can be tested with SPSS Statistics, you can learn more at ourFeatures: One-way ANOVApage.

(Video) One-way ANOVA and Post Hoc Test Using SPSS

1. CliqueAanalyze > Cometroseems means >OANOVA sin control...in the top menu as shown below. Published with written permission of SPSS Statistics, IBM Corporation.

2. You will be presented with theone-way ANOVAdialog box: Published with written permission of SPSS Statistics, IBM Corporation.

3. Transfer the dependent variable,Tempo, NoDmithe drop down list:box and the independent variable,Course, NoFI adore:box using the appropriate (or drag and drop variables into the boxes) as shown below: Published with written permission of SPSS Statistics, IBM Corporation.

(Video) How To... Perform a One-Way ANOVA Test in SPSS
4. click no button. mark theTukeycheckbox as shown below: Published with written permission of SPSS Statistics, IBM Corporation.

5. click no button.
6. click no button. mark theDescriptivecheck box in-Statistics-area, as shown below: (Video) How to do a One-Way ANOVA in SPSS (12-6)

Published with written permission of SPSS Statistics, IBM Corporation.

OBSERVATION:When testing some of the one-way ANOVA assumptions, you will need to check more of these check boxes. We'll walk you through this, including how to interpret the output, in our improved one-way ANOVA guide.

7. click no button.
8. click no button.

Go to thenext pagefor the SPSS Statistics output and an explanation of the output.

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(Video) SPSS - One-Way ANOVA

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## FAQs

### What is the difference between SPSS and ANOVA? ›

Essentially, ANOVA in SPSS is used as the test of means for two or more populations. ANOVA in SPSS must have a dependent variable which should be metric (measured using an interval or ratio scale). ANOVA in SPSS must also have one or more independent variables, which should be categorical in nature.

When can we use the one-way ANOVA procedure in SPSS? ›

Assumption #2: Your independent variable should consist of two or more categorical, independent groups. Typically, a one-way ANOVA is used when you have three or more categorical, independent groups, but it can be used for just two groups (but an independent-samples t-test is more commonly used for two groups).

What is the statistical model for one-way ANOVA? ›

where Y_{ij} represents the j-th observation (j = 1, \, 2, \, \ldots, \, n_i) on the i-th treatment (i = 1, \, 2, \, \ldots, \, k levels). So, Y_{23} represents the third observation using level 2 of the factor.

What is a one-way ANOVA test used for? ›

One-way ANOVA is typically used when you have a single independent variable, or factor, and your goal is to investigate if variations, or different levels of that factor have a measurable effect on a dependent variable.

Which statistical test should I use ANOVA? ›

Use a one-way ANOVA when you have collected data about one categorical independent variable and one quantitative dependent variable. The independent variable should have at least three levels (i.e. at least three different groups or categories).

How do you analyze ANOVA in SPSS? ›

The steps for conducting an ANOVA in SPSS
1. Click Analyze.
2. Drag the cursor over the Compare Means drop-down menu.
3. Click on One-way ANOVA.
4. Click on the continuous outcome variable to highlight it.
5. Click on the arrow to move the outcome variable into the Dependent List: box.
6. Click on the "grouping" variable to highlight it.

What are the four requirements of a one-way ANOVA test? ›

Performing a Hypothesis Test Regarding Three or More Means Using One-Way ANOVA
• Step 1: State the null and alternative hypotheses.
• Step 2: Decide on a level of significance, α.
• Step 3: Compute the test statistic, ...
• Step 4: Determine the P-value.

What is the difference between one-way ANOVA and t test? ›

The One-way ANOVA is extension of independent samples t test (In independent samples t test used to compare the means between two independent groups, whereas in one-way ANOVA, means are compared among three or more independent groups).

What sample size is needed for one-way ANOVA? ›

On the other hand, if you want to perform a standard One Way ANOVA, enter the values as shown: Now the minimum sample size requirement is only 3. This value applies to each sample or group, so for the 3 Sample ANOVA that would mean each sample has n = 3 for a total number of observations = 9.

How do you know if ANOVA is significant in SPSS? ›

The ANOVA test will tell you whether there is a significant difference between the means of two or more levels of a variable. However, if you've got more than two levels it's not going to tell you between which of the various pairs of means the difference is significant. You need to do a post hoc test to find this out.

### How do you analyze one-way ANOVA results? ›

1. Step 1: Determine whether the differences between group means are statistically significant. ...
2. Step 2: Examine the group means. ...
3. Step 3: Compare the group means. ...
4. Step 4: Determine how well the model fits your data. ...
5. Step 5: Determine whether your model meets the assumptions of the analysis.

What are the limitations of ANOVA in SPSS? ›

The biggest limitation of one-way ANOVA is that it is an omnibus test statistic, which means it can indicate that at least two groups are different but it cannot indicate which specific groups are different from each other.

What are the three assumptions of one-way ANOVA? ›

Assumptions for One-Way ANOVA Test

There are three primary assumptions in ANOVA: The responses for each factor level have a normal population distribution. These distributions have the same variance. The data are independent.

What are the different types of ANOVA in SPSS? ›

There are two main types: one-way and two-way. Two-way tests can be with or without replication. One-way ANOVA between groups: used when you want to test two groups to see if there's a difference between them. Two way ANOVA without replication: used when you have one group and you're double-testing that same group.

Do I use chi square or ANOVA? ›

A one-way ANOVA analysis is used to compare means of more than two groups, while a chi-square test is used to explore the relationship between two categorical variables.

Why is ANOVA the most preferred type of statistical data analysis? ›

Statistical tests like ANOVA help us justify if sample results are applicable to populations. The difference between t-test and ANOVA is that t-test can only be used to compare two groups where ANOVA can be extended to three or more groups.

Should I use ANOVA or regression? ›

Regression is used on fixed or independent variables and done with a single independent variable or multiple independent variables. ANOVA is used to find a common between variables of different unrelated groups.

How do you analyze statistics in SPSS? ›

Connect your database to SPSS Statistics. Prepare an analysis. Analyze data.
...
Analyze the data
1. In the IBM SPSS Statistics Data Editor, click Analyze > Descriptive Statistics > Frequencies to open the Frequencies window.
2. In the Frequencies window, select COUNTRY_EN to count the number of retailer sites in each country.

What does the F value tell you in ANOVA? ›

The F value is used in analysis of variance (ANOVA). It is calculated by dividing two mean squares. This calculation determines the ratio of explained variance to unexplained variance.

What does ANOVA mean in SPSS? ›

One-Way ANOVA ("analysis of variance") compares the means of two or more independent groups in order to determine whether there is statistical evidence that the associated population means are significantly different. One-Way ANOVA is a parametric test. This test is also known as: One-Factor ANOVA.

### What are the two main types of ANOVA? ›

There are two types of ANOVA that are commonly used, the one-way ANOVA and the two-way ANOVA.

How do you explain ANOVA in simple terms? ›

Analysis of Variance (ANOVA) is a statistical formula used to compare variances across the means (or average) of different groups. A range of scenarios use it to determine if there is any difference between the means of different groups.

What is SPSS for data analysis? ›

SPSS (Statistical Package for the Social Sciences), also known as IBM SPSS Statistics, is a software package used for the analysis of statistical data. Although the name of SPSS reflects its original use in the field of social sciences, its use has since expanded into other data markets.

What do the results of an ANOVA test tell you? ›

What is this test for? The one-way analysis of variance (ANOVA) is used to determine whether there are any statistically significant differences between the means of three or more independent (unrelated) groups.

What are the assumptions of ANOVA in SPSS? ›

There are three primary assumptions in ANOVA: The responses for each factor level have a normal population distribution. These distributions have the same variance. The data are independent.

What is a weakness with ANOVA? ›

Disadvantages. It is difficult to analyze ANOVA under strict assumptions regarding the nature of data. It is not so helpful in comparison with the t-test that there is no special interpretation of the significance of two means. The requirement of the post-ANOVA t-test for further testing.

What is the minimum sample size for one-way ANOVA? ›

On the other hand, if you want to perform a standard One Way ANOVA, enter the values as shown: Now the minimum sample size requirement is only 3. This value applies to each sample or group, so for the 3 Sample ANOVA that would mean each sample has n = 3 for a total number of observations = 9.

When to use a one or two-way ANOVA? ›

There is only one factor or independent variable in one way ANOVA whereas in the case of two-way ANOVA there are two independent variables. One-way ANOVA compares three or more levels (conditions) of one factor. On the other hand, two-way ANOVA compares the effect of multiple levels of two factors.

Is ANOVA Qualitative or quantitative? ›

However, ANOVA also refers to a statistical technique used to test for diffferences between the means for several populations. While the procedure is related to regression, in ANOVA the independent variable(s) are qualitative rather than quantitative.

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