What is a One Way ANOVA Test ?

    Using ANOVA test in Research

    This easy tutorial will show you how to run the One Way ANOVA test in SPSS, and how to interpret the result.

    One-way ANOVA is a statistical method that examines the effect of a categorical variable with three or more groups (the factor) on one dependent variable (continuous variable). In addition, Analysis of variance (ANOVA) is a statistical procedure concerned with comparing means of several samples. On the other hand, It is kind of as an extension of the t-test for two independent samples to more than two groups. (Source)

    Assumptions of the ANOVA Test:

    When performing an ANOVA procedure the following assumptions are required:

    • Continuous dependent variable
    • The factor consists of two or more independent groups
    • Independence of observations
    • No outliers
    • The dependent variable has a normal distribution (one-way ANOVA is a parametric technique)
    • Homogeneity of variance

    An Example: ANOVA Test

    We use a one-way analysis of variance when we divide the data into groups according to only one factor.

    This guide will explain, step by step, how to run one way ANOVA Test in SPSS statistical software by using an example.

    For example, we will examine the effect of job responsibility on annual wage in dollars. Job responsibility is a categorical variable (factor) with three groups (small, medium, and high), and the annual wage in dollars is a continuous dependent variable.

    Null hypothesis:

    There is no difference in annual wages between small, medium, and high job responsibilities.

    Alternative hypothesis:

    There is a difference in annual wages between small, medium, and high job responsibilities.

    This easy tutorial will show you how to run the One Way ANOVA test in SPSS, and how to interpret the result.


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    How to Run One Way ANOVA Test in SPSS: Explanation Step by Step

    From the SPSS menu choose Analyze – Compare Means – One-way ANOVA

    One Way ANOVA Test SPSS Menu

    Box with variables will open. Transfer the continuous variable wage into the dependent list box, and factor variable responsibility to factor box.

    One Way ANOVA Test SPSS

    Choose Options, and a new window will appear. Check Descriptive, Homogeneity of variance test, Brown-Forsythe, and Welch. Click Continue.

    One Way ANOVA Test: SPSS Options Menu

    Choose Post Hoc test for ANOVA test

    If we assume that we have equal variance across the group so we will use the first box of tests. The Tukey HSD test is the best option for this assumption. On the other hand, if our data does not have equal variance then we can pick up the Games-Howell or the LSD test.

    One Way ANOVA Test

    The results will appear in the output window.

    One Way ANOVA Test

    How to report a Chi-square test for independence results: Explanation Step by Step

    How to Report Descriptive Statistics Table in SPSS Output?

    The first table in the output window shows descriptive statistics.

    One Way ANOVA test SPSS Output

    How to Report Test of Homogeneity of Variances Table in SPSS Output?

    The second table from the output shows the results of the test of homogeneity of variances. It shows Levene statistic, degrees of freedom, and p-value (Sig.) In our example, p = .153 > .05, so we conclude that the assumption of homogeneity of variances is fulfilled and go to step 3.

    Test of Homogeneity of Variance in ANOVA Output

    How to Report P-Value in ANOVA Table SPSS Output?

    The third table in the output, ANOVA results, shows that whether the results between groups are significant or not.

    If the p value is greater than 0.05, then we do not have any statistically significant difference between groups. However, in our example the p value is less than 0.05. Therefore, we conclude that there is a difference in average annual wages between job responsibility groups, F(2, 93) = 24.193, p = .000 < .05.

    ANOVA Test SPSS Output

    How to Report Post-Hoc Test in SPSS output?

    The following table in the output window shows the results of the Post Hoc test.

    The results of the test of homogeneity of variance (step 2) showed that we have equal variances. Therefore, we should look at the results of the Tukey HSD test.

    The column mean difference shows the difference between the means of the two groups compared. For example, -14074.481 is the difference between mean annual wages for small job responsibility and medium job responsibility. Column Sig. (p-value) shows whether the mean difference is statistically significant.

    In conclusion,  there is a difference in annual wages between small and medium job responsibilities and small and high job responsibilities.

    Post-Hoc Test SPSS Output

    How to Interpret a One Way ANOVA Results in APA Style?

    A one-way ANOVA was conducted to determine the effect of job responsibility (small, medium, high) on annual wages. The results indicate a significant effect, [F(2, 93) = 24.193, p = .000]. Post Hoc tests were conducted using Tukey’s HSD test. The comparison revealed significant difference between small (M=22612.06; SD=10792.06) and medium job responsibility (M=36686.55; SD=9500.50); between small (M=22612.06; SD=10792.06) and high job responsibility (M=40831.28; SD=12221.95). We, therefore, reject the null hypothesis that different levels of job responsibility (small, medium, high) have the same effect on annual wages.

    Visit our Reporting One-Way ANOVA test Page for more details.

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