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This guide contains all of the ASC's statistics resources. If you do not see a topic, suggest it through the suggestion box on the Statistics home page.

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The One-Way ANOVA is an extension of the independent-samples t-test and is used when comparing more than 2 independent groups. The ANOVA will tell you if there are *any* significant differences between the groups, but you will need to conduct a *post hoc* analysis to determine which groups are significantly different.

**Assumptions**

- One continuous (interval or ratio) dependent variable and one categorical (nominal or ordinal) independent variable with more than two levels.
- Independence of observations - usually evaluated based on the research design
- No significant outliers - can be assessed using boxplots, scatterplots, and other methods
- The dependent variable is approximately normally distributed
*for each level*of the independent variable. - Homogeneity of variances - can be tested using Levene's Test

**Running a One-Way ANOVA in SPSS**

- Analyze > Compare Means > One-Way ANOVA
- Move the continuous variable into the "Dependent List" box and the categorical variable into the "Factor" box
- Click on the Post Hoc button
- choose the appropriate post hoc analysis for your study
- Select Continue

- You may select additional output, such as descriptive statistics, using the Options button
- Select Continue

- Select OK to run the analysis

**Interpreting the Output**

- Descriptives (if you opted to include them)
- provides measures of central tendency and dispersion based on levels of the IV

- ANOVA
- provides the results of the statistical test
- test statistic = F-ratio
- associated probability = Sig.

- used to make a decision about the null hypothesis

- provides the results of the statistical test
- Multiple Comparisons
- provides the results of the post hoc analysis
- allows you to determine exactly which groups are significantly different than each other
- compare the Sig. to your level of significance (i.e. .05)

**Reporting Results in APA Style**

There was a statistically significant difference between groups as determined by the one-way ANOVA (*F*(2,62) = 5.467, *p* = .012). A Tukey post hoc test revealed that the time to respond was significantly lower for those that received the reaction time training (M = 1.3, SD = .5) and those that were experts in the field (M = 1.7, SD = .8) compared to those that had no training (M = 2.8, SD = .7). There was no statistically significant difference between the training group and the expert group (*p* = .214).

- Last Updated: Nov 30, 2022 3:21 PM
- URL: https://library.ncu.edu/statsresources
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