# Statistics Resources

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.

## One-Way ANOVA

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

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

Running a One-Way ANOVA in SPSS

1. Analyze > Compare Means > One-Way ANOVA
2. Move the continuous variable into the "Dependent List" box and the categorical variable into the "Factor" box
3. Click on the Post Hoc button
• choose the appropriate post hoc analysis for your study
• Select Continue
4. You may select additional output, such as descriptive statistics, using the Options button
• Select Continue
5. 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
• 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).