One-way ANOVA

• One-Way ANOVA


  A statistical test used to compare the means of three or more groups
• The problem with using multiple t-tests to compare more than two groups is that it increases the chance of committing a Type I error
• One-Way ANOVA can be used to compare more than two groups without increasing the Type I error rate
• Null hypothesis (ANOVA)


  The means of all groups are equal
• Alternative hypothesis (ANOVA)


  The means of at least two groups are not equal
• ANOVA does not tell us which specific groups have different means, it only tells us that at least two group means are different
• 1. statistic


  The ratio of the between-groups variance to the within-groups variance
• As the between-groups variance increases or the within-groups variance decreases

  The F-statistic increases
• A larger F-statistic indicates a higher probability of rejecting the null hypothesis
• Sum of Squares (SS)

  A measure of the total variance in the dependent variable

  
• SS_group


  The variance in the dependent variable that is explained by the independent variable
• SS_error


  The variance in the dependent variable that is not explained by the independent variable (random error)
• Degrees of Freedom (df)


  The number of values in the final calculation of a statistic that are free to vary
• df_group


  The degrees of freedom for the between-groups variance
• df_error


  The degrees of freedom for the within-groups variance
• Mean Square (MS)


  The variance estimate, calculated by dividing the Sum of Squares by the Degrees of Freedom
• MS_group


  The variance estimate for the between-groups variance
• MS_error


  The variance estimate for the within-groups variance
• 1. ratio


  Calculated as MS_group / MS_error
• The F-distribution is used to determine the p-value for the F-ratio

  
• The F-distribution is one-tailed, as the F-ratio cannot be negative
• A significant F-ratio indicates that there are differences between the group means, but does not tell us where the differences are
• Planned comparisons


  Follow-up tests that are specified before the ANOVA is conducted
• Post-hoc tests


  Follow-up tests that are conducted after a significant ANOVA to determine which specific groups differ
• Fisher's LSD


  A liberal post-hoc test that does not control the familywise error rate
• Tukey's Test


  A conservative post-hoc test that controls the familywise error rate
• Bonferroni correction


  A conservative method for controlling the familywise error rate when conducting multiple comparisons