ANOVA Dr Dyal Bhatnagar Dependent Variable Independent Variables

ANOVA Dr. Dyal Bhatnagar

Dependent Variable Independent Variable(s) Metric Non-Metric Regression • Discriminant Analysis • Binary/Logistic regression Non-Metric Hypothesis testing Chi-square Test

• If the independent variable (which is nonmetric) has two categories, we will use t-test • And if the independent variable has more than two categories we will use F-test (ANOVA)

ANOVA • ANOVA uses F statistics which is the ratio of variances between groups and variances with-in groups (error variance) • If group means do not differ significantly, one can believe that all group means come from same population and do not differ • Larger the F statistics Larger is the difference between groups as compared to with-in group differences • F Statistics < 1 Indicates no significant difference in the group means and thus Ho is correct.

Assumptions Normality: • Ho Data are normally distributed • Steps to check overall normality – Analyze Non parametric tests Legacy dialogs One sample K S test – p-value of K S Test > 0. 05 Data are normally distributed – p-value of K S Test < 0. 05 Use Non-parametric test • Steps to check category-wise normality – Analyze Descriptive Explore Plots Tick Normality plots with stats • If your sample size for different categories is comparable, and any one or two categories are not normally distributed, even then, F & t are very robust tests - Andy Field

Assumptions Homogeneity of Variance: • We assume that each sample comes from a population with same variance. And thus, variance across samples is homogeneous. • Ho Variances across groups is equal or Homogeneous • Steps to check overall Variance – Analyze Descriptive statistics Descriptives Options Tick Variance • Steps to check category-wise Variance – Analyze Compare Means Options Tick Variance

Leven’s Test p-value > 0. 05 p-value < 0. 05 • Accept Ho Equal Variances assumed • Use ANOVA • Reject Ho Equal Variances not assumed • Use Welch test

Comparing Means Planned comparisons Unplanned comparisons • Exploring the differences in means among all possible pairs of groups, decided a priori by the researcher. • Contrasts • Post Hoc Tests

Post Hoc Tests Leven’s p-value > 0. 05 Leven’s p-value < 0. 05 • Accept Ho Equal Variances assumed • Use ANOVA • Post Hoc companion test: Tukey • Reject Ho Equal Variances not assumed • Use Welch test • Post Hoc Companion test: Games Howell

ANOVA: More than one Independent Variable One way ANOVA Two way ANOVA • Analyze Compare Means One Way ANOVA • Analyse General Linear Model Univariate

Thanks