ANOVA (Analysis of Variance) Flashcards
Statistical Test for One Mean
Z-Test and T-Test
Statistical Test for Two Means
Z-Tests and T-Test (Independent and Paired)
Statistical Test for More Means
ANOVA (One-Way, Two-Way, Repeated measures)
What happens when you conduct multiple T-Test to samples with more than 2 means?
Increases the probability that some comparison will result in type I error
a. Fail to reject (Accepted) the false H0
b. Rejected the True Hɑ
TYPE II error or β
a. Rejected the true H0
b. Accepted the false Ha
TYPE I error or α
- Two-sample t-test (with pooled variance)
- Used when the question involves the comparisons of means from ≥2 independent groups.
- The total variation between groups and within groups is determined
ANOVA (Analysis of Variance)
A test that allows one to make
comparisons between the means of
three or more groups of data
One-Way ANOVA
Characteristics of ONE-WAY ANOVA
- One Independent Variable
- The means of three or more groups of an independent variable on a dependent variable are compared
- Three or more number of group samples
A test that allows the comparing between the means of three or more groups of data, where two independent variables are considered.
Two-way ANOVA
Characteristics of TWO-WAY ANOVA
- Two Independent Variables
- The effect of multiple groups of two independent variables on a dependent variable and on each other are compared
- Each variable should have multiple samples.
Assumptions for ONE-WAY ANOVA
- Independent variable should consist of ≥2 categorical (nominal ordinal) groups (ethnicity, profession, physical activity)
- Dependent variable should be measured at the scale (interval or ratio) level (IQ score, weight)
- Dependent variable should be normally distributed (randomly assigned) for each category of the independent variable
- Independence of observations, no significant outliers & homogeneity of variances (Non-Parametric Counterpart: Kruskal-Wallis)
Examines the influence of two (categorical), independent variables on one (continuous quantitative) dependent variable, as well as the interaction between the two independent variables
Two-way ANOVA
Assumptions for TWO-WAY ANOVA
- No significant outliers
- Dependent variable should be normally distributed for each group of the 2 independent variables
- Homogeneity of variances for each combination of the groups of the two independent variables
• Frequently used experimental designs in health sciences
• Repeated measurements of the same variable are made on ≥3 occasions.
1. change over time (e.g. longitudinal study)
2. change under different conditions
• Subject serves as its own control for extraneous variation among subjects
Repeated Measures ANOVA (with Single Factor)
Assumptions for Repeated Measures ANOVA (with Single Factor)
- The subjects are assigned by simple random sampling (randomness)
- Each observation is independent (size 1 from each of kn)
- The populations (kn) must have the same variance (normality)
- The treatments (k) are fixed (the only interest in the study)
- There is no interaction between treatments and subjects. Treatment effects are additive.
- Dependent variable is measured in scale
- Homogeneity of covariance (sphericity)
• Covariance (correlations) exist among the repeated measures since it was taken on the same individual
• If the means has a significant difference, we proceed with the Post-Hoc Analysis to find out which pair of means are significantly different. E.g. Tukey’s, Bonferroni, Dunnet, Games-Howell
Multiple Comparison Procedures
- Sig. level divided by the no. of individual pairs (/k)
- More power when the number of comparisons is small
- Assumptions are not required to be met
Bonferroni
• More power when testing large numbers of means
• Used when homogeneity of variances is met.
If not, use Games-Howell
- All possible differences between pairs of means are computed
Tukey HSD (honestly significant difference)
