ANOVA (Analysis of Variance)

Question 1

Statistical Test for One Mean

Answer 1

Z-Test and T-Test

Question 2

Statistical Test for Two Means

Answer 2

Z-Tests and T-Test (Independent and Paired)

Question 3

Statistical Test for More Means

Answer 3

ANOVA (One-Way, Two-Way, Repeated measures)

Question 4

What happens when you conduct multiple T-Test to samples with more than 2 means?

Answer 4

Increases the probability that some comparison will result in type I error

Question 5

a. Fail to reject (Accepted) the false H0

b. Rejected the True Hɑ

Answer 5

TYPE II error or β

Question 6

a. Rejected the true H0

b. Accepted the false Ha

Answer 6

TYPE I error or α

Question 7

• 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

Answer 7

ANOVA (Analysis of Variance)

Question 8

A test that allows one to make
comparisons between the means of
three or more groups of data

Answer 8

One-Way ANOVA

Question 9

Characteristics of ONE-WAY ANOVA

Answer 9

• 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

Question 10

A test that allows the comparing between the means of three or more groups of data, where two independent variables are considered.

Answer 10

Two-way ANOVA

Question 11

Characteristics of TWO-WAY ANOVA

Answer 11

• 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.

Question 12

Assumptions for ONE-WAY ANOVA

Answer 12

1. Independent variable should consist of ≥2 categorical (nominal ordinal) groups (ethnicity, profession, physical activity)
2. Dependent variable should be measured at the scale (interval or ratio) level (IQ score, weight)
3. Dependent variable should be normally distributed (randomly assigned) for each category of the independent variable
4. Independence of observations, no significant outliers & homogeneity of variances (Non-Parametric Counterpart: Kruskal-Wallis)

Question 13

Examines the influence of two (categorical), independent variables on one (continuous quantitative) dependent variable, as well as the interaction between the two independent variables

Answer 13

Two-way ANOVA

Question 14

Assumptions for TWO-WAY ANOVA

Answer 14

1. No significant outliers
2. Dependent variable should be normally distributed for each group of the 2 independent variables
3. Homogeneity of variances for each combination of the groups of the two independent variables

Question 15

• 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

Answer 15

Repeated Measures ANOVA (with Single Factor)

Question 16

Assumptions for Repeated Measures ANOVA (with Single Factor)

Answer 16

1. The subjects are assigned by simple random sampling (randomness)
2. Each observation is independent (size 1 from each of kn)
3. The populations (kn) must have the same variance (normality)
4. The treatments (k) are fixed (the only interest in the study)
5. There is no interaction between treatments and subjects. Treatment effects are additive.
6. Dependent variable is measured in scale
7. Homogeneity of covariance (sphericity)
   • Covariance (correlations) exist among the repeated measures since it was taken on the same individual

Question 17

• 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

Answer 17

Multiple Comparison Procedures

Question 18

• 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

Answer 18

Bonferroni

Question 19

• 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

Answer 19

Tukey HSD (honestly significant difference)