ANOVA

Question 1

ANOVA (Analysis of Variance)

Answer 1

ANOVA is a statistical method used to compare means between three or more groups to see if they’re significantly different.
It helps determine if there are real differences in the means of the groups or if those differences could have occurred by chance.

between three or more groups.. e.g. treatments or conditions

Question 2

Key idea of ANOVA

Answer 2

ANOVA tells us if there’s something going on between the groups, but it doesn’t pinpoint exactly which groups are different. That’s where post-hoc tests come in.

Question 3

One-Way ANOVA

Answer 3

Compares means of three or more independent groups to determine if they are significantly different.
Formula: F = Between-group variability / Within-group variability.

A significant F-value indicates at least one group mean is significantly different from the others.

Question 4

Two way ANOVA

Answer 4

Looks at effects of two factors on a variable.
Checks if one factor’s effect changes with another factor.

Question 5

Main Effect

Answer 5

The overall effect of one independent variable on the dependent variable, averaging across the levels of other independent variables.
Indicates whether there is a significant difference in the dependent variable across the levels of one factor.

Question 6

Interaction effect

Answer 6

The effect of one independent variable depends on the level of another independent variable.
Indicates whether the effect of one factor varies depending on the levels of another factor.

Question 7

Assumptions of ANOVA

Answer 7

Independence**: Observations within each group are independent.
- Homogeneity of Variances: Variances of the dependent variable are equal across all groups.
- Normality: Residuals are normally distributed within each group.

Question 8

Post-Hoc Tests

Answer 8

Used after ANOVA to determine which specific groups differ from each other.
Tukey’s HSD, Bonferroni, Scheffé, and Dunnett’s tests are common post-hoc tests.

to find which specific groups are different

Question 9

Repeated Measures ANOVA

Answer 9

Analyzes data where the same subjects are measured at multiple time points or under different conditions.
Determines whether there are significant differences between the means of repeated measures.

Question 10

Orthogonal Contrasts in ANOVA

Answer 10

Comparisons of group means in a way that each comparison is independent of the others.
If the sum of products of corresponding coefficients equals zero, it shows orthogonality.

Question 11

Why are Orthogonal Contrasts important?

Answer 11

They help compare specific combinations of group means without influencing each other, making interpretation clearer and more reliable.

Question 12

Comparing Group A to the average of Groups B and C.

Answer 12

c1 = 1, c2 = -0.5, c3 = -0.5
c1 x mean(Group A) + c2 x Mean(Group B) + c3 x Mean(Group C)

Question 13

Why do we use Levene’s test

Answer 13

Before we run the ANOVA, we first perform Levene’s test. If the p-value from Levene’s test is greater than 0.05 (our chosen significance level), it suggests that the variability in test scores across the three teaching methods is roughly the same.

Question 14

Levene’s Test in ANOVA

Answer 14

A test that checks if the variances of the groups are equal.
Why use it?: Helps make sure that the groups are comparable.
Example: If we’re comparing test scores between classes, Levene’s test helps us see if the variability in scores is about the same for each class.

Question 15

Two-Way Design

Answer 15

Imagine a study comparing the effects of different teaching methods (Factor A) and student engagement levels (Factor B) on exam scores.
Design: This is a two-way design because it involves two independent variables (teaching methods and engagement levels) and their interactions.

Question 16

Mixed Design

Answer 16

A mixed design combines elements of both between-subjects and within-subjects designs. It involves at least one between-subjects factor and one within-subjects factor.

Question 17

Example of Mixed Design ANOVA

Answer 17

In the context of our previous example, a mixed design could involve studying the effects of different teaching methods (between-subjects factor) on students’ performance, measured by pre- and post-tests (within-subjects factor).
Analysis: Researchers conduct an ANOVA that accounts for both between-subjects and within-subjects effects. They analyze the main effects of each factor and their interaction effect, considering both the differences between groups and the changes within each individual over time.

Question 18

Factor A and B

Answer 18

Factor A: This is one thing we’re looking at, like different types of teaching methods or levels of a drug.
Factor B: This is another thing we’re looking at, maybe different times of day or different age groups, it could represent different environmental conditions, participant characteristics, or experimental conditions.

Question 19

Advantages of Within-Subjects Designs

Answer 19

Higher Statistical Power: Within-subjects designs can detect smaller effects because each participant serves as their own control, reducing variability.
Smaller Sample Sizes: Fewer participants are needed compared to between-subjects designs, saving time and resources.

Question 20

Disadvantages of Within-Subjects Designs

Answer 20

Potential for Sequencing Effects: Repeated exposure to conditions may influence participants’ responses, affecting the validity of the results.
Carryover Effects: Effects from one condition may carry over and affect responses in subsequent conditions, confounding the results.

Question 21

Visual Representation of 2x2 Factorial ANOVA:

Answer 21

Interaction plot showing means of the dependent variable for each combination of levels of the independent variables.
Non-parallel lines indicate a significant interaction.

Question 22

Importance of Follow-Up Tests in Factorial ANOVA

Answer 22

After finding significant interactions, follow-up tests help understand why. They show which groups differ from each other and why.

If two treatments affect people differently based on age, follow-up tests reveal which ages benefit most from each treatment.

follow-up tests: pairwise comparisons and simple effects tests

Question 23

Pairwise Comparisons

Answer 23

Pairwise Comparisons: Compare specific groups or levels of one factor against each other to identify where differences lie. For example, comparing the mean scores of two treatment groups to see if one is significantly higher than the other.

specific groups

Question 24

Simple Effects Tests

Answer 24

Investigate how one factor affects the dependent variable at specific levels of another factor. They examine the effect of one factor within each level of another factor. For example, testing if the effect of a teaching method differs between boys and girls by looking at their test scores separately.

specific conditions

Question 25

Cohen’s d Effect Sizes

Answer 25

Small: 0.2
Medium: 0.5
Large: 0.8

Question 26

Post Hoc Power Analysis

Answer 26

An analysis conducted after a study to assess the statistical power of the observed effect.
To determine if the study had sufficient power to detect the observed effect, retrospectively.

Question 27

Caution about Post Hoc Power

Answer 27

Post hoc power analysis can be misleading and should not be used to justify nonsignificant results or make retrospective interpretations.
Post hoc power analysis relies on observed data, which may be influenced by sample size, effect size, and variability. It cannot account for factors that were not measured or controlled during the study.

Question 28

A Priori Power Analysis

Answer 28

Conducted before the study to determine the required sample size for achieving adequate statistical power to detect hypothesized effects.

Question 29

Advantages of A Priori Analysis

Answer 29

Guides study design by ensuring sufficient sample size, minimizing the risk of Type II errors (false negatives), and maximizing the likelihood of detecting true effects.
Provides a proactive approach to study planning, helping researchers make informed decisions before data collection begins.

Question 30

Allocation Ratio

Answer 30

he ratio of participants assigned to different experimental conditions or groups in a study.
Allocation ratios can influence statistical power, the precision of effect estimates, and the generalizability of study findings.

Question 31

Imbalanced allocation rations

Answer 31

may affect the study’s ability to detect treatment effects and lead to unequal group sizes, potentially affecting the reliability and validity of the results.
The allocation ratio should be carefully chosen based on study objectives, ethical considerations, and practical constraints to ensure a balanced and efficient distribution of participants across conditions.

Question 32

How One - Way and Two - Way ANOVA differ

Answer 32

Number of Factors: One-Way ANOVA involves analyzing the effect of a single factor on the dependent variable, while Two-Way ANOVA involves analyzing the effects of two factors simultaneously.
Main Effects and Interaction Effect: One-Way ANOVA examines only the main effect of the single factor on the dependent variable. In contrast, Two-Way ANOVA examines both the main effects of each factor and the interaction effect between the factors.
Interpretation: In One-Way ANOVA, significant differences indicate that at least one group mean is significantly different from the others. In Two-Way ANOVA, significant main effects indicate that there are differences in the dependent variable based on the levels of each factor, while a significant interaction effect indicates that the effect of one factor depends on the levels of the other factor.