L4: Analysis Of ANOVA

What is the primary purpose of ANOVA?

To compare means across multiple groups.

What assumption do both t-tests and ANOVA share regarding data?

The data must be normally distributed.

What are the two parameters that define a normal distribution?

Mean (μ) and standard deviation (σ).

What does the mean (μ) determine in a normal distribution?

The location of the peak of the distribution.

What does the standard deviation (σ) indicate in a normal distribution?

The spread or variability of the distribution.

What percentage of data falls within ±1σ,±2σ, ±3σ in a normal distribution?

68%

95%

99.7%

What is the null hypothesis (H0) in the context of ANOVA?

The two population distributions mostly overlap, indicating no effect.

What is the alternative hypothesis (H1) in ANOVA?

The two population distributions have minimal overlap, indicating an effect.

What is experimental error in the context of ANOVA?

Uncontrolled sources of variability in an experiment.

What are the two main types of experimental error?

Measurement error and individual differences error.

What is measurement error?

Inconsistencies in measuring exam scores.

What does individual differences error refer to?

Natural variations among subjects that affect sample distributions.

What are nuisance variables?

Factors that influence the relationship between independent and dependent variables but are not the focus of the study.

How does experimental error relate to within-group variability in ANOVA?

In ANOVA experimental error is directly represented by the within-group variability (also known as the error sum of squares, SS

What is the key relationship in partitioning deviations in ANOVA?

Total Deviation = Within-groups Deviation + Between-groups Deviation.

What does the F-ratio in ANOVA represent?

The ratio of between-group variance to within-group variance.

What does the within-group variance estimate in ANOVA?

Experimental error only.

What is variance derived from in the context of ANOVA?

Variance = (Sum of squared deviations) / (Degrees of freedom).

What are squared deviation values referred to as in ANOVA?

Sums of squares, abbreviated as SS.

What is the significance of partitioning variability in ANOVA?

It allows comparison of variability due to treatment effects against variability due to other factors.

What does the term 'robustness of tests' refer to in statistical analysis?

The ability of tests to remain valid under certain violations of assumptions.

Why is it important to check assumptions before performing ANOVA?

To ensure the validity of the test results.