Study Notes on Two-Way ANOVA

Definition of ANOVA: ANOVA (Analysis of Variance) is used when comparing three or more means.
Independent Variables (IVs): - Each sample mean is considered a level of the independent variable. - Example: - IV: Grade - Levels: - 1st grade - 2nd grade - 3rd grade

First Example - Car Brands Longevity: - Context: Comparing the longevity of different car brands by taking average maximum mileage for each brand. - Dependent Variable (DV): ??? (This was initially blank) - Independent Variable (IV): ??? (This was initially blank) - Levels: - ??? (This was also initially blank)
Revised Example - Car Brands Longevity: - Context: The same scenario is now complete. - DV: Max mileage. - IV: Car brand. - Levels: - Mercedes - Toyota - Ford
Second Example - Mental Health Benefits of Green Spaces: - Context: Comparing mental health benefits from different types of green space. - Dependent Variable (DV): ??? (Initially blank) - Independent Variable (IV): ??? (Initially blank) - How many levels?: ??? (Initially blank)
Revised Example - Mental Health Benefits of Green Spaces: - DV: Depression levels. - IV: Type of green space (4 levels). - Levels: - Local parks - Neighborhood sidewalks - Backyards - National parks

Definition: A Two-way ANOVA involves two independent variables. It is also known as Factorial ANOVA.
Characteristics: - The independent variables are referred to as factors. - Two-way ANOVA shares the same assumptions as one-way ANOVA. - Every IV has its own levels. - Note: ANOVA can also be applied with three or more IVs (e.g., 3-way ANOVA, 4-way ANOVA, etc.). - Example: Investigating the impact of income and urbanicity on reading levels.

Context: Examining reading proficiency scores across different urbanicities and income levels. - Dependent Variable (DV): Reading proficiency. - Independent Variables (IVs): - IV1: Urbanicity - Levels: - Metropolitan - Small city - Town - Rural - IV2: Income - Levels: - Low income - Middle income - High income
Data Table: - Metropolitan: 30, Small City: 30, Town: 30, Rural: 30 for each income level, with a total sample size of: - $n = 30$ for each group. - $N = 360$ for total observations.

Main Effects: - Definition: Comparison of means to determine if they differ. - Each independent variable (IV) will have its own main effect.
Interactions: - Definition: Examines whether the IVs interact with each other. - There is only one interaction effect in a two-way ANOVA.

For Urbanicity (IV1): - Null Hypothesis (H0): $ext{µ}_1 = ext{µ}_2 = ext{µ}_3 = ext{µ}_4$ (Means for all levels of urbanicity are equal) - Alternative Hypothesis (HA): At least one of the means is different.
For Income (IV2): - Null Hypothesis (H0): $ext{µ}_1 = ext{µ}_2 = ext{µ}_3$ (Means for all levels of income are equal) - Alternative Hypothesis (HA): At least one of the means is different.
Each main effect has its own p-value, and the outcomes could vary such that: - One main effect is statistically significant, - Both main effects are statistically significant, - Neither main effect is statistically significant.

Notation: Interactions are expressed as the product of the IVs, such as $ext{IV1} imes ext{IV2}$ .
Each interaction effect has its own p-value as well.
Interpretation: - The effect of one IV depends on the level of the other IV.

Statistically Significant Interaction: Represented visually when lines cross on a graph. - Interpretation Example: Whether students enjoy the food depends on the condiment used.
Non-Significant Interaction: Indicated by parallel lines, suggesting no interaction between the IVs. - Example Interpretation: The reading level of high-income students is consistent across urban areas regardless of living location.

Specific data point mentioned: 155,395.60. (Context unclear given the transcript; requires additional context).
Additional acronyms or symbols: M+, MRC, 010, S, 2, which need further clarification related to their meaning within the context of the subject matter.