Question

1) What are the assumptions underlying the two-factor analysis of variance.

2) Compare and contrast crossed factors and nested factors.

Answer 1

Ans.

1).

• Analysis of variance (ANOVA) is an important statistical test in any research field such as biology and economy, for the analysis of data sets.
• With the help of this method comparison between the data of more then one groups can be made.
• A two way ANOVA is a hypothesis-based test where every sample is defined in two ways and result can be kept in two categories.
• It analyses the effect of two factors on a dependent variable and also examine the influence of each of these two factors on one another to asses their effect on continuous variable.
• Assumptions of two way ANOVA (two-factor analysis of variance) ;

1. Dependent variable should be of continuous nature and must be measurable on a scale which can be subdivided through increments.
2. Categerisation of two independent variables in independent groups.
3. Sample independency of each sample from the one other.
4. Data variance in the different groups should be identical.
5. Withdrawn of each sample from a normally distributed population.

2). Differences between crossed factors and nested factors ;

• Any categorical independent variable is considered as a factor, which is often altered in experiments or randomized designs.
• Understanding of differences between crossed factors and nested factors is a complex but essential statistical concept.
• Differentiating the factors into cross or nested is important in situations where two factors are involve, as it affects the analysis.
• Co-occurance of every category of one factor in design with each category of the other factor, represent crossing of two factors.
• In crossed factors, in every combination of categories for two other factors, there is atleast one observation.
• Co-occurance of each category of first factor with only category of other, represent a nested factor.
• In nested factors, there is not the representation of all combinations of categories.
• An interaction can be calculated if two factors are crossed where as such calculation is not possible for nested factors as there is a lack of every combination of one factor along every combination of other factor.
• By running a cross tabulation,, it can be determined whether the two factors in design are nested or crossed.