Question

For items T1 – T6, indicate the conditions under which you would use the specific type of ANOVA that we covered in class by checking the box associated with that condition in Table 1. Table 2 provides the list of possible conditions. Keep in mind that not all ANOVAs will have the same number of conditions. Each will have at least 3, but no more than 5.

Table 1.

Item	Type of ANOVA	A	B	C	D	E	F
T1	One way
T2	Repeated Measures
T3	Between-subject Factorial
T4	Repeated Measures Factorial
T5	Mixed Design Factorial
T6	ANCOVA (between-subject)

Table 2.

	Conditions for using ANOVA
A	When testing more than one independent variable
B	When comparing two or more group means (i.e., independent variable is categorical)
C	The dependent variable is continuous
D	The sampled groups are independent of each other (i.e., different people in each group)
E	When you need to account for a variable that may be related to the dependent variable, but is not the variable of interest to get a clear effect for the independent variable.
F	The sampled groups are related to each other (i.e., the same people are in each group)

Answer 1

The required answer is in below table:

Item	Type of ANOVA	A	B	C	D	E	F
T1	One Way		Yes	Yes	Yes
T2	Repeated Measures	Yes	Yes	Yes			Yes
T3	Between Subjects Factorial	Yes	Yes	Yes	Yes
T4	Repeated Measures Factorial	Yes	Yes	Yes			Yes
T5	Mixed Design Factorial	Yes	Yes	Yes	Yes		Yes
T6	ANCOVA (Between Subject)		Yes	Yes	Yes	Yes

Note: Conditions / Assumptions for above types of ANOVA are mentioned below for reference:

Assumptions of One-Way ANOVA?

• Normality – That each sample is taken from a normally distributed population.
• Sample independence – that each sample has been drawn independently of the other samples.
• Variance Equality – That the variance of data in the different groups should be the same.
• Your dependent variable should be continuous – that is, measured on a scale which can be subdivided using increments.

REPEATED MEASURES ANOVA – Analysis of Variance in which subjects are measured more than once to determine whether statistically significant change has occurred, for example, from the pretest to the posttest.

Factorial ANOVA - It is generally assumed that the factorial ANOVA is an ‘analysis of dependencies. ‘It is referred to as such because it tests to prove an assumed cause-effect relationship between the two or more independent variables and the dependent variables. In more statistical terms it tests the effect of one or more independent variables on one dependent variable.

The factorial ANOVA is closely related to both the one-way ANOVA (which we already discussed) and the MANOVA (Multivariate Analysis of Variance). Whereas the factorial ANOVAs can have one or more independent variables, the one-way ANOVA always has only one dependent variable. On the other hand, the MANOVA can have two or more dependent variables.

A MIXED ANOVA compares the mean differences between groups that have been split on two "factors" (also known as independent variables), where one factor is a "within-subjects" factor and the other factor is a "between-subjects" factor.

Assumptions for ANCOVA

The same assumptions as for ANOVA (normality, homogeneity of variance and random independent samples) are required for ANCOVA. In addition, ANCOVA requires the following additional assumptions:

• For each independent variable, the relationship between the dependent variable (y) and the covariate (x) is linear
• The lines expressing these linear relationships are all parallel (homogeneity of regression slopes)
• The covariate is independent of the treatment effects (i.e. the covariant and independent variables are independent.
• An extra assumption of ANCOVA is that there is no significant interaction between the covariate and factor.