My research study is a survey study. My focus is to identify the main effect and interaction effect between 3 IVs and 1 DV. The same participants answered the survey questions to measure the independent variables. In this case, can I use Factorial ANOVA to identify the main and interaction effect? What I understand from my reading is Factorial ANOVA is only used when different participants are involved to measure the IVs.
Please check the assumptions of a ANOVA and those of Factorial ANOVA.
A major ANOVA assumption is that each case (row of data values) must represent a separate person (or other “object”, if you like). It is not allowed for a single person to appear as more than one case.
To the factorial ANOVA:
Firstly, the factorial ANOVA requires the dependent variable in the analysis to be of metric measurement level (that is ratio or interval data) the independent variables can be nominal or better. If the independent variables are not nominal or ordinal they need to be grouped first before the factorial ANOVA can be done.
Secondly, the factorial analysis of variance assumes that the dependent variable approximates a multivariate normal distribution. The assumption needs can be verified by checking graphically (either a histogram with normal distribution curve, or with a Q-Q-Plot) or tested with a goodness of fit test against normal distribution (Chi-Square or Kolmogorov-Smirnov test, the later being preferable for interval or ratio scaled data).
Thirdly, the factorial ANOVA assumes homoscedasticity of error variances, which means that the error variances of all data points of the dependent variable are equal or homogenous throughout the sample.
The factorial ANOVA requires the observations to be mutually independent from each other (e.g., no repeated measurements) and that the independent variables are independent from each other. Since the factorial ANOVA includes two or more independent variables it is important that the factorial ANOVA model contains little or no Multicollinearity. Multicollinearity occurs when the independent variables are intercorrelated and not independent from each other.
Please check the assumptions of a ANOVA and those of Factorial ANOVA.
A major ANOVA assumption is that each case (row of data values) must represent a separate person (or other “object”, if you like). It is not allowed for a single person to appear as more than one case.
To the factorial ANOVA:
Firstly, the factorial ANOVA requires the dependent variable in the analysis to be of metric measurement level (that is ratio or interval data) the independent variables can be nominal or better. If the independent variables are not nominal or ordinal they need to be grouped first before the factorial ANOVA can be done.
Secondly, the factorial analysis of variance assumes that the dependent variable approximates a multivariate normal distribution. The assumption needs can be verified by checking graphically (either a histogram with normal distribution curve, or with a Q-Q-Plot) or tested with a goodness of fit test against normal distribution (Chi-Square or Kolmogorov-Smirnov test, the later being preferable for interval or ratio scaled data).
Thirdly, the factorial ANOVA assumes homoscedasticity of error variances, which means that the error variances of all data points of the dependent variable are equal or homogenous throughout the sample.
The factorial ANOVA requires the observations to be mutually independent from each other (e.g., no repeated measurements) and that the independent variables are independent from each other. Since the factorial ANOVA includes two or more independent variables it is important that the factorial ANOVA model contains little or no Multicollinearity. Multicollinearity occurs when the independent variables are intercorrelated and not independent from each other.
As an alternative, you might try a regression model with main effects, x1 and x2, and their interaction, x1*x2. The type of regression depends on the DV type. See the attached notes. Best wishes, David Booth
The data in this survey, as I have understood, are not adequate for factorial ANOVA.
The line
"The same participants answered the survey questions to measure the independent variables."
is confusing.
Identification of which are independent variables and which are dependent variables are to be clearly mentioned.
If I understand your question correctly, Yes, the same participants are used to determine the main effects and interaction effects.
Each individual needs to have a level on each independent variable. That is, if you have a two way anova with sex and color as your independent variables, then each participant is either male or female, say. But also each individual is either green or blue, say. But also each individual is either female/blue, female/green, male/blue, male/green. So the analysis can tease out the main effects and the interaction effects from this set of individuals.
I'll apologize now if I misunderstood the force of the question.
The answer given by Salvatore Mangiafic is not clear to me on how main effect and interaction effect can be estimated from this set of data. More explanation is required.
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