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# San Jose State University Factorial Design Discussion

San Jose State University Factorial Design Discussion.

A:
Factorial design refers to a study that has more than one independent variable. According to Saleh, Tuzen, and Sar?, (2018), Scholars use A notation to represent the number of levels on one of the independent variables under consideration. In contrast, the second notation B represents the number of levels for the second variable.Factor in statistics refers to a variable that stands on its own and that which cannot be changed by other variables that the researchers want to measure .The main effect in statistics refers to the effect that one of the independent variables has on a variable that depends on others, but the effects of another independent variable must not be taken into consideration (Saleh, Tuzen, and Sar?, 2018).A cell refers to a single box in which an individual can record data pieces .An interaction in statistics refers to what happens after the effect of one independent variable on the dependent one changes depending on another independent variable’s level (Saleh, Tuzen, and Sar?, 2018).
The factorial design ANOVA assumes that the dependent variable used in the analysis should use metric measurement level, whereas the independent variable needs to be nominal or better.  Scholars recommend that independent variables be grouped first if they are not nominal or ordinal before carrying out the factorial ANOVA.  Scholars also assume that the variance analysis on factorial design considers the dependent variable as an approximate of multivariate normal distribution (Breitsohl, 2019). Additionally, statisticians have an assumption that the error variance throughout the sample is the same at all data points.  Statisticians believe that a high variation depicts that the results that have been arrived at are more collect.
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B:
n a factorial design, the main effect of an independent variable is its overall effect averaged across all other independent variables. There is one main effect for each independent variable. There is an interaction between two independent variables when the effect of one depends on the level of the other. A cell means the various model estimates, one parameter is given for every cell, and the intercept is set to 0. They are not useful in overall tests but are used in simple estimate statements. Factors are control experimenter variables during experiments to determine their impact on the variable that is responding. Factors may use a number of values that are limited based on what is chosen by the experimenters. A main effect is the effect of one independent variable on the dependent variable—averaging across the levels of the other independent variable. There is one main effect to consider for each independent variable in the study. Main effects are independent of each other in the sense that whether or not there is a main effect of one independent variable says nothing about whether or not there is a main effect of the other. There is an interaction effect when the effect of one independent variable depends on the level of another. Although this might seem complicated, you already have an intuitive understanding of interactions. As an everyday example, assume your friend asks you to go to a movie with another friend. Your response to her is, well it depends on which movie you are going to see and who else is coming.
The factorial ANOVA has several assumptions that need to be fulfilled by interval data of the dependent variable, normality, homoscedasticity, and no multicollinearities. Furthermore, similar to all tests that are based on variation the quality of results is stronger when the sample contains a lot of variation – i.e., the variation is unrestricted and not truncated. 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. The factorial analysis of variance assumes that the dependent variable approximates a multivariate normal distribution. The assumption needs can be verified by checking graphically or tested with a goodness of fit test against normal distribution. Some statisticians argue that the limit theorem implies that large random samples automatically approximate normal distribution. Small, non-normal samples can be increased in size by bootstrapping. However, if the observations are not completely random, e.g., when a specific subset of the general population has been chosen for the analysis, increasing the sample size might not fix the violation of multivariate normality. In these cases, it is best to apply a non-linear transformation, e.g., log transformation, to the data. The transformation would be correctly described as transforming the scores into an index. For example, we would transform our murder rate per 100,000 inhabitants into a murder index, because the log-transformation of the murder rate would not easily make sense numerically. 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. In simpler terms this means that the variability in the measurement error should be constant along the scale and not increase or decrease with larger values. The Levene’s Test addresses this assumption. As 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. And like most statistical analysis, the higher the variation within the sample the better the results of the factorial ANOVA. Restricted or truncated variance, e.g., because of biased sampling, results in lower F-values, which increases the p-values.
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Recommended Textbooks:
1.Discovering Statistics and Data, 3rd Edition, by Hawkes. Published by Hawkes Learning Systems.
2.Lind, Marchal, Wathen, Statistical Techniques in Business and Economics, 16th Edition.
San Jose State University Factorial Design Discussion

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