Experimental Designs Definition - Assignment Example

Experimental design Number of independent variables and conditions in a 4x6 factorial design The number of independent variable in a factorial design can be determined from its symbolic product representation. Taking the form a*b*c*d……., the number of terms defines the number of independent variables in the design. The number of conditions or cells in a factorial design is however evaluated from the product of terms of representation of the design. This defines the product of the number of factor levels in the involved independent variables. The factorial design represented as 4*6 therefore has two independent variables. one of the independent variables has 4 factor levels while the other has 6 factor levels. the number of cells is therefore 24. The differences between a cell mean and the means used to interpret a main effect The difference between a cell mean and a mean for interpreting a main effect is that a cell mean defines the average of observed values in a given cell with disregard to the involved independent variable while a mean for calculating a main effect defines the mean of all observed values of the dependent variable, but along a given factor. The mean for interpreting the mains effect is therefore also defined as the average of the cell means within an independent variable and has a wider scope that the cell mean. Another difference between the two means is that cell mean is descriptive while the mean for interpreting the main effect is inferential and communicates the significant of an independent variable in a design (Ross and Creyer, 2013). Differences between a complete factorial design and an incomplete factorial design A complete factorial design is an experiment whose factors contain discrete levels and all its experimental units are fully crossed. All factor levels in each independent variable interact with factor levels in other independent variables. This ensures all possible combinations design implementation. An incomplete factorial design however have different number of factor levels in its independent variable. this means that some factor levels may not be crossed with factor levels from other independent variable and the design cannot explore all possible combinations in the design (Jaynes, Ding, Xu, Wong and Ho, n.d.). Difference between a two way ANOVA and a three way ANOVA A two-way ANOVA is a statistical test used to determine the effect of two factors or independent variables on the dependent variable. A three-way ANOVA is a statistical test used to determine the effect of three independent variables on a dependent variable. The two way ANOVA explores main effect of each of the factor levels together with a single interaction effect between the involved two factors. A three way ANOVA however has an extended scope and explore three mains effects of the each factor level and interaction effects for each pair of all the three independent variables. Completing the ANOVA table The following concepts are used in completing the table, df defines the degrees of freedom and it is obtained from the number of cells in a factor level SS refers to the sum of squares MS is the mean sum of squares which obtained by dividing the sum of squares with the degrees of freedom Error sum of squares is obtained by subtracting the other sum of squares from the total sum of squares. F is the It is obtained by dividing the MS by the by the error sum of squares. Source df SS MS F A 1 60 60 9 B 2 40 20 3 A x B 2 90 45 Error 30 200 6.6667 Total 35 390 Factorial notation for the design is 2x3 Number of conditions in the study is 2*3 = 6 Number of subjects in the study is 391. Significant main effect: There is significant mains effect for both factors because the F values are very high and this leads to adoption of the alternative hypothesis that there is significant main effect for factors A and B. Source df SS MS F A 2 40 20 9.6 B 3 60 20 9.6 A x B 6 150 25 12 Error 72 150 2.083 Total 83 400 Factorial notation for the design is 3x4 Number of conditions in the study is 12 Number of subjects in the study is 401 Significant main effect: Both factor have significant main effect because of thehigh F values that lead to rejection of their respective null hypotheses. Source df SS MS F A 1 10 10 6 B 1 60 60 36 A x B 1 20 20 12 Error 36 60 1.6666667 Total 39 150 Factorial notation for the design is 2x2 Number of conditions in the study is 4 Number of subjects in the study is 151 Significant main effect: The two factors have significant mains effects because of their large computed F values. These lead to rejection of the null hypothesis to the conclusion that there are significant effects. ANOVA Table: practice and gender Bellow is the completed ANOVA table for the Source df SS MS F Gender 1 0.027 0.027 0.0162 Practice 2 140.60 70.3 42.18 Gender x Practice 2 0.073 0.0365 0.0219 Error 24 28.00 1.666 Total 29 168.70 Significance of the values of Fobt significant at α=0.5, At α=0.1 At α=0.5, the Fobt is significant for practice. The same case applies to test Conclusions that can be drawn from the F-rations Failing to reject the null hypothesis for gender and interaction means that gender do not have a significant effect on timed task. Rejecting the null hypothesis for the practice time however means that the time spent to practice influences an individual’s performance in a timed task. The hull hypothesis is also not rejected for the interaction effect and this shows that even though practice affect performance of timed tasks, its interaction with gender does not. Practice time is therefore the only significant factor in the study. What is the effect size, and what does this mean? Using Eta squared as the effect size measure, Effect size = Some of squares of the effect/ Total sum of squares =140.6/168.7 =0.833. The high value of effect size, tending to one, means that there exist a strong association between the effect, practice time, and performance of the timed task. Graph the means Difference between multiple independent variables and multiple levels of independent veriables and the better approach Multiple independent variables refers to more than one factor in an experiment. the factors are further independent of each other. Multiple levels of independent variables however implies application of independent variables, each with more than one factor level. Multiple levels independent variables is better because it incorporates multiple independent variables in Blocking, how it reduces noise and its disadvantages Blocking defines stratification of research participants into homogeneous groups. It reduces noise by reducing the level of variations in observations since participants are grouped by similarity in behavior. Disadvantages of blocking include the need to develop preliminary information before sampling and grouping of samples. Definition of a factor and how it can be used to benefit a design A factor is an independent variable in an experiment and plays the role of determining different values of a dependent variable. Main effect and interaction effect Main effect defines impacts of an indepependent variable on a dependent variable without regard to effects of other independent variables. Interaction effect however defines the collective influence of two or more independent variables on a dependent variable. How a covariate reduces noise Covariance reduces noise by eliminating effects of single factors in a design. This converges observations to consistent values. Tradeoffs present in experiments Tradeoffs define compromises that researchers make in their experiments. trade off between validity and reliability, tradeoff between objectivity and ethics and trade off between speed and accuracy are some of the examples and a focus on one of the factors leads to a compromise of another. Focusing on validity for example limits an experiment’s level of reliability while focus on ethical requirements compromises a reseracher’s objectivity (Wiley, 2009). Reference Wiley, R. (2009). Trade-offs in the design experiments. Journal of Comparative Psychology (123.4): 447-449. Ross, W. and Creyer, E. (2013). Interpreting interactions: Raw means or residual means? Journal of Consumer Research (20.2): 330-338 Jaynes, J., Ding, X., Xu, H., Wong, W. and Ho, C. (n.d.). Read More