Factorial ANOVA Case Study
The following is a sample Factorial ANOVA Case Study. There are several key elements required in order to conduct a successful Factorial Analysis of Variance (ANOVA).
The first element is the assessment of the fulfilment of the required assumptions for Factorial ANOVA (normality and homogeneity of variances). Many software packages such SPSS provide appropriate tools for this task, but it is important to know what to do if the assumptions are not met.
The second element consists on the interpretation of the results, the role of the possible interaction terms of different orders and the interpretation of the practical significance of the results obtained (effect size)
Factorial ANOVA for Number of Colonies
The purpose of this analysis is to perform a Factorial ANOVA analysis in order to assess the effect of three independent variables (factors) which are Concentration, Cell Line and Drug on one dependent variable, which is Number of Colonies.
For the purpose of the analysis, a 4 x 2 x 3 Factorial ANOVA design will be used, with a sample size of N = 672. The following descriptive statistics are obtained:
The following box-plot represents the problem graphically:
Factorial ANOVA Results
The Factorial ANOVA analysis is performed with the aid of the SPSS software package. The relevant outputs are shown below.
The assumption of homogeneity of variances is violated, as shown by the Levene Test above, since F(23, 648) = 20.926, p < .001.
The ANOVA table above shows that all the interactions and all main factors are significant. In fact, the third order interaction Concentration*Cell Line*Drug is significant (F(6, 648) = 3.254, p = .004 < .05, ). Also, the second order interaction Concentration*Cell Line is significant (F(3, 648) = 9.640, p < .001, ), same as Concentration*Drug is significant (F(6, 648) = 7.016, p < .001, ) and Cell Line*Drug is significant (F(2, 648) = 12.714, p < .001, ). The main effects are also significant. In fact, Concentration is significant (F(3, 648) = 53.941, p < .001, ), and the same goes for Cell Line (F(1, 648) = 189.157, p < .001, ) and for Drug (F(2, 648) = 22.859, p < .001, ).
This indicates that all the factors affect significantly the DV, and the effect of each factor on the DV depends on the level of the other factors.
The following post-hoc results are obtained:
The best drug is Taxol, and the best concentration is 1 um.
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