##### Robust executed on R studio using the WRS2

Robust ANOVA method of analysis is presented and comprehensive comparisons between the results obtained from
the robust analysis and the previous result obtained from the non-robust method of analysis are obtained. The robust
statistical method commonly used in the experimental design fields is the robust ANOVA. This exercise introduces
the R package called WRS2 package which function is to implement method from WRS package (the original
package) to create a more user-friendly manner. The analysis which involves using the statistical method (Robust
method) will be executed on R studio using the WRS2 package available on CRAN (Mair & Wilcox, 2015).

In this segment, analysis on ANOVA is being carried out. The previous analysis was about analysis of interaction
between the processing style and sematic priming to check its effect on the aggressiveness score. The statistical
robust method is introduced and series of analysis is carried out with the method in order to make some necessary
comparison between the previous (non-robust) results and the current (Robust) method of analysis.

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Bringing into consideration, the first analysis conducted which has to do with the analysis of interaction between a
response variable (Aggressiveness score) and two factors namely: map condition and puzzle condition. The result
obtained from the robust method the p-value for the interaction between the map condition and the puzzle condition.
The results obtained from the statistical robust method shows that the p-value for the interaction between the map
condition and the puzzle condition is 0.4257 while the result obtained from the non-robust method shows that the
interaction between the map condition and puzzle condition has an assigned p-value of 0.51073. The p-value of the
robust analysis is slightly less than that of the non-robust analysis. However slight, following the hypothesis
significant rule, the smaller the p-value, the closer it gets to the region of rejecting the null hypothesis “the interaction
between the factors has no significant effect on the response variable”. Here, two cases are considered in making
the decision to accept or reject the null hypothesis because both statistical methods (robust and non-robust methods)
are not following same inequality direction. That is p-value of robust method < 0.05 < p-value of the non-robust statistical method. To make conclusion on them we say: In the case of the robust method of analysis, we reject the null hypothesis and conclude that the interaction between the map condition and the puzzle condition has a significant effect on the aggressiveness score. And also in the case of the non-robust method, we conclude that the interaction between the map condition and the puzzle condition does not have significant effect on the aggressiveness score. The second interaction test to be considered here is also a two-way ANOVA interaction between the map condition and the puzzle condition. Here, Q5 is acting as the response variable against the two factors. The results obtained from the statistical robust method after which series of operation commands are written in the Rstudio reveals that the p-value of the ANOVA table is 0.336 while the result obtained from the non-robust method of analysis is 0.393. Comparing the robust method p-value is lesser compared to the non-robust statistical method. But still, the two results are less than 0.05 level of significance which applies that: we fail to reject the null hypothesis and conclude that the interaction between the map condition and the puzzle condition have significant effect on the response variable (Q5). In the third segment of the analysis, is the interaction between the regular map condition and the puzzle condition to check their effect on question 8. The statistical robust method is the carried out for comparison to come into place. The p-value of the statistical robust method and the non-robust method are approximately of the same values which shows that the p-value of the non-robust method is holding its best supposed value. The p-value of the robust method is 0.829 while the non-robust method is 0.8293. From the results, we can deduce that the p-values are greater than the level of significance 0.05 and then we proceed to making conclusion by failing to reject the null hypothesis and conclude that the interaction between the two factors namely: map condition and puzzle condition has no significant effect on the response variable (Q8). The second robust method used in this analysis is the regression analysis. With the help of this analysis, one should be able to capture the strange numeric values that do not follow the normal trend of the distribution of the data. This is in short called the outliers. Also, with the regression analysis, the standard errors and the estimates are determined. When data are not in their homogeneity form, it is advised by statisticians to perform a transformation operation on the data set which is most likely to bring about increase in precision of results from analysis and promote the homogeneity to its possible nearest level. From the graph obtained from the regression analysis, it can be seen clearly seen that the data contain two outliers isolated at the top in the graph.

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