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# Number and Inform of Algebraic Expression Discussion & Response

• Will require 2 peer replies after you answer this below question
• Explain the terms factorial design, factor, cell, main effect and interaction. .
• Explain the assumptions required for a factorial design ANOVA.
• Ask an interesting, thoughtful question pertaining to the topic
• Answer a question (in detail) posted by another student or the instructor
• Provide extensive additional information on the topic
• Explain, define, or analyze the topic in detail
• Share an applicable personal experience

1)Although this statistical method (percentile) has many applications, one of the best known is in education. Especially when testing is standardized, it is meant to serve a diverse group of people and accurately gauge not only individual performance, but also comparative performance. When looking at a data set, percentiles can help better gauge the middle or median performance of students. Many students will cluster into the median area, earning percentiles anywhere from 25 to 75, while a few will far surpass this, reaching into the 90s range. Average and median scores are computed into expected results and can show how most people are performing, as well as how each individual student is performing.

Percentiles can further show if performance in certain areas is poor. If every student taking a test answers the same question incorrectly, or if most of the average students do so, this may indicate a problem. It may be that the question is badly worded or it may be that this area of the subject has not been adequately covered during the course. With increasingly standardized tests in the academic setting, this method can weed out bad questions and identify areas for improvement in courses or teaching methods.

2) Factorial design involves a study that has two or more independent variables, or factors. The main effects of each factor is how it influences the dependent variable on its own, while interactions are how the factors work together to influence the dependent variable. In a factorial design, the main effect of an independent variable is its overall effect averaged across all other independent variables. There is an interaction between two independent variables when the effect of one depends on the level of the other.

The factoral ANOVA has a several assumptions that need to be fulfilled – (1) interval data of the dependent variable, (2) normality, (3) homoscedasticity, and (4) no multicollinearity. Furthermore similar to all tests that are based on variation (e.g. t-test, regression analysis, and correlation analyses) the quality of results is stronger when the sample contains a lot of variation – i.e., the variation is unrestricted and not truncated.

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).

Spatz, C. (2019). Exploring statistics: Tales of distributions. Outcrop Publishers.