Multivariate Statistics Compare and Contrast Essay

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Multivariate Techniques



There is a number of mathematical and statistical tools that businesses use to survive and thrive in their respective markets. Some of the math involved is quite simple and basic. Examples of such basic operations would include percentages, standard deviations and so forth. However, there are some fields and realms where much more intricate mathematics are involved and statistics would be a common example of such a complex method. This brief report shall specifically cover the use of multivariate statistics. Three of the more common manifestations of multivariate statistics are factor analysis, cluster analysis and multidimensional scaling. While making things overly complex from a numbers standpoint is usually not wise, there are situations where more robust and complex analysis is necessary or advantageous.

Compare & Contrast



The first multivariate method that shall be discussed is factor analysis. Factor analysis is a technique that is used to reduce a large number of variables down to a smaller list of factors and items. The goal of the technique is to extract the maximum level of common variance from the variables in question so as to come to a common score. When the factors in question are all indexed and put together, they can be used for scoring and other further analysis. Factor analysis is part of the larger general linear model, or GLM. There are also some common assumptions and norms when it comes to factor analysis. This includes that there is no linear relationship when it comes to the variables involved and there is also no multi-collinearity. What is present is some sort of correlation between the variables and factors. With all of that being said, there are five common types of factor analysis. The most common and ubiquitous of the five is known as principal component analysis, or PCA. It starts with extracting the maximum variance and this becomes part of the first factor. After that, the variance is removed when it can be explained by the first factors and there is then the extraction of maximum variance for the second. This process is repeated until the last factor is reached.

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The second most common method is known as common factor analysis. There is the extraction of the common variance and that variance is placed among the factors within the analysis. There is no looking at the unique variance for all variables. This is the method used in SEM, which is short for standard error of the mean (Statistics Solutions, 2017). This is the spread that the mean of a sample of values would resemble if one were to keep taking in values and scores (Sports CI, 2017). The other more common methods of factor analysis are image factoring, maximum likelihood method, least squares and alfa factoring. Finally, there is weight square which is a regression-based method that is used for factoring (Statistics Solutions, 2017). Factor analysis is commonly used as a marketing tool to help analyze and assess the market landscape. The research firm to which this report is being presented can do the same thing when it comes to their marketing and the recommendations they give to their clients (B2B International).



A method of multivariate statistics that complements and often accompanies factor analysis is cluster analysis. Further, there is commonly a sequence that includes, in order, factor analysis, cluster analysis and discrimination analysis. Also like factor analysis, cluster analysis is typically about trying to group and assemble widespread data plots that are perhaps not obviously related and kept together. It is a method that is used to identify structures within the data. It is commonly also referred to as segmentation analysis or taxonomy analysis. The idea is to identify homogenous groups within wider arrays of data. The analysis is explorative in nature and does not distinguish between dependent and independent variables. This is a method of analysis that can commonly done with statistical program packages like IBM's SPSS and similar statistical suites. Just a few of the cluster analysis variants that are commonly used include binary, nominal, ordinal and scale. The scale type can….....

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References

B2B International. "Factor Analysis In Market Research | B2B International." B2B International. n.p., 2017. Web. 21 June 2017.

Sports CI. "New View of Statistics: Mean & SD Or SEM?". Sportsci.org. N.p., 2017. Web. 21 June 2017.

Stat Soft. "Multidimensional Scaling." Statsoft.com. N.p., 2017. Web. 21 June 2017.

Statistics Solutions. "Conduct And Interpret A Cluster Analysis - Statistics Solutions." Statistics Solutions. N.p., 2017. Web. 21 June 2017.

Statistics Solutions. "Factor Analysis - Statistics Solutions." Statistics Solutions. N.p., 2017. Web. 21 June 2017.

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