STT157 Exploratory Data Analysis: Median Polish

Median polish is a method for analyzing two-way tables that helps identify the effect of row and column factors on a response variable.

The iterative process of median polish involves repeatedly subtracting row and column medians and recalculating medians until they converge to a stable value.

The row effect represents the influence of a particular row on the response variable. For example, a positive row effect might indicate a higher response value for that row.

The column effect represents the influence of a particular column on the response variable.

The residual value represents the difference between the observed data and the fitted value based on row and column effects.

The common value (μ) in median polish represents the overall baseline level of the response variable, based on the grand median calculated during the iterative process.

Median polish is particularly useful when the data contains outliers, as it uses medians rather than means, which are more sensitive to extreme values.

In the final iteration of median polish, the row and column effect medians should be close to zero, indicating that the row and column effects have been effectively extracted.

The goal of median polish is to understand how the effects of row and column factors contribute to the variation in the response variable.

Each cell in the table can be modeled as the sum of the common term, the row effect, the column effect, and the residual value.

By analyzing the row and column effects, you can identify which factors have the most significant impact on the response variable.

Median polish can be implemented in R using the 'medpolish()' function. By setting the 'maxiter' parameter, you can control the maximum number of iterations.

The row effect is the amount a particular row deviates from the common value.

The column effect is the amount a particular column deviates from the common value.

A two-way table can be used to represent the relationship between a response variable and two categorical factors.

The residual value measures how well the fitted model captures the real data.

The common term in median polish represents the average effect across all rows and columns.

Median polish is a robust technique for data analysis, meaning it's less likely to be affected by outliers.

Median polish helps us understand how row and column factors influence the response variable within a two-way table.

The 'medpolish()' function in R provides an efficient way to perform median polish analysis.

The 'maxiter' parameter in the 'medpolish()' function allows you to set the maximum number of iterations for the analysis.

Median polish is a useful tool for analyzing data in two-way tables, especially when outliers are present.

The common term, row effects, column effects, and residual values together provide a comprehensive breakdown of the response variable within a two-way table.

By analyzing the results of median polish, you can gain valuable insights into the relationships between variables in a two-way table.

Understanding median polish empowers data analysts to effectively analyze and interpret data from two-way tables, leading to more informed decisions.

Median polish can be used in a variety of fields where two-way tables are common, such as healthcare, economics, and social sciences.

By using median polish, you can gain a deeper understanding of the relationships between variables in two-way tables, leading to more informed and insightful conclusions.