Chapter 2: Examining your data
Chapter preview
The objective of the data examination tasks is as much to reveal what is not apparent as it is to portray
the actual data, because the hidden effects are easily overlooked.
Missing data: a nuisance to researchers and primarily result from errors in data collection or data entry
or from the omission of answers from respondents.
Outliers: extreme responses, may unduly influence the outcome of any multivariate analysis.
Statisticals: the researcher must assess the fit of the sample data with the statistical assumptions
underlying that technique.
E.g. regression analysis: assumptions of normality, homoscedasticity, independence of error and linearity
Dummy variable: a metric variable. The applicability of using a dummy varies with each data analysis
project.
Introduction
The researcher attains a basic understanding of the data and the relationships between variables. A
thorough knowledge of the variable interrelationships can aid immeasurably in the specification and
refinement of the multivariate model as well as provide a reasoned perspective for the interpretation of the
results
The researcher ensures that the data underlying the analysis meet all of the requirements for a
multivariate analysis. Multivariate analysis demands more in terms of analytical sophistication.
Graphical examination of the data
The researcher can be aided immeasurably in gaining a fuller understanding of what these diagnostic
measures mean through the use of graphical techniques, portraying the basic characteristics of individual
variables and relationships between variables in a simple picture.
Scatterplot: two basic elements of a correlation coefficient (the type of relationship [positive or negative]
and the strength of the relationship [the dispersion of the cases], but also a simple visual means for
assessing linearity
Boxplot: overall level of differences across groups, but also the differences between pairs of groups and
the existence of outliers.
The objective of graphical techniques is not to replace empirical measures, but to use them as a
complement to provide a visual representation of the basic relationships
Univariate profiling: examining the shape of the distribution
The starting point for understanding the nature of any variable is to characterize the shape of its
distribution.
Histogram: a graphical representation of a single variable that represents the frequency of occurrence
within the data categories.
For continuous variables, categories are formed within which the frequency of data values is tabulated.
For assessing normality, the normal curve can be superimposed on the distribution.
The histogram can be used to examine any type of metric variable.
Kurtosis measures peakness or flatness of the distribution.
The comparison of the normal curve and the histogram also provide information about the type of
transformation needed to remedy nonnormality.
Bivariate profiling
Scatterplot: a graph of data points based on two metric variables.
One variable per axis
The points in the graph represent the corresponding joint values for the variables.
The pattern of points represents the relationship between the variables.
A strong organization of points along a straight line characterizes a linear relationship or correlation
A curved set of points may denote a nonlinear relationship.
Random pattern of might indicate no relationship
Most often used for MVA: scatterplot matrix, in which scatterplots are represented for all combinations of
variables in the lower portion of the matrix. The diagonal contains histograms of the variables. Above the
diagonal are bivariate correlations.
The scatterplot matrix provides a quick and simple method of not only assessing the strength and
magnitude of any bivariate relationship, but also a means of identifying any nonlinear patterns that might
be hidden from only the bivariate correlations, which are based on a linear relationship.
Chapter preview
The objective of the data examination tasks is as much to reveal what is not apparent as it is to portray
the actual data, because the hidden effects are easily overlooked.
Missing data: a nuisance to researchers and primarily result from errors in data collection or data entry
or from the omission of answers from respondents.
Outliers: extreme responses, may unduly influence the outcome of any multivariate analysis.
Statisticals: the researcher must assess the fit of the sample data with the statistical assumptions
underlying that technique.
E.g. regression analysis: assumptions of normality, homoscedasticity, independence of error and linearity
Dummy variable: a metric variable. The applicability of using a dummy varies with each data analysis
project.
Introduction
The researcher attains a basic understanding of the data and the relationships between variables. A
thorough knowledge of the variable interrelationships can aid immeasurably in the specification and
refinement of the multivariate model as well as provide a reasoned perspective for the interpretation of the
results
The researcher ensures that the data underlying the analysis meet all of the requirements for a
multivariate analysis. Multivariate analysis demands more in terms of analytical sophistication.
Graphical examination of the data
The researcher can be aided immeasurably in gaining a fuller understanding of what these diagnostic
measures mean through the use of graphical techniques, portraying the basic characteristics of individual
variables and relationships between variables in a simple picture.
Scatterplot: two basic elements of a correlation coefficient (the type of relationship [positive or negative]
and the strength of the relationship [the dispersion of the cases], but also a simple visual means for
assessing linearity
Boxplot: overall level of differences across groups, but also the differences between pairs of groups and
the existence of outliers.
The objective of graphical techniques is not to replace empirical measures, but to use them as a
complement to provide a visual representation of the basic relationships
Univariate profiling: examining the shape of the distribution
The starting point for understanding the nature of any variable is to characterize the shape of its
distribution.
Histogram: a graphical representation of a single variable that represents the frequency of occurrence
within the data categories.
For continuous variables, categories are formed within which the frequency of data values is tabulated.
For assessing normality, the normal curve can be superimposed on the distribution.
The histogram can be used to examine any type of metric variable.
Kurtosis measures peakness or flatness of the distribution.
The comparison of the normal curve and the histogram also provide information about the type of
transformation needed to remedy nonnormality.
Bivariate profiling
Scatterplot: a graph of data points based on two metric variables.
One variable per axis
The points in the graph represent the corresponding joint values for the variables.
The pattern of points represents the relationship between the variables.
A strong organization of points along a straight line characterizes a linear relationship or correlation
A curved set of points may denote a nonlinear relationship.
Random pattern of might indicate no relationship
Most often used for MVA: scatterplot matrix, in which scatterplots are represented for all combinations of
variables in the lower portion of the matrix. The diagonal contains histograms of the variables. Above the
diagonal are bivariate correlations.
The scatterplot matrix provides a quick and simple method of not only assessing the strength and
magnitude of any bivariate relationship, but also a means of identifying any nonlinear patterns that might
be hidden from only the bivariate correlations, which are based on a linear relationship.
