This covers statistical methods of summarising a dataset that aim only to summarise the data well, not to make inferences or estimation about some population from which it is assumed the dataset came. As such it is distinct from inferential statistics, i.e. NHST: Null Hypothesis Significance Testing and from estimation: creating confidence intervals around summary statistics.
Details #
Descriptive statistics can be univariate: simply summarising/describing values for one variable; bivariate where the summary/description is of a relationship between values of two variables; and multivariate where the relationships between more than two variables are the focus of the exploration.
Univariate descriptive statistics can be further divided into measures of central location, typically the mean or median; measures of dispersion, typically variance or Standard Deviation; and summaries of the shape of the distribution.
Bivariate descriptive statistics are measures of correlation or association and multivariate descriptive statistics summarise potentially complicated relationships across multiple variables, typically these include Principal Component Analysis (PCA), Exploratory Factor Analysis (EFA), Multi-Dimensional Scaling (MDS) and Cluster Analysis.
Descriptive statistics, particularly bivariate and multivariate methods shade into exploratory statistics and Exploratory Data Analysis (EDA).
My own methodological view is that quantitative work in our area has been, and still is, badly held back by an obsession with inferential statistics and often very implausible generalisation from data where work within the descriptive and exploratory statistical areas would be far more useful to us.
Try also #
Cluster analysis
Confidence intervals
Dispersion
Estimation
Exploratory Factor Analysis
Exploratory statistics & Exploratory Data Analysis (EDA)
Mean (arithmetic mean, average)
Median
Multi-Dimensional Scaling (MDS)
Null hypothesis significance testing (NHST) paradigm
Chapters #
The distinction between descriptive statistics and the realms of inferential statistics and estimation is introduced in Chapter 5.
Online resources #
At the moment the only one of my shiny apps that is purely descriptive is the app that gives sample statistics, histogram, ecdf and qqplot for samples from a true Gaussian population. However, more will follow now I have worked out how to enable people to paste in or upload data.
Dates #
First created 28.iv.24.
