Chapter 8: Measurement and Descriptive Analysis

CHAPTER OBJECTIVES

• Identify and describe the two general functions of statistics

• Describe measurement and variable classification schemes

• Describe and use measures of central tendency and dispersion

• Organize and present data in a scientifically meaningful way

• Differentiate between proportions and rates, including prevalence and incidence

• Describe performance measures for diagnostic tests, including sensitivity, specificity, and predictive value

• Describe receiver operating characteristic curves and their role in diagnostic tests

KEY TERMINOLOGY

• Arithmetic mean

• Bar chart

• Box and whisker plot

• Coefficient of variation

• Continuous variables

• Control variables

• Dependent variable

• Descriptive statistics

• Discrete variables

• False negative rate

• False positive rate

• Frequency table

• Histogram

• Incidence

• Independent variable

• Inferential statistics

• Interquartile range

• Interval data

• Mean

• Measures of central tendency

• Measures of dispersion

• Median

• Mode

• Negative predictive value

• Nominal data

• Ordinal data

• Pie chart

• Positive predictive value

• Prevalence

• Proportion

• Qualitative data

• Quantitative data

• Range

• Rates

• Ratio data

• Receiver operating characteristic (ROC) curve

• Sensitivity

• Skewness

• Specificity

• Standard deviation

• Statistics

• True negative rate

• True positive rate

• Variable classification schemes

• Variance

INTRODUCTION

In research, measurement is the process of collecting and recording observations about the variables that are of interest in a specified project. These collected observations are called data. There are a variety of tools that researchers can employ to collect observations. Some examples of measurement tools include stadiometers (height), sphygmomanometers (blood pressure), enzyme-linked immunosorbent assays (antibodies in serum), and questionnaires (health status). Once observations are collected, these measurements about the variables of interest (i.e., data) are used to inform the research question, and this occurs through the use of statistics. An editorial in Science defined statistics as “…the science of learning from data, and of measuring, controlling, and communicating uncertainty.”¹ Thus, functions of statistics include summarizing, organizing, presenting, analyzing, and interpreting data.²

This chapter is devoted to the summarizing, organizing, and presenting functions of statistics, commonly referred to as descriptive statistics. Analytic (e.g., hypothesis testing) and interpretation functions, which are collectively referred to as inferential statistics, will be covered in subsequent chapters. This chapter introduces various schemes used to classify and summarize variables so that collections of information can be simplified and communicated in a manner that is both straightforward and standardized. Next, we discuss how to visualize and optimally present data so that it is logical and comprehensible. The chapter concludes with a discussion of summary measures used to convey morbidity and mortality information as well as the summary measures used to describe diagnostic test performance.

VARIABLE CLASSIFICATION SCHEMES

At the most fundamental level, data may be qualitative or quantitative in nature. Qualitative data^a, or meaningful information that is collected in words, may provide valuable insight into the condition of individual patients, but are not typically used for the purposes of healthcare research with large populations of patients.³ Written observations or notes found in medical records are ...