Statistics: Basics

Statistical power is the probability of detecting an effect when that effect genuinely exists in the population. Other things being equal, a test based on a large sample has more statistical power than a test involving a small sample. There are also ways to increase power without increasing the sample size. Most published studies have low statistical power, which can lead to serious misinterpretation of results.

Central tendency is a measure of values in a sample that identifies the different central points in the data, often referred to colloquially as “averages.” The most common measurements of central tendency are the mean, median, and mode. Identifying the central value allows other values to be compared to it, showing the spread or cluster of the sample, which is known as the dispersion or distribution. These measurements of dispersion are categorized in 2 groups: measures of dispersion based on percentiles and measures of dispersion based on the mean (which is commonly known as standard deviations). Analysis of data distribution determines whether the data have a strong or a weak central tendency based on their dispersion. When the data distribution is symmetrical and the mean = median = mode, the data are said to have a normal distribution. Other types of distributions are possible as well, and these are known as nonnormal distributions.

One of the main objectives of research and medical studies is to learn what associations or outcomes are not a product of chance. According to the study's design and the data it provides, a hypothesis can be accepted or rejected, allowing for a determination in correlation. Statistical tests are tools used by researchers to obtain information and meaning from pools of variable data. These tests come in several forms, including, for example, the chi-square and Fisher exact tests, and are chosen depending on the needs of the investigators and the characteristics of the variables being analyzed. Study results can be considered statistically significant based on calculated p-values and predetermined levels of significance (known as the α-level). Confidence intervals are another way to express the significance of a statistical result without using a p-value.

Variables represent information about something that can change. The design of the measurement scales, or of the methods for obtaining information, will determine the data gathered and the characteristics of that data. As a result, a variable can be qualitative or quantitative, and may be further classified into subgroups. Every possible way to express the value of a variable, or the range of the variable, is called a domain.

Epidemiological studies are used to establish associations between risk factors and health-related outcomes. These studies can take the form of observational or interventional studies. Observational studies are nonexperimental investigations of the associations between known exposures and outcomes. Interventional studies are designed to evaluate the direct impacts of a risk factor on a disease by applying an intervention to the subjects in an experimental group and prospectively comparing the effects with a control group. Interventional studies are more expensive and time-consuming but tend to provide stronger evidence for an association than observational studies. Depending on the situation, investigators will typically choose a combination of these study designs.