Inferential statistics allow us to make decisions about a large group (usually referred to as a population) based upon observations made within a small group selected from that population (usually referred to as a sample. This ability to infer something about a population based upon a sample allows a deeper understanding of data beyond what descriptive statistics alone can offer. Sometimes knowing the mean of a group of scores is enough information. Still, inferential statistics allows us to compare the means of sets of scores and decide whether the difference is actually present in the population or whether the difference we see is random or due to chance. This ability to infer or generalize to a population based on a sample is the foundation of many research types that affect our everyday lives.

For example, suppose you want to study the ability of a new drug to reduce the frequency of symptoms of a certain disease compared to another treatment. In that case, inferential statistics can be applied to answer that question. One sample of people who have the disease receive the new drug, and another sample receives the standard treatment. The frequency of symptoms could then be compared, and the result can be generalized to the population of all the people who have that disease.

Why not just study the entire population of people with that disease? Populations are generally too large, and trying to do so is very time-consuming and resource-intensive. Based on the study and refinement of statistical techniques, we know we can accurately assess how precisely a sample of observations represents the population and then make decisions based on the result.

A key element to the ability to make these inferences is ensuring that the sample is representative of the population we want to understand. If a sample doesn’t accurately represent the population, our confidence in any inference we make will be limited. If a sample is representative of a population, then our inferences will be accurate and have a higher likelihood of being generalizable to the population of interest.

Inferential statistical techniques, like t-tests and analysis of variance, allow us to understand descriptive statistics in a broader context and begin to make more complex decisions about data.