Before discussing the differences between descriptive and inferential statistics, we must first be familiar with two important concepts in social science statistics: population and sample. A population is the total set of individuals, groups, objects, or events that the researcher is studying. For example, if we were studying employment patterns of recent UK college graduates, our population would likely be defined as every college student who graduated within the past one year from any college across the United Kingdom.
A sample is a relatively small subset of people, objects, groups, or events, that is selected from the population. Instead of surveying every recent college graduate in the United Kingdom, which would cost a great deal of time and money, we could instead select a sample of recent graduates, which would then be used to generalize the findings to the larger population.
Descriptive statistics includes statistical procedures that we use to describe the population we are studying. The data could be collected from either a sample or a population, but the results help us organize and describe data. Descriptive statistics can only be used to describe the group that is being studying. That is, the results cannot be generalized to any larger group.
Descriptive statistics are useful and serviceable if you do not need to extend your results to any larger group. However, much of social sciences tend to include studies that give us “universal” truths about segments of the population, such as all parents, all women, all victims, etc.
Frequency distributions, measures of central tendency (mean, median, and mode), and graphs like pie charts and bar charts that describe the data are all examples of descriptive statistics.
Inferential statistics is concerned with making predictions or inferences about a population from observations and analyses of a sample. That is, we can take the results of an analysis using a sample and can generalize it to the larger population that the sample represents. In order to do this, however, it is imperative that the sample is representative of the group to which it is being generalized.
To address this issue of generalization, we have tests of significance. A Chi-square or T-test, for example, can tell us the probability that the results of our analysis on the sample are representative of the population that the sample represents. In other words, these tests of significance tell us the probability that the results of the analysis could have occurred by chance when there is no relationship at all between the variables we studied in the population we studied.
Examples of inferential statistics include linear regression analyses, logistic regression analyses,ANOVA, correlation analyses, structural equation modeling, and survival analysis, to name a few.
Frankfort-Nachmias, C. & Leon-Guerrero, A. (2006). Social Statistics for a Diverse Society. Thousand Oaks, CA: Pine Forge Press.