How we work with and make sense of quantitative data within sociology falls into two camps: descriptive statistics versus inferential statistics. Simply put, descriptive statistics describe the population or data set under study, whereas inferential statistics allow us to take findings from a sample group and generalize them to a larger population.

Let's dig more deeply into the differences between the two, and learn how each is useful in social science research.

### Descriptive Statistics

Descriptive statistics are the basic statistics that describe what is going on in a population or data set. They are important and useful because they allow us to see patterns among our data, and thus to make sense of that data. It's important to realize that descriptive statistics can only be used to describe the population or data set under study. That is, the results cannot be generalized to any other group or population.

There are two types of descriptive statistics that social scientists use: measures of central tendency and measures of spread.

Measures of central tendency capture general trends within the data, and are calculated and expressed as the mean, median, and mode. A mean tell us the mathematical average of all of our data, like for example average age at first marriage; median represents the middle of the data distribution, like the age that sits in the middle of the range of ages at which people first marry; and mode is the most common value present in the data, like the most common age at which people first marry.

Meanwhile, **measures of spread** describe how the data are distributed and how they relate to each other. Statistical measures that show us this include range (the entire range of values present in a data set), frequency distribution (how many times a particular value occurs within a data set), quartiles (subgroups formed within a data set when all values are divided into four equal parts across the range), mean absolute deviation (the average of how much each value deviates from the mean), variance (illustrates how much of a spread exists in our data), and standard deviation (illustrates the spread of data relative to the mean).

Measures of spread are often visually represented in tables, pie and bar charts, and histograms to aid our understanding of the trends within the data.

### Inferential Statistics

While descriptive statistics tell us basic information about the population or data set under study, inferential statistics are produced by more complex mathematical calculations, and allow us to infer trends about a larger population based on a study of a sample taken from it. We use inferential statistics to examine the relationships between variables within a sample, and then make generalizations or predictions about how those variables will relate within a larger population.

Most quantitative social science operates using inferential statistics because it is typically too costly or time-consuming to study an entire population of people. Using a statistically valid sample and inferential statistics, we can conduct research that otherwise would not be possible.

Techniques that social scientists use to examine the relationships between variables, and thereby to create inferential statistics, include but are not limited to: linear regression analyses, logistic regression analyses, ANOVA, correlation analyses, structural equation modeling, and survival analysis.

When conducting research using inferential statistics it is important and necessary to conduct a test of significance in order to know whether you *can* generalize your results to a larger population. Common tests of significance include the Chi-square and T-test. These tell us the probability that the results of our analysis of the sample are representative of the population that the sample represents.

*Updated by Nicki Lisa Cole, Ph.D.*