Descriptive statistics is the type of statistics that probably springs to most people’s minds when they hear the word “statistics.” Here the goal is to describe. Numerical measures are used to tell about features of a set of data. There are a number of items that belong in this portion of statistics, such as:
- The average, or measure of center, consisting of the mean, median, mode or midrange.
- The spread of a data set, which can be measured with the range or standard deviation.
- Overall descriptions of data such as the five number summary.
- Other measurements such as skewness and kurtosis.
- The exploration of relationships and correlation between paired data.
- The presentation of statistical results in graphical form.
For the area of inferential statistics we begin by differentiating between two groups. The population is the entire collection of individuals that we are interested in studying. It is typically impossible or infeasible to examine each member of the population individually. So we choose a representative subset of the population, called a sample.
Inferential statistics studies a statistical sample, and from this analysis is able to say something about the population from which the sample came. There are two major divisions of inferential statistics:
- A confidence interval gives a range of values for an unknown parameter of the population by measuring a statistical sample. This is expressed in terms of an interval and the degree of confidence that the parameter is within the interval.
- Tests of significance or hypothesis testing tests a claim about the population by analyzing a statistical sample. By design there is some uncertainty in this process. This can be expressed in terms of a level of significance.
Difference Between These Areas
As seen above, descriptive statistics is concerned with telling about certain features of a data set. Although this is helpful in learning things such as the spread and center of the data we are studying, nothing in the area of descriptive statistics can be used to make any sort of generalization. In descriptive statistics measurements such as the mean and standard deviation are stated as exact numbers. Though we may use descriptive statistics all we would like in examining a statistical sample, this branch of statistics does not allow us to say anything about the population.
Inferential statistics is different from descriptive statistics in many ways. Even though there are similar calculations, such as those for the mean and standard deviation, the focus is different for inferential statistics. Inferential statistics does start with a sample and then generalizes to a population. This information about a population is not stated as a number. Instead we express these parameters as a range of potential numbers, along with a degree of confidence.
It is important to know the difference between descriptive and inferential statistics. This knowledge is helpful when we need to apply it to a real world situation involving statistical methods.