Descriptive and Inferential Statistics

Overview

When analysing a group of data, such as the marks that 100 students received for a piece of coursework, it is possible to use both descriptive and inferential statistics to summarize and describe that data.

Descriptive Statistics

Descriptive statistics are useful because they help to summarize a group of data. For example, if 100 students had to complete a piece of coursework, we may be interested in the overall performance of those students. Typically, we would look to summarize their performance using two general types of statistics:

• Measures of central tendency: these are ways of describing the central position of a frequency distribution for a group of data. In this case, the frequency distribution is simply the distribution and pattern of marks scored by the 100 students from the lowest to the highest. We can describe this central position using a number of statistics, including the mode, median, and mean, which are discussed in the statistical guide, Measures of Central Tendency.
• Measures of spread: these are ways of summarizing a group of data by describing how spread out the scores are. For example, the mean score of our 100 students may be 65 out of 100. However, not all students will have scored 65 marks. Rather, their scores will be spread out. Some will be lower and others higher. Measures of spread help us to summarize how spread out these scores are. To describe this spread, a number of statistics are available to us, including the range, quartiles, inter-quartile range, absolute deviation, variance and standard deviation. These are discussed in the statistical guide, Measures of Spread.

When we use descriptive statistics it is useful to summarize our group of data using a combination of tabulated description (i.e. tables), graphical description (i.e. graphs and charts) and statistical commentary (i.e. a discussion of the results).

Inferential Statistics

Whilst descriptive statistics examine our immediate group of data (for example, the 100 students’ marks), inferential statistics aim to make inferences from this data in order to make conclusions that go beyond this data. In other words, inferential statistics are used to make inferences about a population from a sample (see the statistical guide on Sampling) in order to generalize (make assumptions about this wider population) and/or make predictions about the future.

For example, a Board of Examiners may want to compare the performance of 1000 students that completed an examination. Of these, 500 students are girls and 500 students are boys. The 1000 students represent our ‘population’. Whilst we are interested in the performance of all 1000 students, girls and boys, it may be impractical to examine the marks of all of these students because of the time and cost required to collate all of their marks. Instead, we can choose to examine a ‘sample’ of these students and then use the results to make generalizations about the performance of all 1000 students. For the purpose of our example, we may choose a sample size of 200 students. Since we are looking to compare boys and girls, we may select 100 girls and 100 boys in our sample (In reality, we should be more scientific than this. As such, in the statistical guide on sampling we discuss how to choose an appropriate sample size).

Inferential statistics are at the heart of learning about statistical analysis. However, before trying to get to grips with using inferential statistical tests, it is worth reading all of the Statistical Guides in the Essentials series, including Types of Variable, Measures of Central Tendency, Measures of Spread, Frequency Distributions, Hypothesis Testing and Sampling. After this, we recommend that you read the Selecting Statistical Tests guide to know which statistical test(s) to run on your data.