Descriptive and Inferential Statistics

When analysing data, for example, the marks achieved by 100 students for a piece of coursework, it is possible to use both descriptive and inferential statistics in your analysis of their marks. Typically, in most research conducted on groups of people, you will use both descriptive and inferential statistics to analyse your results and draw conclusions. So what are descriptive and inferential statistics? And what are their differences?

Descriptive Statistics

Descriptive statistics is the term given to the analysis of data that helps describe, show or summarize data in a meaningful way such that, for example, patterns might emerge from the data. Descriptive statistics do not, however, allow us to make conclusions beyond the data we have analysed or reach conclusions regarding any hypotheses we might have made. They are simply a way to describe our data.

Descriptive statistics are very important, as if we simply presented our raw data it would be hard to visulize what the data was showing, especially if there was a lot of it. Descriptive statistics therefore allow us to present the data in a more meaningful way which allows simpler interpretation of the data. For example, if we had the results of 100 pieces of students' coursework, we may be interested in the overall performance of those students. We would also be interested in the distribution or spread of the marks. Descriptive statistics allow us to do this. How to properly describe data through statistics and graphs is an important topic and discussed in other Laerd Statistics Guides. Typically, there are two general types of statistic that are used to describe data:

• 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.
• 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, absolute deviation, variance and standard deviation.

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 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 randomly select 100 girls and 100 boys in our sample. We could then use this, for example, to see if there are any statistically significant differences in the mean mark between boys and girls, even though we have not measured all 1000 students.

Why not now read our guide on Types of Variable?