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## Statistical procedures

Statistical procedures can be divided into two major categories: descriptive statistics and inferential statistics. Typically, in most research conducted on groups of people, you will use both descriptive and inferential statistics to analyze your results and draw conclusions. So what are descriptive and inferential statistics? And what are their differences?We have seen that descriptive statistics provide information about our immediate group of data. For example, we could calculate the mean and standard deviation of the exam marks for the 100 students and this could provide valuable information about this group of 100 students. Any group of data like this, which includes all the data you are interested in, is called a population. A population can be small or large, as long as it includes all the data you are interested in.

For example, if you were only interested in the exam marks of 100 students, the 100 students would represent your population. Descriptive statistics are applied to populations, and the properties of populations, like the mean or standard deviation, are called parameters as they represent the whole population (i.e., everybody you are interested in).Often, however, you do not have access to the whole population you are interested in investigating, but only a limited number of data instead. For example, you might be interested in the exam marks of all students in the UK. It is not feasible to measure all exam marks of all students in the whole of the UK so you have to measure a smaller sample of students (e.g., 100 students), which are used to represent the larger population of all UK students.

Properties of samples, such as the mean or standard deviation, are not called parameters, but statistics. Inferential statistics are techniques that allow us to use these samples to make generalizations about the populations from which the samples were drawn. It is, therefore, important that the sample accurately represents the population. The process of achieving this is called sampling (sampling strategies are discussed in detail here on our sister site). Inferential statistics arise out of the fact that sampling naturally incurs sampling error and thus a sample is not expected to perfectly represent the population. The methods of inferential statistics are (1) the estimation of parameter(s) and (2) testing of statistical hypotheses.

## What is a Descriptive Statistic?

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 studied. 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. 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 analyzed or reach conclusions regarding any hypotheses we might have made. They are simply a way to describe our data.

## What is Inferential 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, ANOVA, to name a few.

## What is The Difference Between Descriptive and Inferential Statistics?

Both descriptive and inferential statistics look at a sample from some population. The difference between descriptive and inferential statistics is in what they do with that sample: * Descriptive statistics aims to summarize the sample using statistical measures, such as average, median, standard deviation etc. For example, if we look at a basketball team’s game scores over a year, we can calculate the average score, variance etc. and get a description (a statistical profile) for that team. * Inferential statistics aims to draw conclusions about the population from the sample at hand. For example, it may try to infer the success rate of a drug in treating high temperature, by taking a sample of patients, giving them the drug, and estimating the rate of effectiveness in the population using the rate of effectiveness in the sample.

Descriptive statistics are limited in so much that they only allow you to make summations about the people or objects that you have actually measured. You cannot use the data you have collected to generalize to other people or objects (i.e., using data from a sample to infer the properties/parameters of a population). For example, if you tested a drug to beat cancer and it worked in your patients, you cannot claim that it would work in other cancer patients only relying on descriptive statistics (but inferential statistics would give you this opportunity).

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