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# Inferential Statistics – Guide With Examples

Published by at August 25th, 2021 , Revised On December 12, 2022

Statistics students must have heard a lot of times that inferential statistics is the heart of statistics. Well, that is true and reasonable. While descriptive statistics are easy to comprehend, inferential statistics are pretty complex and often have different interpretations.

If you are also confused about how descriptive and inferential statistics are different, this blog is for you. Everything from the definition of inferential statistics to its examples and uses is all mentioned here.

## Inferential Statistics: An Introduction

To know the origin and definition of inferential statistics, you must know what statistics is and how it came to be.

So, statistics is the branch of math that deals with collecting, assessing, and interpreting data. It includes how this data is presented in the form of numbers and digits. In other words, statistics is the study of quantitative or numerical data.

Statistics is broadly divided into two departments, namely Applied Statistics and Theoretical Statistics. Applied Statistics are further categorized into two sub-groups: Descriptive Statistics and Inferential Statistics.

There are two main areas of Inferential Statistics:

1. Estimating Parameters: It means taking a statistic from a sample and utilizing it to describe something about a population.
2. Hypothesis Testing: it is when you use this sample data to answer various research questions.

Now let’s delve down deeper and see how descriptive and inferential statistics are different from each other.

## Inferential Statistics vs. Descriptive Statistics

Descriptive statistics allow you to explain a data set, while inferential statistics allow you to make inferences or interpretations based on a particular data set.

Here are a few differences between inferential and descriptive statistics:

Firstly, descriptive statistics can be used to describe a particular situation, while inferential statistics are used to dig deeper into the chances of occurrence of a condition.

Secondly, descriptive statistics give information about raw data and how it is organized in a particular manner. The other one, on the contrary, compares data and helps you make predictions and hypotheses with it.

Lastly, descriptive statistics are shown with charts, graphs, and tables, while inferential statistics are achieved via probability. Descriptive statistics have a diagrammatic or tabular representation of the final outcomes, and inferential statistics show results in the probability form.

Are we clear about the differences between these two? Let move on to the next topic then.

## Sampling Error and Inferential Statistics

Can you recall the sample and population? How about statistics and parameters? Great, if you can.

Here is a quick recap for those who cannot remember these terms.

Sample: A sample is a small group taken from the population to observe and draw conclusions.
Population: It is the entire group under study.
Statistic: A statistic is a number that describes a sample. For instance, the sample mean.
Parameter: It is a number that describes the whole population. For instance, a population mean.

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The fact that the size of the sample is much smaller than that of a population, there is a great chance that some of the population is not captured by the sample data. Hence, there is always room for error, which we call sampling error in statistics. It is the difference between the true population values and the captured population values. In other words, it is the difference between parameters and statistics.

A sampling error can occur any time you examine a sample, regardless of the sampling technique, i.e., random or systematic sampling. This is why there is some uncertainty in inferential statistics, no matter what. However, this can be reduced using probability sampling methods.

You can make two kinds of estimates about the population:

Point Estimate-it is a single value estimate of a population parameter.

Interval Estimate-it gives you a wide range of values where the parameter is predicted to lie.

Have you heard of a confidence interval? That is the most used type of interval estimate.

Details are below:

### Confidence Intervals

Confidence intervals tend to use the variability around a sample statistic to deduce an interval estimate for a parameter. They are used for finding parameters because they assess the sampling errors. For instance, if a point estimate reflects a precise value for the population parameter, confidence intervals give you an estimate of the uncertainty of the point estimate.

All these confidence intervals are associated with confidence levels that tell you about the probability of the interval containing the population parameter estimate on repeating the study.

An 85 percent confidence interval means that if you repeat the research with a new sample precisely the same way 100 times, you can predict the estimate to lie within the range of values 85 times.

You might expect the estimate to lie within the interval a certain percentage of the time, but you cannot be 100% confident that the actual population parameter will. It is simply because you cannot predict the true value of the parameter without gathering data from the whole population.

However, with suitable sample size and random sampling, you can expect the confidence interval to contain the population parameter a certain percentage of the time.

## Hypothesis Testing and Inferential Statistics

Hypothesis testing is a practice of inferential statistics that aims to deduce conclusions based on a sample about the whole population. It allows us to compare different populations in order to come to a certain supposition.

These hypotheses are then tested using statistical tests, which also predict sampling errors to make accurate inferences. Statistical tests are either parametric or non-parametric. Parametric tests are thought to be more powerful from a statistics point of view, as they can detect an existing effect more likely.

Some of the assumptions parametric tests make are:

• Sample of a population follows a normal distribution of scores
• The sample size is big enough to represent the whole the population
• A measure of the spread of all groups compared are same

Non-parametric tests are not effective when the data at hand violates any of the assumptions mentioned above. The fact that non-parametric tests do not assume anything about the population distribution they are called “distribution-free tests.”

## Forms of Statistical Tests

The statistical tests can be of three types or come in three versions:

• Comparison Tests
• Correlation Tests
• Regression Tests

### Comparison Tests

As the name suggests, comparison tests evaluate and see if there are differences in means and medians. They also assess the difference in rankings of scores of two or multiple groups.

### Correlation Tests

The correlation tests allow us to determine the extent to which two or more variables are associated with each other.

### Regression Tests

Lastly, the regression tests tell whether the changes in predictor variables are causing changes in the outcome variable or not. Depending on the number and type of variables you have as outcomes and predictors, you can decide which regression test suits you the best.

Statistics is broadly divided into two departments, namely Applied Statistics, and Theoretical Statistics. Applied Statistics are further categorized into two sub-groups: Descriptive Statistics and Inferential Statistics.

They help us compare data and make predictions with it. Inferential statistics allow you to assess a test hypothesis and see whether data is generating the whole population or not.

Statistic: A statistic is a number that defines a sample. For instance, the sample mean.

Parameter: It is a number that describes the whole population. For instance, a population mean.

It is the difference between the true population values and the captured population values.

The statistical tests can be of three types or come in three versions:

• Comparison Tests
• Correlation Tests
• Regression Tests

Comparison Tests

As the name suggests, comparison tests evaluate and see if there are differences in means and medians. They also assess the difference in rankings of scores of two or multiple groups.

Correlation Tests

The correlation tests allow us to find out the extent to which two or more variables are associated with each other.

Regression Tests

The regression tests tell whether the changes in predictor variables are causing changes in the outcome variable or not.

Hypothesis testing is a kind of inferential statistics that aims to deduce conclusions based on samples about the whole population. It allows us to compare different populations in order to come to a certain supposition.