# Inferential Statistics: Definition and Pros and Cons

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Statistics is a branch of mathematics concerned with collecting, organizing, and analyzing data. Scientists employ statistical inference to analyze the correlations between variables within a sample and then make inferences or estimations about how those correlations may relate to a more significant population. Understanding the purpose of statistical inference can assist you in determining when to use this type of calculation. In this article, we explain the meaning of statistical inference, discuss the meaning of descriptive statistics, state the differences between the two, review the pros and cons of using samples, answer some frequently asked questions, and provide an example.

## What is inferential statistics?

Inferential statistics, sometimes called statistical inference, evaluates data sourced from a sample group to make predictions about larger groups. You can also refer to this prediction as a conclusion. A sampling error is a type of statistical error that arises when an analyst fails to choose a sample size that properly represents the total population. As a result, the conclusion is not true for the larger sample.

Statistical inference uses sample data because it's less expensive and time-consuming than collecting data from an entire population. To validate statistical conclusions and inferences, ensure that sampling methods are objective and random. There are several methods for conducting statistical inference, including:

### Hypothesis testing

Hypothesis testing is a form of statistical inference used to analyze relationships between variables and compare populations using sample data. The steps involved in hypothesis testing include developing a research hypothesis, collecting data in accordance with the hypothesis test requirements, analyzing the data using the appropriate test, deciding whether to reject or accept the null hypothesis, and presenting and discussing the findings. The null hypothesis is a widely used statistical theory that asserts that no statistical relationship or relevance exists between two units of measured phenomena or observed data.

Statistical tests consider sampling errors and can be parametric, which means making assumptions about population distribution parameters, or non-parametric, which means not including assumptions about population distribution parameters.

Related: 12 Jobs for Statistics Majors (With Salaries and Duties)

### Confidence intervals

Confidence intervals assess the level of uncertainty or certainty associated with a sampling method for a data set. Confidence intervals are a range of values that express the degree of uncertainty associated with an estimate. You can calculate confidence intervals using techniques such as the t-test. For instance, a researcher may randomly choose samples from the same population and calculate a confidence interval for each sample to determine how well it represents the population's true value. The result of these calculations may vary and some of the data sets may contain the true population parameter, while others do not.

Suppose a child received a standard score of 110, with a 90% confidence interval ranging from 98 to 124. Although you cannot guarantee a score of 110, it is 90% certain that the child's score falls within the given range. If the test gets theoretically administered to this child 100 times and they learn nothing from the retake, 90% of the tests administered may result in a score between 98 and 124. If 100 different samples get taken and a 94% confidence interval gets computed for each sample, approximately 94 of the 100 confidence intervals may contain the real value.

Related: How to Find Critical Value in Two Steps (With Examples)

### Regression analysis

Regression analysis is used to determine the relationship between an experiment's independent and dependent variables. After you have determined the hypothesis test results, you can conduct a regression analysis to find the subject matter's relationship. You can test for various results, including the comparison of the height and weight of different genders.

## What is descriptive statistics?

A descriptive statistic is a statistic that comprehensively describes or summarizes the characteristics of a collection of data, and descriptive statistics is the process of utilizing and analyzing those statistics. In other words, you're condensing the group's findings and reducing them to a few critical elements. In this case, you're only interested in obtaining data from relevant individuals. This necessitates further testing if your findings affect a larger proportion of the population. Several conclusions that you can quantify include:

Central tendency: They are statistical metrics that use a single value to represent the middle of a set of data. The central concept underlying measures of central tendency is that a single value can summarize an entire set of data.

Dispersion: This refers to the scattering of data points from the graph's centre. A small value indicates that the dispersion is closer to the centre, while a large value indicates a greater distance from the graph's epicentre.

Skewness: This refers to a distortion or asymmetry in a set of data that deviates from the symmetrical bell curve, or normal distribution. You can refer to the curve as skewed if it gets shifted to the left or right.

Related: Tips to Get the Most Out of Your Internship in Statistics

## What's the difference between descriptive and statistical inference?

The primary distinction between descriptive and statistical inference is that descriptive statistics get used to quantify definitive data. In contrast, statistical inference gets used to quantify the margin of error associated with research conducted. You can consider the research and development deadlines to determine which statistic is more feasible for you. Statistical inference accounts for sampling errors, which may necessitate the conduct of additional tests on a larger population, depending on the amount of data required. Given that statistical inference gets used to test for variables, descriptive statistics make it easier to create conclusions.

Descriptive statistics remain helpful because they enable you to interpret the data you have. For instance, you may want to determine the weight of a product on a production line or the time required to process an application. Statistical inference enables decision-makers to infer information about the population from sample data. While descriptive statistics are straightforward measures, statistical inference is comprehensive and allows the decision-maker to test their hypothesis. Both descriptive and statistical inference helps the decision-maker determine whether they can use the data to forecast the future and prescribe a solution if a problem exists.

## Key points to note about working with samples

When the properties of a population get estimated using a sample, the sample statistics are unlikely to match the actual population value exactly. For example, your sample mean is nearly impossible to equal the population mean. The sampling error is the difference between the sample statistic and the population value. Statistical inference incorporates estimations of this error into the statistical findings. By contrast, descriptive statistics' summary values are self-explanatory. The average score for a particular class is known because of the measurement of all class members, so there is no uncertainty.

## Frequently asked questions about statistical inference

Here is a list of some frequently asked questions about statistics:

### What is the original purpose of statistics?

Statistics teaches employees how to make clever and accurate inferences about a larger population by analyzing a small sample. The use of tables, graphs, and charts is critical in presenting the data on which they base these conclusions. It was initiated in the mid-nineteenth century as the study of economies, moral actions, and population, and subsequently as the mathematical tool for examining such numbers. Also, consider the resources available to you and your prior knowledge.

### When do I know when to measure for descriptive inference or statistical inference?

If no margin for error or additional variables gets included, you can use descriptive statistics to describe what you're measuring. Otherwise, you can use statistical inference. This way, you may have a clearer idea of when your research is complete.

## Statistical inference example

Here is an example of the result of using statistical inference:

A company called Pizza Palace Co. is currently conducting market research on their customers' pizza-eating habits. The company is attempting to ascertain its customers' preferred tastes to redesign the menu. They hired a marketing consulting company to conduct a focus group study on the subject. The company assembled a group of 50 people of various ages and genders, all of whom were residents of neighbourhoods adjacent to the store.

After the focus group concluded, the marketing firm applied statistical inference to this sample to ascertain the general population's most desired tastes. The results indicated that 75% of the sample preferred pepperoni pizza. 75% of the women in the group preferred pizza with pineapple. By utilizing inferential statistical tools, the company was able to ascertain the preferences of the population they currently serve with a high degree of confidence.

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