Guide to Learning Descriptive vs. Inferential Statistics

By Indeed Editorial Team

Published June 10, 2022

The Indeed Editorial Team comprises a diverse and talented team of writers, researchers and subject matter experts equipped with Indeed's data and insights to deliver useful tips to help guide your career journey.

Statistical analyses provide context for large sets of data using both forward-looking and historical approaches. Determining the best type of statistics to use, whether inferential or differential, is important to proper data understanding and use. Learning how to differentiate between statistical models, and deciding which approach best suits a situation, can help you in all types of careers, ranging from technology to healthcare. In this article, we explore descriptive vs. inferential statistics by first defining these strains of data analysis, explaining both types individually, then exploring the best applications for each statistical maneuver.

What is descriptive vs. inferential statistics?

Understanding the differences between descriptive vs. inferential statistics is a matter of how you use a data set. Descriptive statistics take a data set and summarize its characteristics, allowing you to analyze historical records to provide context to current events. Inferential statistics enables you to pose a hypothesis and assess whether you can generalize that data and apply it to a broader population in a future-facing model. The two approaches are inherent opposites, though both are essential to providing reality-based context for large sets of data.

Read more: Types of Variables in Statistics and Research (With FAQs)

What are descriptive statistics?

Descriptive statistics takes the characteristics of a data set and then summarizes and organizes the information. A data set refers to the observations or responses from a population. It is the first step in any type of quantitative, or numerical, investigation. You take the data and identify the variables, such as age, height, left- or right-handedness, or eye colour. From there, descriptive statistics takes that information and generates correlations between the variables based on apparent patterns. There are three main types of descriptive statistics, as follows:

Frequency

Distribution statistics involve how frequently each variable occurs. Any set of data comprises a series of values that occur a certain number of times within the set. The frequency aspect describes the value and counts its incidences. It allows you to directly attribute the rate at which the incidences occurred in that set. The frequency is a central statistic.

For instance, consider analyzing the population of a town. Frequency of age, for example, could state that the town had 500 residents under the age of 18 in simple frequency analysis. A grouped analysis would, for example, say that 32% of the town's population is under the age of 18.

Central tendency

Central tendency refers to the value averages of a set of data. There are three main ways of calculating the average value. Researchers use all three methods to prevent bias and provide an accurate representation of the information. The ways to find central tendency include:

  • Mean involves adding the total value of the responses and dividing it by the total number of responses.

  • Median is the literal center point of the data set and involves listing the numbers in ascending order and identifying the middle point in the set. If there is an even number of responses, simply find the two numbers in the center and take the average of the two.

  • Mode is when you assess the central tendency by identifying the response that occurred the most times in the data set.

Variability

Also called dispersion, variability refers to how broadly spread the values that occur are. It determines how far apart the lowest and highest values are from each other. For instance, if you take an ordered data set that starts at three and ends at nine, your range is six. Another way to assess variability is by determining the standard deviation of the data set. This tells you how far, on average, each data point lies from the mean value. The lower the standard of deviation, the more reliable the data.

Variance is a statistical term that takes the squared value of the standard deviations and averages them. It measures the degree to which the data spreads across the set. The lower the variance, the more consistent the data. For instance, consider a group of 100 people who assessed an image and rated it between one and 10. If most participants gave the image a five, the study has low variance. Conversely, if the variance level is high, it shows that the participants had split opinions on the art.

Read more: Understanding How to Complete a Risk Analysis

What is inferential statistics?

Inferential statistics is the aspect of statistics that involves drawing conclusions based on the data. Rather than a summary, inferential studies aim to estimate and test. The inference process is to investigate whether the apparent descriptive correlations apply to a larger population. For instance, consider if there was a positive correlation between academic success and height in a data set from Southern Ontario. An inference is to estimate that taller individuals in Southern Ontario are more likely to succeed.

The testing process draws actual conclusions about populations beyond that data set. Inference via testing can mean concluding that shorter individuals have reduced academic success due to more attention on taller individuals. With inferential statistics, it's important to focus on unbiased sampling to reduce the opportunity for errors. A confidence interval estimates the range of numbers that function as parameters for the statistics results. A confidence interval uses endpoints to represent the likelihood for a statistic to recur within those parameters.

Related:

  • Inferential Statistics: Definition and Pros and Cons

  • Example of Positive Correlation (And How to Calculate It)

Applications for descriptive statistics

There are multiple applications for descriptive statistics. They provide the foundational information that researchers require to make inferences. Quantitative studies that comprise descriptive statistics have three main purposes, including:

Providing basic information

Numerical data is essential for any type of statistics. It quantifies any statements and draws correlations within data. The descriptive statistical approach allows you to identify variables and isolate their incidences. The process of gathering basic information and formatting it in a usable manner is the foundation for any statistics.

Highlighting relationships

Once you organize and tally the relationships, the descriptive analysis identifies correlation. Because it both identifies variables and monitors data, descriptive approaches can easily track these relationships. Unlike inferential approaches, this type of statistics focuses only on the relationship, rather than any potential significance.

Offering a visual interpretation

Descriptive statistics use four basic methods of visualizing information. These include:

  • Graphical representations can range from scatter plots to histograms, geographic information systems to sociograms, each capturing a different representation of the data visually.

  • Central tendency uses the mode, median, and mean values to show the patterns of data using a graph or picture.

  • Dispersion visualizes the range, variance, standard deviation, and skew of the data to determine the real value of the analysis.

  • Association is a way to determine whether two variables actually have a relationship, using either the chi-square or the correlation approach.

Applications of inferential statistics

Drawing conclusions is one of the main purposes of statistics. Because of this, inferential approaches are common in any industry that relies heavily on data to inform its decisions. Some common applications include:

Medical

In medicine, producing any treatment requires rigorous testing and inferential statistics inform that testing direction. Doctors and scientists observe large numbers of people and their reactions to certain compounds. This information undergoes descriptive statistics to provide the raw data. From there, the researchers draw conclusions and make inferences about future outcomes.

For instance, consider a study where a trial medication showed 85 percent effectiveness versus the 21 percent success for a placebo. To proceed to the next stage of development, the researchers infer that the compound is effective and repeat the study based on the dispersion between the placebo and the medication.

Read more: How to Become a Medical Researcher (And Salary Expectations)

Marketing

Prediction is essential to any marketing approach, and that requires inferential analytics. Modern inferential statistics takes real-time data from analytic software to learn about audience statistics and engagement patterns. It uses this information to infer how users are likely to react to future marketing approaches.

Supply chain

The inference is essential to the overall supply chain because it allows vendors and purchasers to predict supply and demand. Inferential statistics takes the historical data and uses it to create projections for the upcoming cycle. For example, a supermarket can observe that, in October, turkey sales increase by 82% versus July. As a result, the company can plan to order more turkey in autumn to meet seasonal demand.

Technology

Using inference in technology is the basis for machine learning algorithms. Software engineers and programmers use historically significant data and use it to infer what is likely to follow. Inference programming contributes to predictive algorithms that help with spelling suggestions and search engine patterns.

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