Descriptive vs. Inferential Statistics: What’s the Difference?

Key takeaways

Descriptive statistics summarize, describe, and derive facts, while inferential stats make inferences and draw conclusions about broader populations. 

• Inferential statistics test hypotheses and make predictions, while descriptive statistics look at measures of central tendency, measures of variability, and measures of association. 

• Statistics analyzes data and aims to provide valuable information about the features and structure of a data set.

• You can work with descriptive and inferential statistics in data-driven roles where you want to characterize different aspects of your data and extract meaningful insights. 

Learn to determine when to use each type of statistical test by building a solid understanding of basic statistical concepts, critical differences between differential and inferential statistics, and what the measures of each test represent. Or, start learning with the Google Data Analytics Professional Certificate. In as little as six months, you can gain an immersive understanding of the practices and processes used by a junior or associate data analyst in their day-to-day job. Upon completion, you’ll have a shareable certificate to add to your professional profile. 

Statistics basics 

Statistics is a broad topic and a subset of mathematics. Statistics analyzes data and aims to provide valuable information about the features and structure of a data set. It provides a framework for understanding and making sense of complex information. Statistics help us uncover patterns, relationships, and trends in data, allowing for informed decision-making and drawing meaningful conclusions. 

Using various statistical techniques, such as descriptive and inferential statistics, we can summarize data, test hypotheses, make predictions, and gain insights into the world around us. Ultimately, statistics empowers us to explore, understand, and extract valuable information from data to support research, business, and scientific endeavors.

Read more: What Is Statistical Analysis? Definition, Types, and Jobs

What is a population?

A population in statistics includes the complete data set for a particular problem. It's the entire group that you want to make inferences about. For example, if you study the average weight of all adults in a country, the population would be the entire adult population of that specific country.

What is a sample?

A sample in statistics is more specific than the population and is a smaller group that resides within the population. Instead of collecting data from the entire population, samples save time, resources, or feasibility. The goal is to draw a broad conclusion applicable to the larger population from the analysis conducted on the sample, such as polling a representative sample of citizens of a town instead of every person in that location. A crucial component is to ensure the sample properly represents the overall population to confirm that any conclusions drawn from the sample are valid inferences.

What are descriptive statistics?

Descriptive statistics is a subset of statistics primarily focused on analyzing and generating valuable insights about a set of data's core trends and relationships. It provides tools and techniques capable of extracting meaning from the data. Descriptive statistics explain various measures that characterize different aspects of the data. These measures summarize the data regarding its central tendency, variability, shape, and distribution.

What measures do descriptive statistics look at?

Descriptive statistics involves the examination of various types of measures to summarize and describe a data set. These measures provide insights into different aspects of the data, allowing researchers to gain a comprehensive understanding of its characteristics. The main types of measures that descriptive statistics look at include:

• Measures of central tendency: These measures focus on the center or average of the data. They provide valuable information about the usual or expected value of the data. The standard measures of central tendency are:

• Mean: The average value of all the data points selected from an arithmetic standpoint

• Median: The middle value separating the upper and lower halves of a data set

• Mode: The value or values that appear most frequently in the data set

• Measures of variability: These measures examine the overall spread of data within the entire set. Another term from this is the dispersion of data. These measures aim to quantify a data point's overall deviation from the center. Standard measures of variability include the following:

• Range: The spread between the highest and lowest values in the data set

• Variance: The average of the squared deviations from the mean

• Standard deviation: The square root of the variance provides a measure signifying how far each data point is from the mean of the entire data set on average

• Measures of shape and distribution: These measures provide insights into the data's symmetry, kurtosis, and skewness. Some measures of shape and distribution include:

• Skewness: The skewness shows the overall asymmetry of a data distribution. If the skewness is positive, the right side of the set of data has a longer and flatter curve, while a negative skewness indicates the opposite.

• Kurtosis: This measures a data set's peakedness or flatness and compares the tails in the data distribution to a standard distribution.

• Measures of association: These measures quantify the relationship or association between variables. The overall direction and power of a relationship in data becomes apparent through measures of association. Common measures of association include:

• Correlation coefficient: It measures the linear relationship between two variables and ranges from -1 to +1.

• Covariance: It measures the extent to which two variables vary together.

• Measures of frequency: These measures show the frequency or count of values or categories in a data set. They provide information about the occurrence and relative representation of different values or categories.

• Frequency or count: The total number of instances where a particular value appears in the data set

• Percent: The proportion or relative frequency in terms of parts per hundred, representing the fraction of a whole expressed as a percentage value

What is inferential statistics?

Inferential statistics is a branch of statistics that deals with making inferences or conclusions about a population based on data from a sample. It involves the use of sample data chosen from the larger population to make broad generalizations about the entire data population. Inferential statistics allows researchers to make predictions, test hypotheses, and confidently estimate population parameters.

What measures do inferential statistics look at?

Inferential statistics goes beyond descriptive statistics by utilizing sample data to draw meaningful insights that pertain to a larger population. It involves several types of measures to support the process of inference:

• Confidence intervals: These measures provide a range of numbers that a population parameter may fall within for a specific proportion of instances. A confidence interval quantifies the uncertainty associated with the estimate and provides a level of confidence (for example, 95 percent) that the valid population parameter falls within the interval.

• Hypothesis testing: This process tests hypotheses centered around the population parameters. Hypothesis tests assess the likelihood of observing a particular result under a given hypothesis and help determine whether evidence exists to support or reject the hypothesis.

• P-values: The p-value represents how strongly the underlying evidence disproves the provided null hypothesis in the test. P-values represent the probability that an outcome happened by chance. The null hypothesis has more evidence going against it if a lower p-value exists.

• Regression analysis: This statistical technique examines one dependent variable and one or more independent variables to determine their overall trend and relationship. It allows for estimating parameters, predicting outcomes, and understanding the direction and strength of associations.

• Analysis of variance (ANOVA): This measure tests for differences in the averages between multiple subsets of data. It assesses whether the observed variation between groups is statistically significant.

• Probability distributions: These provide the basis for making probabilistic inferences and conducting hypothesis tests. Examples include the normal distribution and the chi-square distribution. 

Descriptive statistics vs. inferential statistics examples

Imagine you are a nurse working in health care, and you have a set of patient data. Examples of descriptive statistics in this scenario would include measures like the range of patient blood pressure readings, the average patient body mass index or age, the percent of patients with a diagnosis like diabetes, and so on. In contrast, inferential statistics might include predicting the likelihood of a patient developing diabetes based on their age, blood pressure, and body mass index. Or, measuring the correlation between patient activity level and blood pressure reading. Descriptive statistics describe, while inferential statistics predict and infer.

When to use descriptive vs. inferential statistics

Descriptive and inferential statistics apply in different situations, depending on the goals and nature of the data analysis. Descriptive statistics summarize and describe the characteristics of a data set, whereas inferential statistics make inferences, generalize findings, test hypotheses, and support decision-making processes. 

The objectives of your research and the type of data analysis you aim to run should guide your choice of which is appropriate. For example, if you wanted to research instances of a specific disease, using inferential statistics is most helpful. It allows you to pick a sample of individuals rather than trying to gain insights from every medical record available. The analysis and conclusions obtained from the sample apply to the broader population. Understanding the context of your experiment allows you to determine if you need descriptive or inferential statistics. 

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