What Is Inferential Statistics?

Inferential statistics help us test hypotheses and estimate population parameters based on sample data. This process is often used to compare two groups in order to make informed generalizations about a larger population.

What Are Inferential Statistics Used For?

Inferential statistics is used to estimate population parameters from sample data and to test hypotheses about relationships or differences between groups.

Inferential statistics is among the most useful tools for making educated predictions about how a set of data will scale when applied to a larger population of subjects. These statistics help set a benchmark for hypothesis testing, as well as a general idea of where specific parameters will land when scaled to a larger data set, such as the larger set’s mean.

Inferential methods can involve calculating a z-score, which expresses how many standard deviations a data point lies from the mean of a normally distributed sample or population.

Types of Inferential Statistics Methods

Inferential statistics has two main types or methods it uses: hypothesis testing and regression analysis.

1. Hypothesis Testing

Hypothesis testing is a statistical method used to test the strength of an assumption from a hypothesis. It helps determine if there is enough evidence from sample data to draw conclusions about a larger population. Hypothesis testing involves the following steps:

1. State a null hypothesis (Ho) and alternative hypothesis (Ha or H1).
2. Choose the significance level (α).
3. Collect data for the statistical test.
4. Perform an appropriate statistical test and calculate a test statistic.
5. Compare the test statistic against the critical value.
6. Reject or fail to reject the null hypothesis based on findings.

Types of Statistical Tests in Hypothesis Testing

Common types of statistical tests used for hypothesis testing include:

• Z-test: Compares the means of two groups (used when standard deviation is known and sample is large).
• T-test: Compares the means of two groups (used when standard deviation is unknown and/or sample is small).
• Chi-square test: Compares categorical variables, like determining whether sample data matches population data (chi-square goodness of fit test) or if two categorical variables are related (chi-square test of independence).
• ANOVA (Analysis of Variance): Compares the difference between three or more groups of a single independent variable (one-way ANOVA), or tests the effect of one or more independent variables on two or more dependent variables (MANOVA).
• Confidence interval: Estimates the parameters of a population, or the probability that a population parameter will fall between two set values. While not a type of hypothesis test, it can be used in conjunction with or as an alternative to a hypothesis test.

2. Regression Analysis

Regression analysis is a statistical technique used to estimate the relationship between a dependent variable and one or more independent variables. 

Types of Regression Analysis

There are multiple types of regression, with some of the most common types used in inferential statistics being:

• Linear regression: Simple linear regression estimates the relationship between one dependent variable and one independent variable, and multiple linear regression estimates the relationship between one dependent variable and two or more independent variables.
• Logistic regression: Models the probability of a binary outcome (e.g., yes/no) based on one or more independent variables.

Inferential Statistics Examples

Any situation where data is extracted from a group of subjects and then used to make inferences about a larger group is an example of inferential statistics at work. Though data sets may have a tendency to become large and have many variables, inferential statistics do not have to be complicated equations. Here are a few examples of inferential statistics.

Example 1

If you poll 100 people on whether or not they enjoy coffee, and 85 of those 100 people answer yes, while 15 answer no, the data will show that 85 percent of the sample enjoy coffee. Using that data, you might estimate that 85 percent or a similar percentage of the general population enjoys coffee.

Example 2

You randomly selected a sample of all Bar Exam takers in the state of California and collected their exam scores. Using that data, you could then construct a confidence interval to estimate the average score for all California Bar Exam takers, or perform a hypothesis test to determine whether a specific study method leads to higher scores for California Bar Exam takers.

Inferential Statistics vs. Descriptive Statistics

Descriptive statistics summarize and organize characteristics of a data set, including measures of central tendency (mean, median) and dispersion (standard deviation). They describe the data without making predictions about a larger population and may also outline the sample’s distribution shape.

Inferential statistics are used to make generalizations about a population based on sample data. While they rely on the same sample data as descriptive statistics, they go a step further by estimating population parameters and testing hypotheses to assess how results might scale to the broader group. Inferential statistics are primarily used to either estimate population parameters, such as the mean, or to test hypotheses through statistical methods.

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