From ANOVA to regression: 10 key statistical analysis methods explained

Every action we take generates data. When you stream a video, browse a website, or even make a purchase, valuable data is created. However, without statistical analysis, the potential of this information remains untapped. 

No matter your industry, statistical analysis turns data into actionable insights, driving everything from product innovation to public policy and research. Whether optimizing user experiences, shaping evidence-based policies, or validating scientific discoveries, statistical analysis allows you to leverage data to fuel growth and innovation.

Understanding how different statistical analysis methods work can help you make the right choice. Each is applicable to a certain situation, data type, and goal.

Statistical analysis is the process of collecting, organizing, and interpreting data. The goal is to identify trends and relationships. These insights help analysts forecast outcomes and make strategic business decisions.

This type of analysis can apply to multiple business functions and industries, including the following:

• Finance: helps companies assess investment risks and performance

• Marketing: enables marketers to identify customer behavior patterns, segment markets, and measure the effectiveness of advertising campaigns

• Operations: helps streamline process optimization and reduce waste

• Human resources: helps track employee performance trends or analyze turnover rates

• Product development: helps with feature prioritization, evaluating A/B test results, and improving product iterations based on user data

• Scientific research: supports hypothesis testing, experiment validation, and the identification of significant relations in data

• Government: informs public policy decisions, such as understanding population demographics or analyzing inflation

With high-quality statistical analysis, businesses can base their decisions on data-driven insights rather than assumptions. This helps build more effective strategies and ultimately improves the bottom line.

Statistical analysis is an integral part of working with data. Implementing it at different stages of operations or research helps you gain insights that prevent costly errors.

Here are the key benefits of statistical analysis:

Informed decision-making

Statistical analysis allows businesses to base their decisions on solid data rather than assumptions.

By collecting and interpreting data, decision-makers can evaluate the potential outcomes of their strategies before they implement them. This approach reduces risks and increases the chances of success.

Understanding relationships and trends

In many complex environments, the key to insights is understanding relationships between different variables. Statistical methods such as regression or factor analysis help uncover these relationships.

Uncovering correlations through statistical methods can pave the way for breakthroughs in fields like medicine, but the true impact lies in identifying and validating cause-effect relationships. By distinguishing between simple associations and meaningful patterns, statistical analysis helps guide critical decisions, such as developing potentially life-saving treatments.

Predicting future outcomes

Statistical analysis, particularly predictive analysis and time series analysis, provides businesses with tools to forecast events based on historical data.

These forecasts help organizations prepare for future challenges (such as fluctuations in demand, market trends, or operational bottlenecks). Being able to predict outcomes allows for better resource allocation and risk mitigation.

Improving efficiency and reducing waste

Using statistical analysis can lead to improved efficiency in areas where waste occurs. In operations, this can result in streamlining processes.

For example, manufacturers can use causal analysis to identify the factors contributing to defective products and then implement targeted improvements to eliminate the causes.

Enhancing accuracy in research

In scientific research, statistical methods ensure accurate results by validating hypotheses and analyzing experimental data.

Methods such as regression analysis and ANOVA (analysis of variance) allow researchers to draw conclusions from experiments by examining relationships between variables and identifying key factors that influence outcomes.

Without statistical analysis, research findings may not be reliable. This could result in teams drawing incorrect conclusions and forming strategies that cost more than they’re worth.

Validating business assumptions

When businesses make assumptions about customer preferences, market conditions, or operational outcomes, statistical analysis can validate them.

For example, hypothesis testing can provide a framework to either confirm or reject an assumption. With these results at hand, businesses reduce the likelihood of pursuing incorrect strategies and improve their overall performance.

The two main types of statistical analysis are descriptive and inferential. However, there are also other types. Here’s a short breakdown:

Descriptive analysis

Descriptive analysis focuses on summarizing and presenting data in a clear and understandable way. You can do this with simple tools like graphs and charts.

This type of statistical analysis helps break down large datasets into smaller, digestible pieces. This is usually done by calculating averages, frequencies, and ranges. The goal is to present the data in an orderly fashion and answer the question, “What happened?”

Businesses can use descriptive analysis to evaluate customer demographics or sales trends. A visual breakdown of complex data is often useful enough for people to come to useful conclusions.

Diagnostic statistics

This analysis is used to determine the cause of a particular outcome or behavior by examining relationships between variables. It answers the question, “Why did this happen?”

This approach often involves identifying anomalies or trends in data to understand underlying issues.

Inferential analysis

Inferential analysis involves drawing conclusions about a larger population based on a sample of data. It helps predict trends and test hypotheses by accounting for uncertainty and potential errors in the data.

For example, a marketing team can arrive at a conclusion about their potential audience’s demographics by analyzing their existing customer base. Another example is vaccine trials, which allow researchers to come to conclusions about side effects based on how the trial group reacts.

Predictive analysis

Predictive analysis uses historical data to forecast future outcomes. It answers the question, “What might happen in the future?”

For example, a business owner can predict future customer behavior by analyzing their past interactions with the company. Meanwhile, marketers can anticipate which products are likely to succeed based on past sales data.

This type of analysis requires the implementation of complex techniques to ensure the expected results. These results are still educated guesses—not error-free conclusions.

Prescriptive analysis

Prescriptive analysis goes beyond predicting outcomes. It suggests actionable steps to achieve desired results.

This type of statistical analysis combines data, algorithms, and business rules to recommend actual strategies. It often uses optimization techniques to suggest the best course of action in a given scenario, answering the question, “What should we do next?”

For example, in supply chain management, prescriptive analysis helps optimize inventory levels by providing specific recommendations based on forecasts. A bank can use this analysis to predict loan defaults based on economic trends and adjust lending policies accordingly.

Exploratory data analysis

Exploratory data analysis (EDA) allows you to investigate datasets to discover patterns or anomalies without predefined hypotheses. This approach can summarize a dataset’s main characteristics, often using visual methods.

EDA is particularly useful for uncovering new insights that weren’t anticipated during initial data collection.

Causal analysis

Causal analysis seeks to identify cause-and-effect relationships between variables. It helps determine why certain events happen, often employing techniques such as experiments or quasi-experimental designs to establish causality.

Understanding the “why” of specific events can help design accurate proactive and reactive strategies.

For example, in marketing, causal analysis can be applied to understand the impact of a new advertising campaign on sales.

Bayesian statistics

This approach incorporates prior knowledge or beliefs into the statistical analysis. It involves updating the probability of a hypothesis as more evidence becomes available.

Depending on your industry, needs, and budget, you can implement different statistical analysis methods. Here are some of the most common techniques:

1. T-tests

A t-test helps determine if there’s a significant difference between the means of two groups. It works well when you want to compare the average performance of two groups under different conditions.

There are different types of t-tests, including independent or dependent.

T-tests are often used in research experiments and quality control processes. For example, they work well in drug testing when one group receives a real drug and another receives a placebo. If the group that received a real drug shows significant improvements, a t-test helps determine if the improvement is real or chance-related.

2. Chi-square tests

Chi-square tests examine the relationship between categorical variables. They compare observed results with expected results. The goal is to understand if the difference between the two is due to chance or the relationship between the variables.

For instance, a company might use a chi-square test to analyze whether customer preferences for a product differ by region.

It’s particularly useful in market research, where businesses analyze responses to surveys.

3. ANOVA

ANOVA, which stands for analysis of variance, compares the means of three or more groups to determine if there are statistically significant differences among them.

Unlike t-tests, which are limited to two groups, ANOVA is ideal when comparing multiple groups at once.

• One-way ANOVA: analysis with one independent variable and one dependent variable

• Two-way ANOVA: analysis with two independent variables

• Multivariate ANOVA (MANOVA): analysis with more than two independent variables

Businesses often use ANOVA to compare product performance across different markets and evaluate customer satisfaction across various demographics. The method is also common in experimental research, where multiple groups are exposed to different conditions.

4. Regression analysis

Regression analysis examines the relationship between one dependent variable and one or more independent variables. It helps businesses and researchers predict outcomes and understand which factors influence results the most.

This method determines a best-fit line and allows the researcher to observe how the data is distributed around this line.

It helps economists with asset valuations and predictions. It can also help marketers determine how variables like advertising affect sales.

A company might use regression analysis to forecast future sales based on marketing spend, product price, and customer demographics.

6. Time series analysis

Time series analysis evaluates data points collected over time to identify trends. An analyst records data points at equal intervals over a certain period instead of doing it randomly.

This method can help businesses and researchers forecast future outcomes based on historical data. For example, retailers might use time series analysis to plan inventory around holiday shopping trends, while financial institutions rely on it to track stock market trends. An energy company can use it to evaluate consumption trends and streamline the production schedule.

7. Survival analysis

Survival analysis focuses on time-to-event data, such as the time it takes for a machine to break down or for a customer to churn. It looks at a variable with a start time and end time. The time between them is the focus of the analysis.

This method is highly useful in medical research—for example, when studying the time between the beginning of a patient’s cancer remission and relapse. It can help doctors understand which treatments have desired or unexpected effects.

This analysis also has important applications in business. For example, companies use survival analysis to predict customer retention, product lifespan, or time until product failure.

8. Factor analysis

Factor analysis (FA) reduces large sets of variables into fewer components. It’s useful when dealing with complex datasets because it helps identify underlying structures and simplify data interpretation. This analysis is great for extracting maximum common variance from all necessary variables and turning them into a single score.

For example, in market research, businesses use factor analysis to group customer responses into broad categories. This helps reveal hidden patterns in consumer behavior.

It’s also helpful in product development, where it can use survey data to identify which product features are most important to customers.

9. Cluster analysis

Cluster analysis groups objects or individuals based on their similarities. This technique works great for customer segmentation, where businesses group customers based on common factors (such as purchasing behavior, demographics, and location). 

Distinct clusters help companies tailor marketing strategies and develop personalized services. In education, this analysis can help identify groups of students who require additional assistance based on their achievement data. In medicine, it can help identify patients with similar symptoms to create targeted treatment plans.

10. Principal component analysis

Principal component analysis (PCA) is a dimensionality-reduction technique that simplifies large datasets by converting them into fewer components. It helps remove similar data from the line of comparison without affecting the data’s quality.

PCA is widely used in fields like finance, marketing, and genetics because it helps handle large datasets with many variables. For example, marketers can use PCA to identify which factors most influence customer buying decisions.

Since numerous statistical analysis methods exist, choosing the right one for your needs may be complicated. While all of them can be applicable to the same situation, understanding where to start can save time and money.

Define your objective

Before choosing any statistical method, clearly define the objective of your analysis. What do you want to find out? Are you looking to compare groups, predict outcomes, or identify relationships between variables?

For example, if your goal is to compare averages between two groups, you can use a t-test. If you want to understand the effect of multiple factors on a single outcome, regression analysis could be the right choice for you.

Identify your data type

Data can be categorical (like yes/no or product types) or numerical (like sales figures or temperature readings).

For example, if you’re analyzing the relationship between two categorical variables, you may need a chi-square test. If you’re working with numerical data and need to predict future outcomes, you could use a time series analysis.

Evaluate the number of variables

The number of variables involved in your analysis influences the method you should choose. If you’re working with one dependent variable and one or more independent variables, regression analysis or ANOVA may be appropriate.

If you’re handling multiple variables, factor analysis or PCA can help simplify your dataset.

Determine sample size and data availability

The size of your dataset impacts the method you should use. Large datasets with numerous data points might require more complex techniques like regression or cluster analysis. However, smaller datasets can benefit from simpler approaches such as t-tests or chi-square tests. You can use this calculator to calculate your sample size data.

Consider the assumptions of each method

Each statistical method has its own set of assumptions, such as the distribution of the data or the relationship between variables.

For example, ANOVA assumes that the groups being compared have similar variances, while regression assumes a linear relationship between independent and dependent variables.

Understand if observations are paired or unpaired

When choosing a statistical test, you need to figure out if the data is paired or unpaired.

• Paired data: the same subjects are measured more than once, like before and after a treatment or when using different methods.

• Unpaired data: each group has different subjects.

For example, if you’re comparing the average scores of two groups, use a paired t-test for paired data and an independent t-test for unpaired data.

Each statistical analysis method is designed to simplify the process of gaining insights from a specific dataset. Understanding which data you need to analyze and which results you want to see can help you choose the right method.

With a comprehensive approach to analytics, you can maximize the benefits of insights and streamline decision-making. This isn’t just applicable in research and science. Businesses across multiple industries can reap significant benefits from well-structured statistical analysis.