What Is Statistical Analysis: Types, Methods, Steps & Examples

What Is Statistical Analysis: Definition

Statistical analysis is a set of techniques used to analyze data and draw inferences about the population being studied. It involves organizing data, summarizing key patterns , and calculating the probability that observations could have occurred randomly. Statistics help to test hypotheses and determine the link between independent and dependent variables.

It is widely used to optimize processes, products, and services in various fields, including:

• Healthcare
• Business
• Economics
• Education
• Psychology
• Social sciences, etc.

The ultimate goal of statistical analysis is to extract meaningful insights from data and make predictions about causal relationships. It can also allow researchers to make generalizations about entire populations.

Types of Statistical Analysis

In general, there are 7 different types of statistical analysis, with descriptive, inferential and predictive ones being the most commonly used.

• Descriptive analysis
  • Summarizes data in tables, charts, or graphs to help you find patterns.
  • Includes calculating averages, percentages, mean, median and standard deviation.
• Inferential analysis
  • Draws inferences from a sample and estimates characteristics of a population, generalizing insights from a smaller group to a larger one.
  • Includes hypothesis testing and confidence intervals.
• Predictive analysis
  • Uses data to oversee future trends and patterns.
  • Relies on regression analysis and machine learning techniques.
• Prescriptive analysis
  • Uses data to make informed decisions and suggest actions.
  • Comprises optimization models and network analysis.
• Exploratory data analysis
  • Investigates data and discovers relationships between variables.
  • Requires cluster analysis, principal component analysis, and factor analysis.
• Causal analysis
  • Examines the effect of one or more independent variables on a dependent variable.
  • Implies experiments, surveys, and interviews.
• Mechanistic analysis
  • Studies how different variables interact and affect each other.
  • Includes mathematical models and simulations.

What Are Statistics Used for?

People apply statistics for a variety of purposes across numerous fields, including research, business and even everyday life. Researchers most frequently opt for statistical methods in research in such cases:

• To scrutinize a dataset in experimental and non-experimental research designs and describe the core features
• To test the validity of a claim and determine whether occurring outcomes are due to an actual effect
• To model a causal connection between variables and foresee potential links
• To monitor and improve the quality of products or services by spotting trends
• To assess and manage potential risks.

As you can see, we can avail from statistical analysis tools in literally any area of our life to interpret our surroundings and observe tendencies. Any assumptions that we make after studying a sample can either make or break our research efforts. And a meticulous statistical analysis will ensure that you are making the best guess.

Statistical Analysis Methods

There is no shortage of statistical methods and techniques that can be exercised to make assumptions. When done right, these methods will streamline your research and enlighten you with meaningful insights into the correlation between various factors or processes.

As a student or researcher, you will most likely deal with the following statistical methods of data analysis in your studies:

• Mean: average value of a dataset.
• Standard deviation: measure of variability in data.
• Regression: predicting one variable based on another.
• Hypothesis testing: statistical testing of a hypothesis.
• Sample size: number of individuals to be observed.

Let's discuss each of these statistical analysis techniques in more detail.

Mean

Imagine that you need to figure out the standard value in a set of numbers. Mean is a common type of statistical research methods that gives a measure of the average value.

The mean value is calculated by summing up all data points and then dividing it by the number of individuals. It's a useful method for exploratory analysis as it shows how much of the data fall close to the average.

Example

You want to calculate the average age of 500 people working in your enterprise. You would add up the ages of all 500 people and divide by 500 to calculate the mean age: (25+31+27+28+34...)/500=27.

Standard Deviation

Sometimes, you will need to figure out how your data is distributed. That's where a standard deviation comes in! The standard deviation is a statistical method that gives a clue of how far your data is located from the average value (mean).

A higher standard deviation indicates that the data is more spread out from the mean, while a lower standard deviation indicates that the data is more tightly clustered around the mean.

Example

Let's take the same example as above and calculate how much the ages fluctuate from the average value, which is 27. You would subtract each age from the mean and then square the result. Then you add up all results and divide them by 500 (the number of individuals). You would end up with the standard deviation of your data set.

Regression

Regression is one of the most powerful types of statistical methods, as it allows you to make accurate predictions based on existing data. It showcases the link between two or more variables and allows you to estimate any unknown values. By using regression, you can measure how one factor impacts another one and forecast future values of the dependent variable.

Example

You want to predict the price of a house based on its size. You would retrieve details on the size and price of several houses in a given district. You would then use regression analysis to determine if the size affects pricing. After recognizing a positive correlation between variables, you could then develop an equation that will allow to prognose the price of a house based on its size.

Hypothesis Testing

Hypothesis testing is another statistical analysis tool which allows you to ascertain if your assumptions hold true or not. By conducting tests, you can prove or disprove your hypothesis.

Example

You are testing a new drug and would like to know if it has any effect on lowering cholesterol level. You can use hypothesis testing to compare the results of your treatment group and control group. Significant difference between results would imply that the drug can decrease cholesterol levels.

Sample Size

In order to draw reliable conclusions from your data analysis, you need to have a sample size large enough to provide you with accurate results. The size of the sample can greatly influence the reliability of your analysis, so it's important to decide on the right number of individuals.

Example

You want to conduct a survey about customer satisfaction in your business. The sample size should be broad enough to offer you representative results. You would need to question as many clients as possible to obtain insightful information.

These are just a few examples of statistical analysis and its methods. By using them wisely, you will be able to make accurate verdicts.

Statistical Analysis Process

Now that you are familiar with the most essential methods and tools for statistical analysis, you are ready to get started with the process itself. Below we will explain how to perform statistical analysis in the right order. Stick to our detailed steps to run a foolproof study like a professional statistical analyst.

1. Prepare Your Hypotheses

Before you start digging into the numbers, it's important to formulate a hypothesis. 

Generally, there are two types of hypotheses that you will need to divide – a null hypothesis and an alternative hypothesis. The null assumption implies that the studied phenomenon is not true, while the alternative one suggests that it’s actually true.

First, detect a research question or problem that you want to investigate. Then, you should build 2 opposite statements that outline the relationship between variables in your study.

For example if you want to check how some specific exercise influences a person's resting heart rate, your hypotheses might look like this:

Example

Null hypothesis: The exercise has no effect on resting heart rate.

Alternative hypothesis: The exercise reduces resting heart rate.

2. Collect Data

Your next step in conducting statistical data analysis is to make sure that you are working with the right data. After all, you don't want to realize that the information you obtained doesn't fit your research design.

To choose appropriate data for your study, keep a few key points in mind. First, you'll want to identify a trustworthy data source. This could be data from the primary source – a survey, poll or experiment you've conducted, or the secondary source – from existing databases, research articles, or other scholarly publications. If you are running an authentic research, most likely you will need to organize your own experimental study or survey.

You should also have enough data to work with. Decide on an adequate sample size or a sufficient time period. This will help make your data analysis applicable to broader populations.

As you're gathering data, don't forget to check its format and accessibility. You'll want the data to be in a usable form, so you might need to convert or aggregate it as needed.

Sampling Techniques for Data Analysis

Now, let's ensure that you are acquainted with the sampling methods. In general, they fall into 2 main categories: probability and non-probability sampling.

Example

If you are performing a survey to investigate the shopping behaviors of people living in the USA, you can use simple random sampling. This means that you will randomly select individuals from a larger population.

3. Arrange and Clean Your Data

The information you retrieve from a sample may be inconsistent and contain errors. Before doing further manipulations, you will need to preprocess data. This is a crucial step in the process of statistical analysis as it allows us to prepare information for the next step.

Arrange your data in a logical fashion and see if you can detect any discrepancies. At this stage, you will need to look for potential missing values or duplicate entries. Here are some typical issues researchers deal with when digesting their data for a statistical study:

• Handling missing values Sometimes, certain entries might be absent. To fix this, you can either remove the entries with missing values or fill in the blanks based on already available data.
• Transforming variables In some cases, you might need to change the way a variable is measured or presented to make it more suitable for your data analysis. This can involve adjusting the scale of the variable or making its distribution more "normal."
• Resampling data Resampling is a technique used to alter data organization, like taking a smaller sample from a larger dataset or rearranging data points to create a new sample. This way, you will be able to enhance the accuracy of your analysis or test different scenarios.

Once your data is shovel-ready, you are ready to select statistical tools for data analysis and scrutinize the information.

4. Perform Data Analysis

Finally, we got to the most important stage – conducting data analysis. You will be surprised by the abundance of statistical methods. Your choice should largely depend on the type and scope of your research proposal or project. Keep in mind that there is no one-size-fits-all approach and your preference should be tailored to your particular research objective.

In some cases, descriptive statistics may be sufficient to answer the research question or hypothesis. For example, if you want to describe the characteristics of a population, such as the average income or education level, then descriptive statistics alone may be appropriate.

In other cases, you may need to use both descriptive and inferential statistics. For example, if you want to compare the means of 2 or more groups, such as the average income of men and women, then you would need to develop predictive models using inferential statistics or run hypothesis tests.

We will go through all scenarios so you can pick the right statistical methods for your specific instance.

Summing Up Data With Descriptive Statistics

To perform efficient statistical analysis, you need to see how numbers create a bigger picture. Some patterns aren't apparent from the first glance and may be hidden deep in raw data.

That's why your data should be presented in a clear manner. Descriptive statistics is the best way to handle this task.

Using Graphs

Your departure point is categorizing your information. Divide data into logical groups and think how to further visualize it. There are various graphical methods to uncover patterns:

• Bar charts: present relative frequencies of different groups
• Line charts: demonstrate how different variables change over time
• Scatter plots: show the connection between two variables
• Histograms: enable to detect the shape of data distribution
• Pie charts: provide visual representation of relative frequencies
• Box plots: help to identify significant outliers.

Example

Imagine that you are analyzing the relationship between a person's age and their income. You have collected data on the age and income of 50 individuals, and you want to confirm if there is any relationship. You decide to use a scatter plot with age on x-axis and income on y-axis. When you look at the scatter plot, you might notice that there is a general trend of income increasing with age. This might indicate that older individuals tend to have higher incomes. However, there may be some variation in data, with some people having higher or lower incomes than you expected.

Calculating Averages

Based on how your data is distributed, you will need to calculate your averages, otherwise known as measures of central tendency. There are 3 methods allowing to analyze statistical data:

• Mean: useful when data is normally distributed.
• Median: a better measure in data sets with extreme outliers.
• Mode: handy when looking for the most common value in a data set.

Assessing Variability

In addition to measures of central tendency, statistical analysts often want to assess the spread or variability of their data. There are several measures of variability popular in statistical analysis:

• Range: Difference between the maximum and minimum values.
• Interquartile range (IQR): Difference between the 75th percentile and 25th percentile.
• Standard deviation: Measure of how widely values are dispersed from the mean.
• Variance: Measure of how far a set of numbers is spread out.

While range is the simplest one, it can be influenced by extreme values. The variance and standard deviation require additional calculations, but they are more robust in terms of showing the distance of each data point from the mean.

Testing Hypotheses with Inferential Statistics

After conducting descriptive statistics, researchers can use inferential statistics to build assumptions about a larger population.

One common method of inferential statistics is hypothesis testing. This involves determining the probability that the null hypothesis is correct. If the probability is low, the null hypothesis can be denied and the alternative hypothesis is accepted. When testing hypotheses, it is important to pick the appropriate statistical test (test statistic or p value) and consider factors such as sample size, statistical significance, and effect size.

Example

Researchers test whether a new medication is effective at treating a medical condition by randomly assigning patients to a treatment group and a control group. They measure the outcome of interest and use a t-test to determine whether the medication is effective. As a result of calculation, researchers reveal that their t-value is less than the critical value. This indicates that the difference between the treatment and control groups is not statistically significant and the null hypothesis cannot be denied. As a result, researchers can conclude that the new medication is not effective at treating this medical condition.

Another method of inferential statistics is confidence intervals, which estimate the range of values that the true population parameter is likely to fall within.

If certain conditions for variables are satisfied, you can draw statistical inference using regression analysis. This technique helps researchers devise a scheme of how variables are interconnected in a study. There are different types of regression depending on the variables you're working with:

• Linear regression: used for predicting the value of a continuous variable.
• Logistic regression: chosen if scientists work with categorical data.
• Multiple regression: used to determine the relationship between several independent variables and a single outcome variable.

As you can see, there are various approaches in statistical analytics. Depending on the kind of data you are processing, you have to choose the right type of statistical analysis.

5. Interpret the Outcomes

After conducting the statistical analysis, it is important to interpret the results. This includes determining whether a hypothesis was accepted or rejected. If the hypothesis is accepted, it means that the data supports the original claim. You should further assess if data followed any patterns, and if so, what those patterns mean.

It is also important to consider any errors that could have occurred during the analysis, such as measurement error or sampling bias. These errors can affect your results and can lead to incorrect interpretations if not accounted for.

Make sure you communicate the results effectively to others. This may involve creating reports, or giving a presentation to other members of your research team. The choice of format for presenting the results will depend on the intended audience and the goals of your statistical analysis. You may also need to check the guidelines of any specific paper format you are working with. For example, if you are writing in APA style, you might need to learn more about reporting statistics in APA. 

Example

After conducting a regression analysis, you found that there is a statistically significant positive relationship between the number of hours spent studying and the exam scores. Specifically, for every additional hour of studying, the exam score increased by an average of 5 points (β = 5.0, p < 0.001). Based on these results, you can conclude that the more time students spend studying, the higher their exam scores tend to be. However, it's important to note that there may be other factors that could also be influencing the exam scores, such as prior knowledge or natural ability. Therefore, you should account for these confounding variables when interpreting the results.

Benefits of Statistical Analysis

Statistics in research is a solid instrument for understanding numerical data in a quantitative study. Here are some of the key benefits of statistical analysis:

1. Identifying patterns and relationships
2. Testing hypotheses
3. Making assumptions and forecasts
4. Measuring uncertainty
5. Comparing data.

Statistics Drawbacks

Statistical analysis can be powerful and useful, but it also has some limitations. Some of the key cons of statistics include:

1. Reliance on data accuracy and quality
2. Inability to provide complete explanations for results
3. Chance of incorrect interpretation or application of results
4. Need for specialized knowledge or software
5. Complexity of analysis.

Bottom Line on Statistical Analysis

Statistical analysis is an essential tool for any researcher, scientist, or student who are coping with quantitative data. However, accuracy of data is paramount in any statistical analysis – if the data fails, then the results can be misleading. Therefore, you should be aware of how to do statistics and account for potential errors to obtain dependable results.