# Statistical Analysis: Types, Examples and Process

Published
19th Mar, 2023
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The Only Way to Learn Coding

Is by Doing    Data Science is an interdisciplinary field of study that doesn’t require one to work in a certain domain to thrive. Professionals from any domain could solve business problems in the industry by leveraging the available data.

To solve these problems, often, a certain set of tools and techniques are implied, which helps to extract meaningful information from the data. Such a process of uncovering trends and patterns in the data by usage of various tools and functionalities could be referred to as Statistical Analysis. The Data Scientist online course provides a detailed understanding of various statistical analysis methods.

## What is Statistical Analysis in Data Science?

Statistics is a science concerned with collection, analysis, interpretation, and presentation of data. In Statistics, we generally want to study a population. You may consider a population as a collection of things, persons, or objects under experiment or study. It is usually not possible to gain access to all of the information from the entire population due to logistical reasons. So, when we want to study a population, we generally select a sample.

In sampling, we select a portion (or subset) of the larger population and then study the portion (or the sample) to learn about the population. Data is the result of sampling from a population.

## Types of Statistical Analysis

In the modern world, data comes in the form of 3V’s – Volume, Velocity, and Variety. The advancement of technology has resulted in businesses generating tremendous volumes of data across various sources at a very rapid pace. Companies like Google and Meta have their data servers to store dynamic data.

To extract rich information from all these diverse high-volume datasets, there are certain statistical analysis types that are in place. The following is a list of seven such statistical analysis techniques: Source: Researchgate.com

### 1. Descriptive Statistical Analysis

As mentioned earlier, every company stores large chunks of historical data, which carries a rich set of information. Descriptive Analysis is a way to analyze historical data through a series of basic statistical analysis. It gives a more holistic view of how the business has operated by identifying the weaknesses and strengths of its operation.

Some of common examples could be monthly sales growth, yearly price changes, and so on. Any business could get its answer of “what has happened?” through descriptive analysis.

### 2. Inferential Statistical Analysis

In the real world, often, the sheer volume of data makes it challenging for an analyst to draw conclusions about the entire population. Instead, you fetch a sample from the population and try to validate some of the basic assumptions from the data. This process of generating inferences about the population from the fetched sample by leveraging some of the statistical analysis tools is referred to as Inferential statistics.

To generate inferences about the population, several statistical testing methods such as mean, variance, etc., could be performed. Additionally, you would need to use some sampling techniques to fetch relevant samples from the population. Hypothesis testing and Regression Analysis could be termed as two main types of inferential statistics.

### 3. Associational Statistical Analysis

Causality is an important field in Data Science and Statistics. The urge to confidently say the ‘Why’ behind any drawn inference drives an organization and brings business value. Such an analysis that helps in identifying the relationship between multiple variables could be referred to as associational statistical analysis.

Since this type of analysis is a bit advanced, it requires the latest cutting-edge statistical analysis software. Techniques such as regression analysis, co-relation, etc., are widely used for associational statistics.

## Other Types of Statistical Analysis

### 1. Predictive Analysis

Most businesses nowadays are looking to set up a system that helps them reduce the uncertainty in an event to a large extent. For e.g., many retail stores would like to forecast the demand of their products to plan for labor and inventory accordingly. To build such systems, you need to understand the relation in the data and predict the unseen event. This entire process is known as predictive analysis.

To perform predictive analysis, knowledge of Machine Learning is required which is capable to capture the relation in huge volumes of data and generate predictions.

### 2. Prescriptive Analysis

Often a business wants to understand what it needs to do to achieve a certain event. This type of analysis is referred to as prescriptive analysis.

The decisions made in the prescriptive analysis are based on facts instead of instinct. Graph analysis, simulation, etc., could be used to perform prescriptive analysis.

### 3. Exploratory Data Analysis

When you work in a Data Science project, one of the key steps you need to perform before going to predictive modeling is exploratory data analysis.

It gives a deeper understanding of the historical data. You could perform several analysis such as checking missing values, duplicates, univariate, bi-variate, multi-variate relations, and so on.

### 4. Causal Analysis

Many organizations want to know the reason behind the model predictions. E.g.- A bank would want to know why a loan has been defaulted, or a HR would like a reason behind employees leaving. All these reasoning could be determined using causal analysis.

A lot of research is going on around model interpretability and causal analysis. Causal analysis is one such statistical research techniques that could fetch rich dividends for any company if applied correctly. You can go for KnowledgeHut Data Scientist online course to further enhance your learning and knowledge on Data Science.

## Statistical Analysis Process [Step-by-Step]

While building a statistical pipeline, it is important to follow a few steps to ensure the analysis is conducted smoothly and relevant important steps are captured:

### Step 1: Write your Hypothesis and Plan Research Design

Defining the hypothesis is the first step to understand what kind of validation is needed and the relevant data to be captured. It could be classified into Null and Alternate hypotheses. The null hypothesis is referred to the condition where any observed event is happening by chance, and it is not statistically driven. On the other hand, the alternate hypothesis tends to contradict the null hypothesis stating that the observed event is statistically driven.

Additionally, a research design could be classified into an experimental design which identifies a causal relationship, a correlation design which captures the bi-variate relation, and a descriptive design which identifies the statistical properties in historical data.

### Step 2: Collect Data from a Sample

Once the hypothesis is drawn, relevant data could be captured from various sources. Sometimes, fetching the entire corpus of data could be challenging.

Hence, samples are drawn from the population by means of various sampling techniques such as random sampling, stratified sampling, periodic sampling, and so on. As a rule of thumb, a sample size of 30 per sub-groups is recommended.

### Step 3: Summarize Data with Descriptive Statistics

The first step to understanding the information carried by the raw data is to perform a descriptive analysis on it. These would tell us how the historical data is behaving.

As part of descriptive statistics, you can find the distribution of numeric variables and frequency plots for categorical data and calculate statistical measures like mean, median, mode, standard deviation, various percentiles, and so on.

As part of descriptive statistics, you can find the distribution of numeric variables and frequency plots for categorical data and calculate statistical measures like mean, median, mode, standard deviation, various percentiles, and so on.

### Step 4: Test the Hypothesis or Make Estimates with Inferential Statistics

You can estimate parameters as well as perform hypothesis testing on the data. It could be a point estimate or a range of estimates. A point estimate gives the exact value of a certain parameter, whereas in a range of estimate you will get a range within which a certain parameter is expected to lie.

For hypothesis testing, you can calculate the p-value which would tell whether the observed event is statistically significant given the null hypothesis is true. Beyond that, there are other comparison tests such as z and t tests which will help to identify if two samples belong to the same population.

### Step 5: Interpret your Results

Calculating the p-value and identifying whether the event is statistically significant is an important part of result interpretation.

You can also calculate Type I or Type II errors while rejecting or accepting a null hypothesis.

## Top Five Considerations for Statistical Data Analysis

Data can be messy. Even a small blunder may cost you a fortune. Therefore, special care when working with statistical data is of utmost importance. Here are a few key takeaways you must consider minimizing errors and improve accuracy.

1. Define the purpose and determine the location where the publication will take place.
2. Understand the assets to undertake the investigation.
3. Understand the individual capability of appropriately managing and understanding the analysis.
4. Determine whether there is a need to repeat the process.
5. Know the expectation of the individuals evaluating reviewing, committee, and supervision.

## Statistical Analysis Methods

To carry out statistical analysis, there are certain methods which give more robust information about the data. ### 1. Mean

It is nothing but average of a numeric variable. A mean value is often used to impute missing data or get a rough estimate about the magnitude of the numeric variable. However, it is affected by outliers in the data. E.g. – You have few points 3, 4, 6, 2, 9, 6, 5, 8, 1, then the average would sum of all these points divided by 9.

mean = (3+4+6+2+9+6+5+8+1) / 9 = 4.88

### 2. Standard Deviation

It shows how the data is varying around the mean. The spread of data around the mean is captured by standard deviation.

`std = sqrt(sum(xi – mean)^2/n)`

Taking the previous example, the std would be sqrt((3-4.88)^2 +….+ (1-4.88)^2)/9) which is 2.514.

### 3. Regression

Regression analysis in statistics could be defined as a line drawn to determine the relation between independent variables with a dependent variable. E.g., in case of simple linear regression, the equation would be y = mx + c, where m is slope and c is intercepted, and ‘x’ is an independent variable here whereas ‘y’ is dependent on ‘x’.

### 4. Hypothesis Testing

In hypothesis testing, you calculate the p-value and set the significance level based on the use case. E.g., in simple linear regression, you can use p values to determine if an independent variable is statistically significant.

The null hypothesis is that the independent variable doesn’t capture any variance in the dependent variable which would be rejected if the p-value is less than the significance level which is generally kept at 0.05 by the rule of thumb.

### 5. Sample Size Determination

In situations like twitter sentiment analysis, where the dataset is so enormous, getting a sample is recommended. Hence, getting the right sample size is important which could be based on several sampling techniques or determined by the business objectives.

## Terms Used to Describe Data

When working with data, you will need to search, inspect, and characterize them. To understand the data in a tech-savvy and straightforward way, we use a few statistical terms to denote them individually or in groups.

The most frequently used terms used to describe data include data point, quantitative variables, indicator, statistic, time-series data, variable, data aggregation, time series, dataset, and database. Let us define each one of them in brief:

• Data points: These are the numerical files formed and organized for interpretations.
• Quantitative variables: These variables present the information in digit form.
• Indicator: An indicator explains the action of a community's social-economic surroundings.
• Time-series data: The time-series defines the sequential data.
• Data aggregation: A group of data points and data set.
• Database: A group of arranged information for examination and recovery.
• Time-series: A set of measures of a variable documented over a specified time.

## Benefits of Statistical Analysis

• Statistical Analysis helps a business to uncover some of the hidden patterns in the data. It helps to validate certain hypothesis and make informed decisions. On top of that, executing any Data Science workflow requires a thorough exploratory data analysis wherein you perform several descriptive as well model agnostic causal analysis.
• Even the application of statistics in business is so heavy that many organizations completely rely on simple statistical analysis to boost their workplace performance and drive business growth.

## Statistical Analysis Software/Tools

You can use languages like Python and R to execute various statistical techniques. Additionally, you can also perform statistical analysis in Excel. However, there are a few software available in the market which readily allow you to implement the statistical analysis.

### 1. SPSS Statistics

Helps in analyzing large datasets for quick insights and decision-making. SPSS Statistics is developed by IBM.

### 2. SAS

A cloud-based platform that helps in analysis and visualization of data. The SAS statistical analysis system helps in predictive modelling as well.

### 3. Stata

Used by Data Scientists for manipulation and exploration of data. It is available in four different versions depending on the data size.

## Statistical Analysis Examples

Given a dataset with both numeric and categorical features, some of the examples of statistical analysis that could be performed are-

1. Calculation of Central Tendencies– Helps to reduce the data to one representative value which helps to understand a large population.
2. Outliers in Numeric Data– Outliers often impact model performance. Hence, identifying and dealing with them would be helpful before executing an ML model.
3. Frequency Distribution of Ordinal Variable– To get a better understanding of an ordinal variable, and for better feature engineering, a frequency distribution plot is useful.
4. Inter-quartile Ranges– It is often used to identify outliers in a numeric variable.
5. Correlation- Relation between two variables could be understood by looking at their co-relation coefficient values. E.g.- In linear regression, we check how two variables are correlated during feature selection.

### Chi-square Test

Chi-square test records the contrast of a model to actual experimental data. Data is unsystematic, underdone, equally limited, obtained from independent variables, and a sufficient sample.

It relates the size of any inconsistencies among the expected outcomes and the actual outcomes, provided with the sample size and the number of variables in the connection.

## Types of Variables and Frequencies

### Types of variables

A variable is any digit, amount, or feature that is countable or measurable. Simply put, it is a variable characteristic that varies. The six types of variables include the following:

1. Dependent variable

A dependent variable has values that vary according to the value of another variable known as the independent variable.

2. Independent variable

An independent variable on the other side is controllable by experts. Its reports are recorded and equated.

3. Intervening variable

An intervening variable explicates fundamental relations between variables.

4. Moderator variable

A moderator variable upsets the power of the connection between dependent and independent variables.

5. Control variable

A control variable is anything restricted to a research study. The values are constant throughout the experiment.

6. Extraneous variable

Extraneous variable refers to the entire variables that are dependent but can upset experimental outcomes.

### Types of Frequencies

Frequency refers to the number of repetitions of reading in an experiment in a given time. Three types of frequency distribution include the following:

• Grouped, ungrouped.
• Cumulative, relative
• Relative cumulative frequency distribution.

### Features of Frequencies

• The calculation of central tendency and position (median, mean, and mode).
• The measure of dispersion (range, variance, and standard deviation).
• Degree of symmetry (skewness).
• Peakedness (kurtosis).

### Correlation Matrix

The correlation matrix is a table that shows the correlation coefficients of unique variables. It is a powerful tool that summarizes datasets points and picture sequences in the provided data. A correlation matrix includes rows and columns that display variables. Additionally, the correlation matrix exploits in aggregation with other varieties of statistical analysis.

### Inferential Statistics

Inferential statistics use random data samples for demonstration and to create inferences. They are measured when analysis of each individual of a whole group is not likely to happen.

### Applications of Inferential Statistics

Inferential statistics in educational research is not likely to sample the entire population that has summaries. For instance, the aim of an investigation study may be to obtain whether a new method of learning mathematics develops mathematical accomplishment for all students in a class.

1. Marketing organizations: Marketing organizations use inferential statistics to dispute a survey and request inquiries. It is because carrying out surveys for all the individuals about merchandise is not likely.
2. Finance departments: Financial departments apply inferential statistics for expected financial plan and resources expenses, especially when there are several indefinite aspects. However, economists cannot estimate all that use possibility.
3. Economic planning: In economic planning, there are potent methods like index figures, time series investigation, and estimation. Inferential statistics measures national income and its components. It gathers info about revenue, investment, saving, and spending to establish links among them.

## Conclusion

Statistical Analysis is one of the crucial aspects of any business who are looking to leverage the full potential of data for maximum value. The latest tools and software allow organizations to perform several analysis and generate real-time insights. These insights are then used by stakeholders for better decision-making. KnowledgeHut’s Data Science Bootcamp covers statistical analysis in depth.

### 1. What are the five basic methods of statistical analysis?

The 5 basic methods of statistical analysis are: Mean, Standard deviation, Regression, Hypothesis testing and Sample size determination.

### 2. What is the difference between data analysis and statistical analysis?

Data Analysis helps in inspecting and reporting data to non-technical people. Statistical Analysis gives more in-depth representation of the large population of data.

### 3. Why do we need to do statistical analysis?

Statistical Analysis gives a robust understanding of the data. It helps in generating insights which brings business value.

### 4. Is statistical analysis quantitative or qualitative?

Statistical analysis is quantitative in nature as it is applied on numeric data. It generates rich information by performing various descriptive and predictive analysis.

### 5. Which tool can be used for statistical analysis?

There are several tools or software available for statistical analysis. Some of them are SPSS statistics, SAS, Stata.  #### Suman Dey

Author

Suman is a Data Scientist working for a Fortune Top 5 company. His expertise lies in the field of Machine Learning, Time Series & NLP. He has built scalable solutions for retail & manufacturing organisations.