The 11 Statistical Methods That Take Data To The New Level

In our data-rich era, data has grown to become overpowering. And the trick here is to navigate this massive ocean of information available to organizations and businesses and fish mission-critical data bits. But to fetch those insights, you need the right statistical data analysis tools.

The statistics look discouraging, though. Despite the immense volume of data we generate daily, a mere just 0.5% of this is used for analysis and further implementation. With the staggering amount of data and a pathetic lot of time, knowing exactly how to gather, cherry-pick, systematize, and make sense of all this information can be an uphill struggle — but statistical methods can lend you a helping hand.

With that said, here’s the lowdown on the most interesting statistical methods used for crunching data.

Top Statistical Methods In Data Analysis

Correlation analysis

Put simply, the concept of correlation is to identify whether things are similar to each other or polar opposites. Scientific-wise, correlation analysis is a method of statistical data processing, which lies in studying the correlation coefficients between variables. It is used to compare correlation coefficients between one pair or a set of pairs of attributes to establish statistical relationships between them. The correlation coefficient varies between -1 and 1. The 1 here stands for something that is equal to each other, whereas a negative one refers to polar opposites.

As a basic example of such analysis, we can apply the correlation method to compare the Dow Jones Industrial Average and the Euro Dollar. The result will tell us that those two notions do not trade the same. On the contrary, if we analyze the Dow Jones Industrial Average and the ETF of the Dow Jones Industrial Average, they do trade the same for the most part, thus having correlation between them. And that is exactly what the correlation analysis does for business. It helps us find out whether something trades effectively together or it should trade the inverse of something.

Regression analysis

IIn statistical modeling, regression analysis is a method of examining the relationship between two or more variables. Thus, this analytical method is used to predict the values ​​of one variable (dependent) based on other variables.

Regression analysis uses the chosen estimation method, the dependent variable, and one or more explanatory variables for the equation, the estimating variables.

The regression model includes outputs such as R2 and p-values ​​that tell you how well the model estimates the dependent variable.

Charts, such as scatter plot matrix, bar chart, and scatter plot, are also used in regression analysis to analyze relationships and validate assumptions.

Regression analysis is used to solve the following types of problems:

• Determine which independent variable is associated with the dependent.

• Understand the relationship between the dependent and independent variables.

• Predict the unknown values ​​of the dependent variable.

A good example of regression analysis is the relationship between home price and square footage.

In addition, regression analysis goes hand in hand with correlation analysis. Correlation analysis examines the direction and tightness of the relationship between quantitative variables, just as regression analysis examines the shape of the relationship between quantitative variables. That is, both methods study the same relationship, but from different angles, and complement each other.

Discriminant analysis

Discriminant analysis is a technique used by a researcher to analyze research data when a criterion or dependent variable is categorical and the predictor or independent variable is interval in nature. Simply put, in this analytical method, you distinguish something or group objects based on variables or other characteristics. Recall that the term categorical variable means that the dependent variable is divided into several categories. For example, three brands of computers — computer A, computer B, and computer C — might be a categorical dependent variable.

The goal of discriminant analysis is to develop discriminant functions, which are nothing more than a linear combination of independent variables that will ideally distinguish between categories of the dependent variable. This allows the researcher to examine whether there are significant differences between groups in terms of predictor variables. It also evaluates the classification accuracy.

Discriminant analysis is described by the number of categories that the dependent variable possesses.

As in statistics, everything is assumed to be infinite, so in this case, when the dependent variable has two categories, two-group discriminant analysis is used. If the dependent variable has three or more than three categories, then multiple discriminant analysis is used. The main difference between the types of discriminant analysis is that only one discriminant function can be obtained for two groups. On the other hand, in the case of multiple discriminant analysis, more than one discriminant function can be computed.

There are Linear Discriminant Analysis (Linear Discriminant Analysis) and Quadratic Discriminant Analysis (Quadratic Discriminant Analysis) — these are two classical classifiers with, as their name suggests, linear and quadratic decision-making surfaces, respectively.

There are many examples that can explain when discriminant analysis is appropriate. Let’s say you want to buy a beautiful two-story house. In this case, you are subjected to an analysis of your credit rating, and success means whether you are approved for this purchase. The constant variables here are salary, experience, age group and other decisive factors. The result of discriminant analysis will be that you will fall into either a good credit group or a bad credit group.

In the field of psychology, it can be used to distinguish between price-sensitive and price-insensitive buyers of products in terms of their psychological properties or characteristics. In the business realm, it can be used to understand the characteristics or attributes of a customer with store loyalty and a customer without store loyalty.

Factor analysis

Factor analysis is a way to reduce the number of variables related to the available observations to a smaller number of independent variables, called factors. Factors may include:

Variables that are highly correlated among themselves.

Variables from different factors that are weakly correlated with each other.

The theory behind this method is that there exist deeper factors that account for the fundamental concepts in your data. And once you figure them out, you can avoid the lower-level variables that are budding from them.

Factor analysis is also sometimes called dimensionality reduction. You can reduce the “size” of your data to one or more “supervariables”, also known as unobservables or hidden variables.

Factor analysis is not the only technique, but a family of statistical techniques that can be used to uncover hidden factors that influence observed variables.

Classification trees

Classification trees or decision tree learning is one of the most effective tools for data mining and predictive analytics that allow solving classification and regression problems. These are hierarchical tree structures consisting of rules in the “If …, then …” format. The rules are automatically generated in the process of training on the training set.

And as they are formulated almost in human language (for example, “If the sales volume is more than 1000 pieces, then the product is promising”), decision trees as analytical models are more verbalizable and interpretable than, say, neural networks.

Decision trees consist of :

Nodes: Test for the value of a certain attribute.

Branch: Refers to the test result is connected to the next node or leaf.

Leaf nodes: Terminal nodes that forecast the result (represent class labels or class distribution).

Principal component analysis and classification.

Principal component analysis or PCA is the fundamental dimensionality-reduction technique for probability and statistics. PCA is one of the go-to approaches in data science and machine learning applied to uncover the low-dimensional pattern to build models from big sets of data and reduce the dimensionality of large data sets.

Lowering the number of data variables usually presupposes compromising accuracy. And the main idea of PCA is to trade a little accuracy for simplicity while keeping as much information as possible.

The applications of principal component analysis vary greatly from domains like facial recognition and computer vision to finance, data mining, and bioinformatics.

Time series

Time series analysis is a statistical method that handles time-series data or trend analysis. It deals with sets of ordered data values observed at successive points in time.Thus, time series prediction consists of building a model to predict future events based on known past events and predicting future data before it is measured.

A typical example is predicting the opening price of a stock exchange based on its previous activity. Time series analysis has also found wide application in business planning, including such use cases as:

• Demand forecasting
• Traffic forecasting
• Anomaly detection
• Prediction of user spending habits
• Forecasting staff rotation, and others

Neural networks

Last but not least on our list of data analysis — neural networks. A neural network is a series of algorithms that try to recognize the underlying relationships in a dataset through a process that mimics the work of the human brain.

The structure of the neural network came to the programming world directly from biology.

Neural networks in the world of finance help in the design of processes such as time series forecasting, algorithmic trading, securities classification, credit risk modeling, and the construction of proprietary indicators and derived prices.

The neural network works in a similar way to the human brain’s neural network. A “neuron” in a neural network is a mathematical function that collects and classifies information according to a specific architecture. The network is very similar to statistical methods such as curve fitting and regression analysis.

Artificial neural networks (ANNs) are composed of layers of nodes containing an input layer, one or more hidden layers, and an output layer. Each node or artificial neuron connects to another and has an associated weight and threshold. If the output of any individual node exceeds a specified threshold, that node is activated, sending data to the next layer of the network. Otherwise, no data is transferred to the next layer of the network.

Neural networks rely on training data to learn and improve their accuracy over time. However, once these learning algorithms are tuned for accuracy, they become powerful tools, allowing us to classify and cluster data at high speed. Speech or image recognition tasks can take minutes, rather than hours, compared to manual identification by human specialists.

The Bottom Line

We look into data to find meanings in it. To turn scattered data bits into something useful, data scientists apply a wide array of methods and techniques based on the type of data in question. Together, these methods allow us to realize actionable insights that can be made use of instantly based on existing queries.