Types of Statistical Data Analysis

Statistics data analysis is a class of analysis that includes different techniques and methods for collection, data analysis, interpretation and presentation of data. Knowing the approach to data analysis is one of the crucial aspects that allows drawing a meaningful conclusion. In this article, the most fundamental types of statistical data analysis will be described. The authors will explain all the terms and concepts easily.

Statistical data analysis is the process of collecting, examining, and interpreting data to uncover patterns, trends, relationships, and insights. It involves the application of statistical methods and techniques to analyze data sets and draw meaningful conclusions. This process is fundamental in various fields, including business, science, engineering, healthcare, and social sciences, to make informed decisions based on empirical data.

Descriptive statistics are intended to make a basic summary of data and variables in the sample while providing point measures as the main features of a dataset.

Measures of Central Tendency

• Mean: The arithmetical mean, which is the mean value of all observation points. It is done by summing up all the values and dividing them by the total number of values.
• Median: The central value in a dataset when the values are linearly sorted in order of rise. The median is computed as the average of the two middle numbers if the dataset is even where there is an equal number of observations.
• Mode: This is the most recurring value in a set of data. It can be used as the only mode, multiple modes, or it can have no modes at all.

Measures of Variability

• Range: Such as Minimum/Maximum. The difference between the highest and lowest data points in a dataset. It delineates the values by generating a primary method of their spread.
• Variance: The averaging of the squared deviations away from the mean. This helps to find out how much the data values in the data set are uniformity with the mean.
• Standard Deviation: The square root of the variance which gives us the standard deviation. It is a more intuitive measure of variability as the scale of the estimate is matched the data units.
• Interquartile Range (IQR): It scores the distance stretching from the 25th percentile (IQR: 1) to 75th percentile (IQR:3). It monitors at what tier the middle 50th percentile of the distribution lies.

Frequency Distribution

• Histogram: Trend line representing the frequency distribution of a dataset. The horizontal axis (X-axis) is divided into blocks of length, and the height of each bar represents the frequency of points within each interval.
• Bar Chart: A chart with rectangular bars as the frequency or count of the categorical data in the form of bars below each other. Bar sizes reflect the amount they are worth.
• Pie Chart: A circular graph of dedicated spaces to various sectors, each having a proportion of the total area. It is a useful tool for making proportional relations between the whole and its parts.

• Contingency Tables: Tables made of variable category set up in order to analyze the relatives of two categorical variables. For each cell in the table there are a given number of references or counts for a certain combination of variables.

Statistical concepts known as inferential statistics are those on which a population can make a conclusion after a sample of data from the same population has been taken.

Estimation

• Point Estimation: Offers an assessment via a single statistic that estimates the population parameter (m). g. Herein comes the all-important step of graphical data exploration, which involves both overall consumption visualizations via charts (histograms or line graphs) and juxtapositions of particular mean items as an estimate of population mean).
• Interval Estimation (Confidence Intervals): Ranges where the parameters of the population require at the confidence at certain levels, are. g. 95% confidence interval).

Hypothesis Testing

The key terms in hypothesis testing are:

• Null Hypothesis (H0): The hypothesis postulates the existence of no effect or no differences. The very rebuttal of the hypothesis is the test that will be conducted.
• Alternative Hypothesis (H1): In the aspect of presenting my hypothesis in the significance question, I will say that there is an effect or difference. This is the information or insight which the researcher wants to show that the inquiry activity should be engaged in.
• P-value: The risk of observing the data or something more extreme (though less likely), when we are right if the null hypothesis is true. A lower p-value indicates that it is highly improbable that they falsify the null hypothesis.

Regression Analysis

• Simple Linear Regression: A procedure of investigating the interaction between two independent variables plotted on a graph and fitting a straight line equation to recorded observations is known as linear regression.
• Multiple Regression: Digital treatment extends simple linear regression from using a single independent variable to a few by predicting the dependent variable.
• Logistic Regression: Used for determining results of 2 outcomes which are categorical. g. Prediction of a response is the main objective of this modeling technique that utilizes one or more predictor variables for the same.

The data analysis approach includes techniques that aim to give a short description of key characteristics through the use of visual methods.

Graphical Techniques

• Scatter Plots: Charts indicating the correlation between two variables with their values. Periodically, each mark in the grid stands for an observation.
• Box Plots: The chart displays raw data that indicate distribution through their quartiles. They can highlight outliers.
• Stem-and-Leaf Plots: A statistic demonstrates how data is evenly distributed. We assign each number to be the stem (the first part) and the leaf (the last digit).

• Summary Statistics: Another relevant measure is mean, median and mode, which serve the purpose of summarizing the data.
• Correlation Analysis: It gauges the level of influence and the direction of one variable’s impact on another variable. This measure is quantified by the linear correlation coefficient, which may range from -1 with a maximum positive value of 1.

Retrospective analysis enables deriving inferences about future results via the sensitive evaluation of prior events.

Time Series Analysis

• Moving Averages: Fitting techniques that estimate the curvature of data points to identify trends in the data.
• Exponential Smoothing: A forecasting technique which employs an exponential moving average, taking the significance of decreasing past observations into consideration, in order to predict future values.
• ARIMA Models (AutoRegressive Integrated Moving Average): Utilizes autoregression to make the data stationary, combines it with the moving average model for the purpose of time series forecasting.

Multivariate analysis seeks to study numerous parameters and then to see their connections and consequences.

Factor Analysis

Identifying Underlying Relationships: Conversion of data volume into latent arrays of variables that explain the observed correlations between different variables.

Principal Component Analysis (PCA)

Reducing Dimensionality: PCA Transforms data into principal components by using them in the first tower to show the peak of variations and simplifying the data set while retaining most of the information.

Cluster Analysis

• K-means Clustering: Partition data into k clusters sharing similarity of content by minimizing the variance internal to the clusters.
• Hierarchical Clustering: Hierarchical structure accomplished by creating a sequence based on distance metric values to form a tree-like structure.

Bayesian Analysis

• Bayesian analysis like the prior information is already given during the modeling process.
• MCMC (Markov Chain Monte Carlo) represents one of the most crucial steps in mixture clustering algorithms.
• Sampling Methods: Techniques like Metropolis-Hastings algorithm and Gibbs sampling are used in order to get the posterior distribution, if it is hard or impossible to compute directly.

Non-parametric methods, on just the contrary, do not presuppose the specific parameters of the data and therefore, they work for any kind of data.

Rank-Based Tests

• Mann-Whitney U Test: A nonparametric test based on the chi-squared statistic fitting for finding out whether independent groups differ from each other.
• Kruskal-Wallis Test: Addition to the one sample Mann-Whitney U test where more than two groups are compared.

Distribution-Free Methods

• Bootstrapping: A sampling method that repeatedly carries out a process of drawing samples from the dataset in order to estimate the probability distribution of sampling.
• Permutation Tests: Check the null hypothesis using the ratios of test statistics calculated from randomizing the order of the data points.