# Top 5 Statistical Methods of Data Science In this tutorial, we will learn about top 5 statistical methods of Data Science. In the era where Data Science is evolving day by day, statistical methods play a pivotal role in extracting meaningful insights from data. These methods not only provide a framework for understanding data but also aid in making informed decisions and predictions. We will learn about top 5 most used statistical methods in Data Science in the upcoming sections of this tutorial. So let’s get started.

## Data Science Overview

Data Science is a interdisciplinary field that combines statical analysis, machine learning, computer science and domain expertise to extract insights and knowledge from structured and unstructured data. It encompasses various techniques and tools used to process, analyze, visualize and interpret large volumes of data. Below are the Key components of Data Science.

Statistics and Mathematics

• Data scientists use statistical methods to draw meaningful conclusions from data. Mathematics, especially linear algebra and calculus forms the foundation for machine learning and algorithms.

Machine Learning

• Machine learning Algorithms enable computers to learn from data and make predictions or decisions. Supervised learning, unsupervised learning and deep learning are the common techniques.

Data Exploration and Preparation

• Data preprocessing involves cleaning, transforming and organizing raw data into a format suitable for analysis. Exploratory Data Analysis (EDA) technique help in understanding data patters.

Data Visualization

• Visualization tools like Matplotlib, Seaborn and D3.js are used to create charts, graphs and interactive visual representations, aiding in understanding complex data relationships.

Big Data Technologies

• Data Science often deals with large datasets. Technologies like Hadoop and Spark help in processing and analyzing big data efficiently.

Domain Knowledge

• Understanding the specific domain (finance, healthcare etc.) is crucial. Data scientists need domain expertise to formulate relevant questions and interpret results in context.

## 1. Descriptive Statistics

Descriptive statistics in data science refer to the analysis and interpretation of data to describe its main features. These statistics summarize and organize large datasets into meaningful patterns, providing a clear understanding of the data. Descriptive statistics are fundamental in data analysis, helping researchers, analysts and data scientists to draw insights from the data. Below are the key aspects of descriptive statistics.

Measures of Central Tendency

• Mean: The average of all the values in the dataset.
• Median: The middle value when the dataset is sorted in numerical order.
• Mode: The most frequently occurring value in the dataset.

Measures of Dispersion

• Range: The difference between the maximum and minimum values.
• Variance: Measures how far a set of numbers are spread out from their average.
• Standard Deviation: The square root of the variance. It represents the average deviation from the mean.

Measure of Relationship

• Correlation: Indicates the strength and direction of a linear relationship between two variables.
• Covariance: Measures how much two variables change together.

Frequency Distributions

• Histograms: Represent the distribution of a continuous variable.
• Bar Charts: Display the frequency distribution of categorical data.

Percentiles and Quartiles

• Percentiles: Represent the value below which a given percentage of observations fall.
• Quartiles: Divide the data into four parts, each representing 25% of the dataset.

## 2. Probability Distributions

In data science, probability distributions are mathematical functions that describe the likelihood of different outcomes in a random experiment. They are fundamental concepts used to model and analyze uncertainty and variability in various data driven applications. Understanding probability distributions is crucial in statistical analysis, machine learning and data modelling. Below are the two common types of probability distributions used in data science.

Normal Distribution (Gaussian Distribution)

• Normal Distribution is characterized by its symmetric, bell-shaped curve. Many natural phenomena such as heights and IO scores tend to follow a normal distribution.
• It is defined by its mean and standard deviation. The mean determines the center of the distribution and the standard deviation controls the spread.
• Normal distributions are essential in hypothesis testing and are the basis for various statistical methods.
• Example: IQ scores of a population often follow a normal distribution.

Binomial Distribution

• Binomial Distribution models the number of successes in a fixed number of independent Bernoulli trials, where each trail has two possible outcomes (success or failure).
• It is characterized by two parameters, the number of trials (n) and the probability of success in each trial (p).
• It is used in scenarios involving binary outcomes such as success or failure of a marketing campaign.
• Example: Tossing a coin multiple times and counting the number of heads.

## 3. Hypothesis Testing

Hypothesis testing is a fundamental concept in statistics and data science used to make inferences about populations based on sample data. It allows data scientists to evaluate assumptions and draw conclusions about the underlying population from which the sample is drawn. Below are the key steps involved in Hypothesis testing.

Formulate Hypothesis

• Null Hypothesis (HO): It represents the default or status for assumption. It states that there is no significant difference or effect.
• Alternative Hypothesis (H1 or Ha): It represents the claim you want to test. It states that there is a significant difference or effect.

Select Significance Level (Alpha)

• Significance level is the probability of rejecting the null hypothesis when it is true. Commonly used values are 0.05 or 0.01.

Choose a Test statistic and Distribution

• The choice of the test statistic (Example: t-test, chi-square test, ANOVA) depends on the type of data and the research question.

Collect and Analyze Data:

• Collect sample data and calculate the test statistic from the sample.

Calculate p-value

• The p-value is the probability of observing the sample data or more extreme results if the null hypothesis is true. A smaller p-value suggests stronger evidence against the null hypothesis.

Make a Decision

• If the p-value is less than or equal to the chosen significance level. reject the null hypothesis in favor of the alternative hypothesis.
• If the p-value is greater than the chosen significance level, fail to reject the null hypothesis.

Draw Conclusion

• Based on the decision, draw conclusions about the population. If the null hypothesis is rejected, it implies there is enough evidence to support the alternative hypothesis.

## 4. ANOVA

ANOVA (Analysis of Variance) is a statistical technique used in data science to analyze the differences among group means in a sample. It helps determine whether the means of several groups are equal or if there are significant differences between them. ANOVA is particularly useful when comparing means of three or more groups, as it provides a way to understand the variation within and between these groups. Below are the steps involved in ANOVA.

Calculate Group Means

• Find the mean of each group being compared.

Calculate Overall Mean

• Compute the overall mean of all the data points from different groups.

Calculate Sum of Squares(SS)

• Between-Groups Sum of Squares (SSB):  Measures the variation between group means.
• Within-Groups Sum of Squares (SSW):  Measures the variation within each group.

Degrees of Freedom

• Calculate degrees of freedom for both between-groups and within-groups variances.

Mean Squares

• Divide the sum of squares by their respective degrees of freedom to calculate mean squares for both between-groups and within-groups variations.

F-Ratio

• Calculate the F-ratio by dividing the mean square between (MSB) by the mean square within (MSW).

F-Test

• Compare the Calculated F-ratio with the critical F-value from the F-distribution table. If the calculated F-ratio is greater than the critical F-vale, reject the null hypothesis.

## 5. Chi-Squared Test

The Chi-Squared test is a statistical test used in data science to determine if there is a significant association between categorical variables in a dataset. it is particularly useful for analyzing data where variables are categorical, meaning they represent categories or groups rather than numerical values. Below are the use-cases of Chi-Squared test in data science.

Feature Selection

• Chi-Squared test can be used in feature selection to identify the most important features in a dataset by evaluating the relationship between each feature and the target variable.

A/B Testing

• It can be used to analyze the outcomes of A/B tests, especially when the outcomes are categorical to determine if there is a significant difference between the test groups.

Text Analysis

• In a natural language processing, Chi-Squared test can be used to identify significant associations between words and categories in text data.

## Summary

We have seen 5 most used statistics methods in Data Science. There are many other methods which also plays vital role in Data Scientists activities like Linear regression, Logistic regression, Time Series analysis and so on. If you are a beginner in Data Science, I suggest you to grab some basic understanding on this field before diving into it. Refer to Data Science in Depth for more understanding.