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Reading list

Machine Learning Basics for a Newbie
6 Steps of Machine learning Lifecycle Introduction to Predictive Modeling
Introduction to Exploratory Data Analysis & Data Insights Descriptive Statistics Inferential Statistics How to Understand Population Distributions?
Reading Data Files into Python Different Variable Datatypes
Probability for Data Science Basic Concepts of Probability Axioms of Probability Conditional Probability
Central Tendencies for Continuous Variables Spread of Data KDE plots for Continuous Variable Overview of Distribution for Continuous variables Normal Distribution Skewed Distribution Skeweness and Kurtosis Distribution for Continuous Variable
Central Tendencies for Categorical Variables Understanding Discrete Distributions Performing EDA on Categorical Variables
Dealing with Missing Values Understanding Outliers Identifying Outliers in Data Outlier Detection in Python Outliers Detection Using IQR, Z-score, LOF and DBSCAN
Sample and Population Central Limit Theorem Confidence Interval and Margin of Error
Bivariate Analysis Introduction
Covariance Pearson Correlation Spearman's Correlation & Kendall's Tau Correlation versus Causation Tabular and Graphical methods for Bivariate Analysis Performing Bivariate Analysis on Continuous-Continuous Variables
Tabular and Graphical methods for Continuous-Categorical Variables Introduction to Hypothesis Testing P-value Two sample Z-test T-test T-test vs Z-test Performing Bivariate Analysis on Continuous-Catagorical variables
Chi-Squares Test Bivariate Analysis on Categorical Categorical Variables
Multivariate Analysis A Comprehensive Guide to Data Exploration The Data Science behind IPL
Supervised Learning vs Unsupervised Learning Reinforcement Learning Generative and Descriminative Models Parametric and Non Parametric model
Machine Learning Pipeline Preparing Dataset Build a Benchmark Model: Regression Build a Benchmark Model: Classification
Evaluation Metrics for Machine Learning Everyone should know Confusion Matrix Accuracy Precision and Recall AUC-ROC Log Loss R2 and Adjusted R2
Dealing with Missing Values Replacing Missing Values Imputing Missing Values in Data Working with Categorical Variables Working with Outliers Preprocessing Data for Model Building
Understanding Cost Function Understanding Gradient Descent Math Behind Gradient Descent Assumptions of Linear Regression Implement Linear Regression from Scratch Train Linear Regression in Python Implementing Linear Regression in R Diagnosing Residual Plots in Linear Regression Models Generalized Linear Models Introduction to Logistic Regression Odds Ratio Implementing Logistic Regression from Scratch Introduction to Scikit-learn in Python Train Logistic Regression in python Multiclass using Logistic Regression How to use Multinomial and Ordinal Logistic Regression in R ? Challenges with Linear Regression Introduction to Regularisation Implementing Regularisation Ridge Regression Lasso Regression
Introduction to K Nearest Neighbours Determining the Right Value of K in KNN Implement KNN from Scratch Implement KNN in Python
Bias Variance Tradeoff Introduction to Overfitting and Underfitting Visualizing Overfitting and Underfitting Selecting the Right Model What is Validation? Hold-Out Validation Understanding K Fold Cross Validation
Introduction to Feature Selection Feature Selection Algorithms Missing Value Ratio Low Variance Filter High Correlation Filter Backward Feature Elimination Forward Feature Selection Implement Feature Selection in Python Implement Feature Selection in R
Introduction to Decision Tree Purity in Decision Tree Terminologies Related to Decision Tree How to Select Best Split Point in Decision Tree? Chi-Squares Information Gain Reduction in Variance Optimizing Performance of Decision Tree Train Decision Tree using Scikit Learn Pruning of Decision Trees
Introduction to Feature Engineering Feature Transformation Feature Scaling Feature Engineering Frequency Encoding Automated Feature Engineering: Feature Tools
Introduction to Naive Bayes Conditional Probability and Bayes Theorem Introduction to Bayesian Adjustment Rating: The Incredible Concept Behind Online Ratings! Working of Naive Bayes Math behind Naive Bayes Types of Naive Bayes Implementation of Naive Bayes
Understanding how to solve Multiclass and Multilabled Classification Problem Evaluation Metrics: Multi Class Classification
Introduction to Ensemble Techniques Basic Ensemble Techniques Implementing Basic Ensemble Techniques Finding Optimal Weights of Ensemble Learner using Neural Network Why Ensemble Models Work well?
Introduction to Stacking Implementing Stacking Variants of Stacking Implementing Variants of Stacking Introduction to Blending Bootstrap Sampling Introduction to Random Sampling Hyper-parameters of Random Forest Implementing Random Forest Out-of-Bag (OOB) Score in the Random Forest IPL Team Win Prediction Project Using Machine Learning Introduction to Boosting Gradient Boosting Algorithm Math behind GBM Implementing GBM in python Regularized Greedy Forests Extreme Gradient Boosting Implementing XGBM in python Tuning Hyperparameters of XGBoost in Python Implement XGBM in R/H2O Adaptive Boosting Implementing Adaptive Boosing LightGBM Implementing LightGBM in Python Catboost Implementing Catboost in Python
Different Hyperparameter Tuning methods Implementing Different Hyperparameter Tuning methods GridsearchCV RandomizedsearchCV Bayesian Optimization for Hyperparameter Tuning Hyperopt
Understanding SVM Algorithm SVM Kernels In-depth Intuition and Practical Implementation SVM Kernel Tricks Kernels and Hyperparameters in SVM Implementing SVM from Scratch in Python and R
Introduction to Principal Component Analysis Steps to Perform Principal Compound Analysis Computation of Covariance Matrix Finding Eigenvectors and Eigenvalues Implementing PCA in python Visualizing PCA A Brief Introduction to Linear Discriminant Analysis Introduction to Factor Analysis
Introduction to Clustering Applications of Clustering Evaluation Metrics for Clustering Understanding K-Means Implementation of K-Means in Python Implementation of K-Means in R Choosing Right Value for K Profiling Market Segments using K-Means Clustering Hierarchical Clustering Implementation of Hierarchial Clustering DBSCAN Defining Similarity between clusters Build Better and Accurate Clusters with Gaussian Mixture Models
Understand Basics of Recommendation Engine with Case Study
8 Ways to Improve Accuracy of Machine Learning Models
Introduction to Dask Working with CuML
Introduction to Machine Learning Interpretability Framework and Interpretable Models model Agnostic Methods for Interpretability Implementing Interpretable Model Understanding SHAP Out-of-Core ML Introduction to Interpretable Machine Learning Models Model Agnostic Methods for Interpretability Game Theory & Shapley Values
Introduction to Machine Learning Interpretability Framework and Interpretable Models model Agnostic Methods for Interpretability Implementing Interpretable Model Understanding SHAP Out-of-Core ML Introduction to Interpretable Machine Learning Models Model Agnostic Methods for Interpretability Game Theory & Shapley Values
Introduction to AutoML Implementation of MLBox Introduction to PyCaret TPOT Auto-Sklearn EvalML
Pickle and Joblib Introduction to Model Deployment
Deploying Machine Learning Model using Streamlit Deploying ML Models in Docker Deploy Using Streamlit Deploy on Heroku Deploy Using Netlify Introduction to Amazon Sagemaker Setting up Amazon SageMaker Using SageMaker Endpoint to Generate Inference Deploy on Microsoft Azure Cloud Introduction to Flask for Model Deploying ML model using Flask
Model Deployment in Android Model Deployment in Iphone

The Beginner’s Guide to Statistical Analysis | 5 Steps & Examples

Yana Khare
Yana Khare Last Updated : 02 Nov, 2023
7 min read

Introduction

Statistical analysis means investigating trends, patterns, and relationships using quantitative data. It is a crucial research tool used by scientists, governments, businesses, and other organizations. To draw valid results, statistical analysis requires planning from the start of the research process. You need to specify your hypotheses and decide about your research design, sample size, and sampling procedure.

A guide to explain the entire process of statistical analysis can be beneficial. Therefore, this step-by-step guide is curated to ease the understanding of the analysis. Review and get started with updating your statistical analysis knowledge. 

Table of contents

What is Statistical Analysis?

Statistical analysis is the process of collecting data and then using statistics and other data analysis techniques to identify trends, patterns, and insights. In the professional world, statistical analysts take raw data and find relationships between variables. These experts are responsible for new scientific discoveries, improving the health of our communities, and guiding business decisions.

What are the Steps for Statistical Analysis?

Statistical analysis requires five significant steps. These steps are discussed as follows: 

Step 1: Write your hypotheses and plan your research design

Hypotheses writing | Steps for Statistical Analysis
Source: Freepik

In Step 1 of the research process, the focus is on writing hypotheses and planning the research design. Hypotheses are clear statements or predictions about the relationships between variables in a study. These statements guide the research and set the direction for data collection and analysis. The process involves a literature review to understand existing knowledge on the topic and identify gaps the research aims to address.

The researcher plans the research design, defining the overall strategy for conducting the study. This includes decisions on whether the research will be experimental, observational, cross-sectional, or longitudinal. Researchers identify variables and select methods for data collection and analysis during this phase. They also consider ethical considerations and practical constraints.

A well-constructed research design is essential for the validity and reliability of the research outcomes. It illustrates the following steps, ensuring the data collected is relevant to testing the hypotheses. This step lays the foundation for a structured and systematic approach to research, helping researchers define the scope and methodology of their investigation.

Step 2: Collect Data


In this step, the research process transitions from planning to execution, with researchers collecting data from a sample. They should carefully choose the sample, which is a subset of the population under investigation, to ensure a meaningful connection with the findings.

Data Collection | Steps for statistical analysis
Source: Freepik

Data collection methods vary depending on the research design. Surveys, experiments, interviews, observations. Researchers minimize biases and enhance the reliability and validity of their data.

The sample’s representativeness is essential for drawing accurate conclusions. Random sampling or other systematic methods are often used to ensure a fair representation. Researchers carefully record and organize the collected data to facilitate subsequent analysis.

Throughout Step 2, attention is paid to the quality of the data. Successfully navigating this step is essential for producing trustworthy results in the following stages of data analysis and interpretation in the research process.

Step 3: Summarize your data with descriptive statistics

Step 3 involves the process of summarizing the data using descriptive statistics. This step is essential for understanding the dataset’s key features. Descriptive statistics include measures such as the mean, median, mode, range, and standard deviation. The primary goal of this step is to simplify the raw data, providing a clear overview. Descriptive statistics transform the collected information into meaningful patterns and trends. These summaries enable researchers to identify tendencies, assess the variability of the data, and recognize any notable problems.

Using descriptive statistics, researchers can communicate critical characteristics of their data to an audience. This summary serves as a base for the subsequent statistical analyses, guiding researchers in making informed decisions about hypothesis testing or estimating population parameters. Successful execution of this enhances the interpretability of the dataset.

Descriptive statistics and inferential statistics | Steps for Statistical Analysis
Source: Freepik

Step 4: Test hypotheses or make estimates with inferential statistics

Step 4 involves the application of inferential statistics to test hypotheses or make estimates based on the collected data. This step plays a primary role in drawing meaningful conclusions about the broader population from which the sample was drawn.

Researchers employ various statistical tests depending on the nature of their hypotheses and the research design. Standard techniques include t-tests, ANOVA, regression analysis, and more. The research objectives and the characteristics of the variables involved determine the choice of the appropriate test. This step consists of calculating probabilities, confidence intervals, and p-values to assess the statistical significance of findings.

Researchers interpret the results in the context of their hypotheses and the research objectives. Statistical significance indicates whether the results are genuine or could have occurred by chance. The outcomes of inferential statistics guide researchers in either accepting or rejecting hypotheses and contribute to the overall understanding of the process under investigation.

Successful execution of Step 4 is essential for deriving meaningful insights from the data and informing decision-making.

Step 5: Interpret your results

Results from analysis | Steps for Statistical Analysis
Source: Freepik

The final phase of the research process is interpreting the results derived from inferential statistics and concluding. Researchers analyze the statistical findings in research questions. This step involves considering the significance of the results in addition to their statistical significance. Transparency is essential for understanding the results accurately and precisely. 

The interpretation phase also involves comparing the results with existing literature, theories, or practical applications. Researchers may identify areas for further modifications to existing models. Clear communication of the study’s implications is essential to accurate results.

Example of Statistical Analysis

Problem Statement

You’re a researcher interested in understanding if there’s a relationship between the number of hours students spend studying and their final exam scores. You want to test the hypothesis that more study hours increase scores. Here’s how you can go through each step of the research process:

Step 1: Write your hypotheses and plan your research design

  • Null Hypothesis (H0): There is no significant relationship between the number of study hours and final exam scores.
  • Alternative Hypothesis (H1): There is a significant positive relationship between the number of study hours and final exam scores.

Research Design: You will collect data from a random sample of students and analyze the relationship between study hours and exam scores.

Step 2: Collect data

You collect data from 50 students by recording their study hours and final exam scores. Here’s a sample of the data:

import pandas as pd

data = {

    'Study_Hours': [3, 4, 2, 6, 5, 5, 7, 8, 9, 4, 6, 3, 2, 7, 8, 5, 4, 6, 7, 5, 4, 2, 3, 6, 8, 7, 5, 4, 2, 3, 5, 6, 7, 9, 5, 4, 3, 2, 7, 8, 9, 4, 5, 6, 2, 3, 5, 7],

    'Exam_Scores': [75, 80, 70, 85, 90, 95, 88, 92, 96, 78, 87, 72, 68, 89, 93, 86, 80, 85, 91, 88, 78, 70, 75, 86, 91, 89, 82, 80, 73, 69, 77, 85, 92, 94, 81, 79, 76, 70, 89, 93, 96, 81, 88, 92, 71, 74, 84, 90]

}

df = pd.DataFrame(data)

Step 3: Summarize your data with descriptive statistics

You need to get an overview of the data:

# Summary statistics

summary_stats = df.describe()

# Correlation between study hours and exam scores

correlation = df['Study_Hours'].corr(df['Exam_Scores'])

Explanation:

The described function provides statistics like mean, standard deviation, minimum, maximum, and quartiles for study hours and exam scores.

The corr function calculates the correlation coefficient to understand the relationship between study hours and exam scores.

Step 4: Test hypotheses or make estimates with inferential statistics

Inferential statistics can help you test the hypothesis. You can perform a simple linear regression to understand the relationship between study hours and exam scores:

import statsmodels.api as sm

# Add a constant to the independent variable

X = sm.add_constant(df['Study_Hours'])

# Fit the regression model

model = sm.OLS(df['Exam_Scores'], X).fit()

# Get regression results

regression_results = model.summary()

Explanation:

You use the OLS (Ordinary Least Squares) regression method to fit a linear model to the data.

The summary provides information about the relationship, including coefficients and p-values.

Step 5: Interpret your results

In this example, we would interpret the results from the regression analysis. If the p-value is less than your chosen significance level (e.g., 0.05), we may conclude that there is a significant positive relationship between study hours and exam scores.  

Conclusion

Statistical analysis helps generate meaningful insights from a large dataset. Statistical analysis includes writing hypotheses, planning, collecting, summarizing, and interpreting. 

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Frequently Asked Questions

Q1. What are the five basic statistical analyses?

Ans. The five basic statistical analyses are descriptive statistics, inferential statistics, regression analysis, hypothesis testing, and analysis of variance (ANOVA).

Q2. What is an example of a statistical analysis?

Ans. An example of a statistical analysis is determining if there’s a correlation between study hours and exam scores using regression analysis.

Q3. Why is statistical analysis used so much?

Ans. Statistical analysis is used extensively because it enables data-driven decision-making, helps identify trends, patterns, and relationships in data, and provides a scientific basis for understanding complex phenomena.

Q4. What are the two branches of statistical analysis?

Ans. The two branches of statistical analysis are descriptive statistics, which summarizes data, and inferential statistics, which draws conclusions and makes predictions based on data.

Yana Khare
Yana Khare

A 23-year-old, pursuing her Master's in English, an avid reader, and a melophile. My all-time favorite quote is by Albus Dumbledore - "Happiness can be found even in the darkest of times if one remembers to turn on the light."

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