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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

Essential Statistical Concepts for Data Cognizance

Asmath
Asmath Last Updated : 13 Feb, 2021
6 min read

This article was published as a part of the Data Science Blogathon.

“You can have data without information, but you cannot have information without data.”

– Daniel Keys Moran

The very existence of Data Science is due to the need for understanding data. Data Science is multi-disciplinary, and arguably the strongest pillar of data science is Statistics. Remove the programming and technical components from a Data Scientist, and you have a Statistician.

A statistical mindset is key to making sense of the data. Before diving into Machine learning algorithms, it’s paramount to know what you’re dealing with!

Statistics not only enables us to fathom the data we have but also gives better direction to the Analysis. This is popularly known as Exploratory Data Analysis in Data Science, which combines statistics with programming.

The knowledge of key statistical concepts, in order to truly interpret exploratory data analysis are:

  •  Levels of Measurement
  •  Measures of Central Tendency
  •  Measures of Dispersion
  •  Measures of symmetry
  •  Correlation

Let’s grasp these concepts by asking some key questions.

 

Levels of Measurement

“What type of data am i dealing with?”

A dataset is comprised of many different columns or features. The first and foremost step is to identify which level of measurement a feature belongs to. A feature can belong to the nominal, ordinal, interval, or ratio scales.

Nominal – Used for labeling categories in the data, based on the attributes of the data.

Example: Male or Female, O positive or B positive.

Ordinal – Assigning a rank/order to data

Example: Small, Medium, or Large

Both Nominal and Ordinal Scales are used for Qualitative/Categorical Features.

Interval – This shows the magnitude of difference between observations as a fixed unit, along with their order. How small or How Large an observation is when compared to another?

Example: Temperature

Ratio – Not only measures the magnitude of difference between observations, but also the proportions in these differences.

Example: Kilograms

Both Interval and Ratio Scales are used for Quantitative/Numerical features.

Knowing the level of measurement allows us to apply suitable analytical techniques to the data.

If a categorical feature has many categories, it can be binned into fewer, more meaningful ones. It is also not required to standardize such features. Categorical Data is best visualized through Bar charts, Pie charts, and Pareto diagrams.

Numerical Data is best visualized through Histograms, Line plots, Scatter plots, and Bubble plots. Such features need to be standardized, for further analysis and modeling.

Let’s explore the diamond dataset and identify categorical and numerical variables.

statistical concepts imports

As we can observe, the features ‘cut’ and ‘clarity’ are ordinal categorical variables, labeling and ranking diamonds according to their quality and clarity respectively. Let’s visualize the ‘cut’ feature, by way of a bar chart using seaborn:

statistical concepts graph

In the dataset, the variables ‘price’ and ‘carat’ are numerical variables, of ratio scale, as they have a true zero. Let’s visualize with a scatter plot:

Statistical Concepts scatter plot

Measures of Central Tendency

“What is one value, that describes my entire data?”

A measure of central tendency is a value around which most numerical values in the dataset tend to cluster.

Mean, Median and Mode are the most commonly used measures of central tendency.

Mean or Average is the value most representative of the data. It is the sum of all observations divided by the total number of observations.

Median is the middlemost value, dividing the data into two equal parts. It is more representative of the data than the mean, in the presence of outliers.

The mode is the most recurring value in the data.

meme Statistical Concepts

 

Measures of Dispersion

“How much does my data vary?”

A measure of dispersion shows the extent to which data points disperse/ vary from the average. Such measures enable us to test the reliability of an average.

Common measures of dispersion are Range, Interquartile range and their coefficient, Variance and Standard Deviation.

Standard Deviation is probably the most popular measure, independent of any unit of measurement.

Statistical Concepts dispersion

 

Measures of Symmetry

“Which way is my data going?”

Measure the direction of the variation/dispersion of data points. They show on which side the data points in distribution are mostly concentrated. Data can be symmetrical or asymmetrical.

symmetry

The Measures of Central Tendency, Dispersion, and Skewness are broadly termed as ‘Descriptive Statistics’.

Analyzing all of them allows us to identify the main characteristics and distribution of our data.

For example, even before plotting a variable on a graph, we can tell its type by simply looking at the mean, median, and mode.

If the Mean > Median > Mode, we have a positively skewed distribution i.e. outliers lie in the right tail of the distribution.

If the Mean < Median < Mode, we have a negatively skewed distribution i.e. outliers lie in the left tail of the distribution.

If the Mean = Median = Mode, we have a symmetrical/normal distribution, which is best for data analysis and modeling.

Let’s find these measures for the ‘price’ of diamonds. You can find them individually or use the ‘.describe()‘ method for this purpose.

.describe()
output describe

 

Here the Mean (3933) > Median (2401) > Mode (605) , so we have a positively skewed distribution.

Let’s plot a histogram to confirm:

distplot

The tail of the distribution is on the right, and most of the
observations are concentrated to the left. Most of the diamonds are
priced below $2,000.

Moreover, inspecting descriptive statistics is the first step in Outlier Detection.

If the value of the mean is significantly different from the median, we immediately know that there is a presence of outliers in our data.

We can also visualize the above measures by way of box plots:

boxplot

The dots are the outliers, whereas the box represents the interquartile range. The line in the box is the median. We can see that Premium quality diamonds have the highest carats compared to other qualities.

 

Correlation

“Is there any degree of association between these features in my data?

When trying to understand the relationship between two quantitative variables, Correlation analysis is favorable.

Correlation indicates the strength and direction of the relationship between two variables. The numerical value representing correlation is called the “Correlation coefficient”.

correlation

The Correlation coefficient lies between -1 and 1.

A value of 1 or close to 1 means a high positive correlation i.e. The value of one variable increases, with the increase in the value of the other.

A value of -1 or close to -1 means a high negative correlation i.e. The value of one variable decreases, with the increase in the value of the other.

A value of 0 means there is no relation between the two variables.

Correlation is best represented by way of scatter plots and heat maps.

Let’s see the correlation between ‘carat’ and ‘price’ of diamonds, by using the ‘.corr()‘ method:

diamond plot

The correlation is 0.92, which is a high positive correlation. This means that when the carats increase, the price of the diamond increases. Let’s plot this using a heatmap:

heatmap

Correlation analysis helps us in Feature Selection. Features with high correlation, have the same impact on the dependent variable, and hence one of them can be dropped for better results.

 

Final Thoughts

A profound understanding of the concepts discussed above will enable you to not only judge your data, but also improve its quality by dealing with outliers, dropping redundant features, and normalizing the data distribution, resulting in significantly better-performing machine learning models and accurate insights!

The media shown in this article are not owned by Analytics Vidhya and is used at the Author’s discretion.

Asmath
Asmath

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