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Machine Learning Model Evaluation

If we were to list the technologies that have revolutionized and changed our lives for the better, then Machine Learning will occupy the top spot. This cutting-edge technology is used in a wide variety of applications in day-to-day life. ML has become an integral component in most of the industries like Healthcare, Software, Manufacturing, Business and aims to solve many complex problems while reducing human effort and dependency. This it does by accurately predicting solutions for problems and various applications.Generally there are two important stages in machine learning. They are Training & Evaluation of the model. Initially we take a dataset to feed to the machine learning model, and this process of feeding the data to our Designed ML model is called Training. In the training stage, the model learns the behavior of data, capable of handling different forms of data to better suit the model, draws conclusion from the data and finally predicts the end results using the model.This technique of training helps a user to know the output of the designed machine learning model for the given problem, the inputs given to the model, and the output that is obtained at the end of the model.But as machine learning model engineers, we might doubt the applicability of the model for the problem and have questions like, is the developed Machine learning model best suited for the problem, how accurate the model is, how can we say this is the best model that suits the given problem statement and what are the measures that describe model performance?In order to get clarity on the above questions, there is a technique called Model Evaluation, that describes the performance of the model and helps us understand if the designed model is suitable for the given problem statement or not.This article helps you to know, the various measures involved in calculating performance of a model for a particular problem and other key aspects involved.What is Model Evaluation?This technique of Evaluation helps us to know which algorithm best suits the given dataset for solving a particular problem. Likewise, in terms of Machine Learning it is called as “Best Fit”. It evaluates the performance of different Machine Learning models, based on the same input dataset. The method of evaluation focuses on accuracy of the model, in predicting the end outcomes.Out of all the different algorithms we use in the stage, we choose the algorithm that gives more accuracy for the input data and is considered as the best model as it better predicts the outcome. The accuracy is considered as the main factor, when we work on solving different problems using machine learning. If the accuracy is high, the model predictions on the given data are also true to the maximum possible extent.There are several stages in solving an ML problem like collection of dataset, defining the problem, brainstorming on the given data, preprocessing, transformation, training the model and evaluating. Even though there are several stages, the stage of Evaluation of a ML model is the most crucial stage, because it gives us an idea of the accuracy of model prediction. The performance and usage of the ML model is decided in terms of accuracy measures at the end.Model Evaluation TechniquesWe have known that the model evaluation is an Integral part in Machine Learning. Initially, the dataset is divided into two types, they are “Training dataset” and “Test dataset”. We build the machine learning model using the training dataset to see the functionality of the model. But we evaluate the designed Model using a test dataset, which consists of unseen or unknown samples of the data that are not used for training purposes. Evaluation of a model tells us how accurate the results were. If we use the training dataset for evaluation of the model, for any instance of the training data it will always show the correct predictions for the given problem with high accuracy measures, in that case our model is not adequately effective to use.  There are two methods that are used to evaluate a model performance. They are  Holdout Cross ValidationThe Holdout method is used to evaluate the model performance and uses two types of data for testing and training. The test data is used to calculate the performance of the model whereas it is trained using the training data set.  This method is used to check how well the machine learning model developed using different algorithm techniques performs on unseen samples of data. This approach is simple, flexible and fast.Cross-validation is a procedure of dividing the whole dataset into data samples, and then evaluating the machine learning model using the other samples of data to know accuracy of the model. i.e., we train the model using a subset of data and we evaluate it with a complementary data subset. We can calculate cross validation based on the following 3 methods, namely Validation Leave one out cross validation (LOOCV) K-Fold Cross ValidationIn the method of validation, we split the given dataset into 50% of training and 50% for testing purpose. The main drawback in this method is that the remaining 50% of data that is subjected to testing may contain some crucial information that may be lost while training the model. So, this method doesn’t work properly due to high bias.In the method of LOOCV, we train all the datasets in our model and leave a single data point for testing purpose. This method aims at exhibiting lower bias, but there are some chances that this method might fail because, the data-point that has been left out may be an outlier in the given data; and in that case we cannot produce better results with good accuracy. K-fold cross validation is a popular method used for evaluation of a Machine Learning model. It works by splitting the data into k-parts. Each split of the data is called a fold. Here we train all the k subsets of data to the model, and then we leave out one (k-1) subset to perform evaluation on the trained model. This method results in high accuracy and produces data with less bias.Types of Predictive ModelsPredictive models are used to predict the outcomes from the given data by using a developed ML model. Before getting the actual output from the model, we can predict the outcomes with the help of given data. The prediction models are widely used in machine learning, to guess the outcomes from the data before designing a model. There are different types of predictive models: Classification model Clustering model Forecast model Outlier modelA Classification model is used in decision making problems. It separates the given data into different categories, and this model is best suited to answer “Yes” or “No” questions. It is the simplest of all the predictive models.Real Life Applications: Projects like Gender Classification, Fraud detection, Product Categorization, Malware classification, documents classification etc.Clustering models are used to group the given data based on similar attributes. This model helps us to know how many groups are present in the given dataset and we can analyze what are the groups, which we should focus on to solve the given problem statement.Real Life Applications: Projects like categorizing different people present in a classroom, types of customers in a bank, identifying fake news, spam filter, document analysis etc.A forecast model learns from the historical data in order to predict the new data based on learning. It majorly deals with metric values.Real Life Applications: Projects like weather forecast, sales forecast, stocks prices, Heart Rate Monitoring etc.Outlier model focuses on identifying irrelevant data in the given dataset. If the data consists of outliers, we cannot get good results as the outliers have irrelevant data. The outliers may have categorical or numerical type of data associated with them.Real Life Applications: Major applications are used in Retail Industries, Finance Industries, Quality Control, Fault Diagnosis, web analytics etc.Classification MetricsIn order to evaluate the performance of a Machine Learning model, there are some Metrics to know its performance and are applied for Regression and Classification algorithms. The different types of classification metrics are: Classification Accuracy Confusion Matrix Logarithmic Loss Area under Curve (AUC) F-MeasureClassification AccuracyClassification accuracy is similar to the term Accuracy. It is the ratio of the correct predictions to the total number of Predictions made by the model from the given data.We can get better accuracy if the given data samples have the same type of data related to the given problem statement. If the accuracy is high, the model is more accurate and we can use the model in the real world and for different types of applications also.If the accuracy is less, it shows that the data samples are not correctly classified to suit the given problem.Confusion MatrixIt is a NxN matrix structure used for evaluating the performance of a classification model, where N is the number of classes that are predicted. It is operated on a test dataset in which the true values are known. The matrix lets us know about the number of incorrect and correct predictions made by a classifier and is used to find correctness of the model. It consists of values like True Positive, False Positive, True Negative, and False Negative, which helps in measuring Accuracy, Precision, Recall, Specificity, Sensitivity, and AUC curve. The above measures will talk about the model performance and compare with other models to describe how good it is.There are 4 important terms in confusion matrix: True Positives (TP): The cases in which our predictions are TRUE, and the actual output was also TRUE. True Negatives (TN): The cases in which our predictions are FALSE, and the actual output was also FALSE. False Positives (FP): The cases in which our predictions are TRUE, and the actual output was FALSE. False Negative (FN): The cases in which our predictions are FALSE, and the actual output was TRUE. The accuracy can be calculated by using the mean of True Positive and True Negative values of the total sample values. It tells us about the total number of predictions made by the model that were correct. Precision is the ratio of Number of True Positives in the sample to the total Positive samples predicted by the classifier. It tells us about the positive samples that were correctly identified by the model.  Recall is the ratio of Number of True Positives in the sample to the sum of True Positive and False Negative samples in the data.  F1 ScoreIt is also called as F-Measure. It is a best measure of the Test accuracy of the developed model. It makes our task easy by eliminating the need to calculate Precision and Recall separately to know about the model performance. F1 Score is the Harmonic mean of Recall and Precision. Higher the F1 Score, better the performance of the model. Without calculating Precision and Recall separately, we can calculate the model performance using F1 score as it is precise and robust.Sensitivity is the ratio of Number of actual True Positive Samples to the sum of True Positive and False Positive Samples. It tells about the positive samples that are identified correctly with respect to all the positive data samples in the given data. It is also called as True Positive Rate.  Specificity is also called the True Negative Rate. It is the ratio of the Number of True Negatives in the sample to the sum of True negative and the False positive samples in the given dataset. It tells about the number of actual Negative samples that are correctly identified from the given dataset. False positive rate is defined as 1-specificity. It is the ratio of number of False Positives in the sample to the sum of False positive and True Negative samples. It tells us about the Negative data samples that are classified as Positive, with respect to all Negative data samples.For each value of sensitivity, we get a different value of specificity and they are associated as follows:   Area Under the ROC Curve (AUC - ROC)It is a widely used Evaluation Metric, mainly used for Binary Classification. The False positive rates and the True positive rates have the values ranging from 0 to 1. The TPR and FPR are calculated with different threshold values and a graph is drawn to better understand about the data. Thus, the Area Under Curve is the plot between false positive rate and True positive rate at different values of [0,1].Logarithmic LossIt is also called Log Loss. As we know, the AUC ROC determines the model performance using the predicted probabilities, but it does not consider model capability to predict the higher probability of samples to be more likely positive. This technique is mostly used in Multi-class Classification. It is calculated to the negative average of the log of correctly predicted probabilities for each instance. where, y_ij, indicates whether sample i belongs to class j or not p_ij, indicates the probability of sample i belonging to class j Regression MetricsIt helps to predict the state of outcome at any time with the help of independent variables that are correlated. There are mainly 3 different types of metrics used in regression. These metrics are designed in order to predict if the data is underfitted or overfitted for the better usage of the model.  They are:-  Mean Absolute Error (MAE)  Mean Squared Error (MSE) Root Mean Squared Error (RMSE)Mean Absolute Error is the average of the difference of the original values and the predicted values. It gives us an idea of how far the predictions are from the actual output. It doesn’t give clarity on whether the data is under fitted or over fitted. It is calculated as follows:The mean squared error is similar to the mean absolute error. It is computed by taking the average of the square of the difference between original and predicted values. With the help of squaring, large errors can be converted to small errors and large errors can be dealt with.  It is computed as follows. The root mean squared error is the root of the mean of the square of difference of the predicted and actual values of the given data. It is the most popular metric evolution technique used in regression problems. It follows a normal distribution and is based on the assumption that errors are unbiased. It is computed using the below formulae.Bias vs VarianceBias is the difference between the Expected value and the Predicted value by our model. It is simply some assumptions made by the model to make the target function easier to learn. The low bias indicates fewer assumptions, whereas the high bias talks about more assumptions in the target data. It leads to underfitting of the model.Variance takes all types of data including noise into it. The model considers the variance as something to learn, and the model learns too much from the trained data, and at the end the model fails in giving out accurate results to the given problem statement. In case of high variance, the model learns too much and it can lead to overfitting of the model. ConclusionWhile building a machine learning model for a given problem statement there are two important stages, namely training and testing. In the training stage, the models learn from the data and predict the outcomes at the end. But it is crucial that predictions made by the developed model are accurate. This is why the stage of testing is the most crucial stage, because it can guarantee how accurate the results were to implement for the given problem.  In this blog, we have discussed about various types of Evaluation techniques to achieve a good model that best suits a given problem statement with highly accurate results. We need to check all the above-mentioned parameters to be able to compare our model performance as compared to other models.

Machine Learning Model Evaluation

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Machine Learning Model Evaluation

If we were to list the technologies that have revolutionized and changed our lives for the better, then Machine Learning will occupy the top spot. This cutting-edge technology is used in a wide variety of applications in day-to-day life. ML has become an integral component in most of the industries like Healthcare, Software, Manufacturing, Business and aims to solve many complex problems while reducing human effort and dependency. This it does by accurately predicting solutions for problems and various applications.

Generally there are two important stages in machine learning. They are Training & Evaluation of the model. Initially we take a dataset to feed to the machine learning model, and this process of feeding the data to our Designed ML model is called Training. In the training stage, the model learns the behavior of data, capable of handling different forms of data to better suit the model, draws conclusion from the data and finally predicts the end results using the model.

This technique of training helps a user to know the output of the designed machine learning model for the given problem, the inputs given to the model, and the output that is obtained at the end of the model.

But as machine learning model engineers, we might doubt the applicability of the model for the problem and have questions like, is the developed Machine learning model best suited for the problem, how accurate the model is, how can we say this is the best model that suits the given problem statement and what are the measures that describe model performance?

In order to get clarity on the above questions, there is a technique called Model Evaluation, that describes the performance of the model and helps us understand if the designed model is suitable for the given problem statement or not.

This article helps you to know, the various measures involved in calculating performance of a model for a particular problem and other key aspects involved.

What is Model Evaluation?

This technique of Evaluation helps us to know which algorithm best suits the given dataset for solving a particular problem. Likewise, in terms of Machine Learning it is called as “Best Fit”. It evaluates the performance of different Machine Learning models, based on the same input dataset. The method of evaluation focuses on accuracy of the model, in predicting the end outcomes.

Out of all the different algorithms we use in the stage, we choose the algorithm that gives more accuracy for the input data and is considered as the best model as it better predicts the outcome. The accuracy is considered as the main factor, when we work on solving different problems using machine learning. If the accuracy is high, the model predictions on the given data are also true to the maximum possible extent.

There are several stages in solving an ML problem like collection of dataset, defining the problem, brainstorming on the given data, preprocessing, transformation, training the model and evaluating. Even though there are several stages, the stage of Evaluation of a ML model is the most crucial stage, because it gives us an idea of the accuracy of model prediction. The performance and usage of the ML model is decided in terms of accuracy measures at the end.

How to solve a problem

Model Evaluation Techniques

We have known that the model evaluation is an Integral part in Machine Learning. Initially, the dataset is divided into two types, they are “Training dataset and “Test dataset”. We build the machine learning model using the training dataset to see the functionality of the model. But we evaluate the designed Model using a test dataset, which consists of unseen or unknown samples of the data that are not used for training purposesEvaluation of a model tells us how accurate the results wereIf we use the training dataset for evaluation of the model, for any instance of the training data it will always show the correct predictions for the given problem with high accuracy measures, in that case our model is not adequately effective to use.  

There are two methods that are used to evaluate a model performance. They are  

  1. Holdout 
  2. Cross ValidationModel Evaluation Techniques

The Holdout method is used to evaluate the model performance and uses two types of data for testing and training. The test data is used to calculate the performance of the model whereas it is trained using the training data set.  This method is used to check how well the machine learning model developed using different algorithm techniques performs on unseen samples of dataThis approach is simple, flexible and fast.

Cross-validation is a procedure of dividing the whole dataset into data samples, and then evaluating the machine learning model using the other samples of data to know accuracy of the model. i.e., we train the model using subset of data and we evaluate it with a complementary data subset. We can calculate cross validation based on the following 3 methods, namely 

  1. Validation 
  2. Leave one out cross validation (LOOCV) 
  3. K-Fold Cross Validation

In the method of validation, we split the given dataset into 50% of training and 50% for testing purpose. The main drawback in this method is that the remaining 50% of data that is subjected to testing may contain some crucial information that may be lost while training the model. So, this method doesn’t work properly due to high bias.

In the method of LOOCV, we train all the datasets in our model and leave a single data point for testing purpose. This method aims at exhibiting lower bias, but there are some chances that this method might fail because, the data-point that has been left out may be an outlier in the given data; and in that case we cannot produce better results with good accuracy. 

K-fold cross validation is a popular method used for evaluation of a Machine Learning model. It works by splitting the data into k-parts. Each split of the data is called a fold. Here we train all the k subsets of data to the model, and then we leave out one (k-1) subset to perform evaluation on the trained model. This method results in high accuracy and produces data with less bias.

Types of Predictive Models

Predictive models are used to predict the outcomes from the given data by using a developed ML model. Before getting the actual output from the model, we can predict the outcomes with the help of given data. The prediction models are widely used in machine learning, to guess the outcomes from the data before designing a model. There are different types of predictive models:

  1. Classification model
  2. Clustering model
  3. Forecast model
  4. Outlier model

A Classification model is used in decision making problems. It separates the given data into different categories, and this model is best suited to answer “Yes” or “No” questions. It is the simplest of all the predictive models.

Real Life Applications: Projects like Gender Classification, Fraud detection, Product Categorization, Malware classification, documents classification etc.

Clustering models are used to group the given data based on similar attributes. This model helps us to know how many groups are present in the given dataset and we can analyze what are the groups, which we should focus on to solve the given problem statement.

Real Life Applications: Projects like categorizing different people present in a classroom, types of customers in a bank, identifying fake news, spam filter, document analysis etc.

A forecast model learns from the historical data in order to predict the new data based on learning. It majorly deals with metric values.

Real Life Applications: Projects like weather forecast, sales forecast, stocks prices, Heart Rate Monitoring etc.

Outlier model focuses on identifying irrelevant data in the given dataset. If the data consists of outliers, we cannot get good results as the outliers have irrelevant data. The outliers may have categorical or numerical type of data associated with them.

Real Life Applications: Major applications are used in Retail Industries, Finance Industries, Quality Control, Fault Diagnosis, web analytics etc.

Classification Metrics

In order to evaluate the performance of a Machine Learning model, there are some Metrics to know its performance and are applied for Regression and Classification algorithms. The different types of classification metrics are: 

  1. Classification Accuracy 
  2. Confusion Matrix 
  3. Logarithmic Loss 
  4. Area under Curve (AUC) 
  5. F-Measure

Classification Accuracy

Classification accuracy is similar to the term Accuracy. It is the ratio of the correct predictions to the total number of Predictions made by the model from the given data.Classification Accuracy formula

We can get better accuracy if the given data samples have the same type of data related to the given problem statementIf the accuracy is high, the model is more accurate and we can use the model in the real world and for different types of applications also.

If the accuracy is less, it shows that the data samples are not correctly classified to suit the given problem.

Confusion Matrix

It is a NxN matrix structure used for evaluating the performance of a classification model, where N is the number of classes that are predicted. It is operated on a test dataset in which the true values are known. The matrix lets us know about the number of incorrect and correct predictions made by a classifier and is used to find correctness of the model. It consists of values like True Positive, False Positive, True Negative, and False Negative, which helps in measuring Accuracy, Precision, Recall, Specificity, Sensitivity, and AUC curve. The above measures will talk about the model performance and compare with other models to describe how good it is.

There are 4 important terms in confusion matrix: 

  1. True Positives (TP): The cases in which our predictions are TRUE, and the actual output was also TRUE. 
  2. True Negatives (TN): The cases in which our predictions are FALSE, and the actual output was also FALSE. 
  3. False Positives (FP): The cases in which our predictions are TRUE, and the actual output was FALSE. 
  4. False Negative (FN): The cases in which our predictions are FALSE, and the actual output was TRUE. 

The accuracy can be calculated by using the mean of True Positive and True Negative values of the total sample values. It tells us about the total number of predictions made by the model that were correct. 

Precision is the ratio of Number of True Positives in the sample to the total Positive samples predicted by the classifier. It tells us about the positive samples that were correctly identified by the model.  

Recall is the ratio of Number of True Positives in the sample to the sum of True Positive and False Negative samples in the data.  

F1 Score

It is also called as F-Measure. It is a best measure of the Test accuracy of the developed model. It makes our task easy by eliminating the need to calculate Precision and Recall separately to know about the model performance. F1 Score is the Harmonic mean of Recall and Precision. Higher the F1 Score, better the performance of the model. Without calculating Precision and Recall separately, we can calculate the model performance using F1 score as it is precise and robust.

Sensitivity is the ratio of Number of actual True Positive Samples to the sum of True Positive and False Positive Samples. It tells about the positive samples that are identified correctly with respect to all the positive data samples in the given data. It is also called as True Positive Rate.  

Specificity is also called the True Negative Rate. It is the ratio of the Number of True Negatives in the sample to the sum of True negative and the False positive samples in the given dataset. It tells about the number of actual Negative samples that are correctly identified from the given dataset. 

False positive rate is defined as 1-specificity. It is the ratio of number of False Positives in the sample to the sum of False positive and True Negative samples. It tells us about the Negative data samples that are classified as Positive, with respect to all Negative data samples.

For each value of sensitivity, we get a different value of specificity and they are associated as follows:   

Area Under the ROC Curve (AUC - ROC)

It is a widely used Evaluation Metric, mainly used for Binary ClassificationThe False positive rates and the True positive rates have the values ranging from 0 to 1The TPR and FPR are calculated with different threshold values and a graph is drawn to better understand about the data. Thus, the Area Under Curve is the plot between false positive rate and True positive rate at different values of [0,1].

Logarithmic Loss

It is also called Log LossAs we know, the AUC ROC determines the model performance using the predicted probabilities, but it does not consider model capability to predict the higher probability of samples to be more likely positive. This technique is mostly used in Multi-class Classification. It is calculated to the negative average of the log of correctly predicted probabilities for each instance. 

where, 

  • y_ij, indicates whether sample i belongs to class j or not 
  • p_ij, indicates the probability of sample i belonging to class j 

Regression Metrics

It helps to predict the state of outcome at any time with the help of independent variables that are correlated. There are mainly 3 different types of metrics used in regression. These metrics are designed in order to predict if the data is underfitted or overfitted for the better usage of the model.  

They are:-  

  1. Mean Absolute Error (MAE)  
  2. Mean Squared Error (MSE) 
  3. Root Mean Squared Error (RMSE)

Mean Absolute Error is the average of the difference of the original values and the predicted values. It gives us an idea of how far the predictions are from the actual output. It doesn’t give clarity on whether the data is under fitted or over fitted. It is calculated as follows:

  • The mean squared error is similar to the mean absolute error. It is computed by taking the average of the square of the difference between original and predicted values. With the help of squaring, large errors can be converted to small errors and large errors can be dealt with It is computed as follows. 
  • The root mean squared error is the root of the mean of the square of difference of the predicted and actual values of the given data. It is the most popular metric evolution technique used in regression problems. It follows a normal distribution and is based on the assumption that errors are unbiased. It is computed using the below formulae.

Bias vs Variance

Bias is the difference between the Expected value and the Predicted value by our model. It is simply some assumptions made by the model to make the target function easier to learn. The low bias indicates fewer assumptions, whereas the high bias talks about more assumptions in the target data. It leads to underfitting of the model.

Variance takes all types of data including noise into it. The model considers the variance as something to learn, and the model learns too much from the trained data, and at the end the model fails in giving out accurate results to the given problem statement. In case of high variance, the model learns too much and it can lead to overfitting of the model. 

Conclusion

While building a machine learning model for a given problem statement there are two important stages, namely training and testing. In the training stage, the models learn from the data and predict the outcomes at the end. But it is crucial that predictions made by the developed model are accurateThis is why the stage of testing is the most crucial stage, because it can guarantee how accurate the results were to implement for the given problem.  

In this blog, we have discussed about various types of Evaluation techniques to achieve a good model that best suits a given problem statement with highly accurate results. We need to check all the above-mentioned parameters to be able to compare our model performance as compared to other models.

Harsha

Harsha Vardhan Garlapati

Blog Writer at KnowledgeHut

Harsha Vardhan Garlapati is a Data Science Enthusiast and loves working with data to draw meaningful insights from it and further convert those results and implement them in business growth. He is a final year undergraduate student and passionate about Data Science. He is a smart worker, passionate learner,  an Ice-Breaker and loves to participate in Hackathons to work on real time projects. He is a Toastmaster Member at S.R.K.R Toastmasters Club, a Public Speaker, a good Innovator and problem solver.

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Different types of discrete distributions that use discrete data are: Binomial Distribution Hypergeometric Distribution Geometric Distribution Poisson Distribution Negative Binomial Distribution Multinomial Distribution  Continuous data: It can obtain any value irrespective of bound or limit. Example: weight, height, any trigonometric value, age, etc. Different types of continuous distributions that use continuous data are: Beta distribution Cauchy distribution Exponential distribution Gamma distribution Logistic distribution Weibull distribution Types of Probability Distribution explained Here are some of the popular types of Probability distributions used by data science professionals. (Try all the code using Jupyter Notebook) Normal Distribution: It is also known as Gaussian distribution. It is one of the simplest types of continuous distribution. This probability distribution is symmetrical around its mean value. It also shows that data at close proximity of the mean is frequently occurring, compared to data that is away from it. Here, mean = 0, variance = finite valueHere, you can see 0 at the center is the Normal Distribution for different mean and variance values. Here is a code example showing the use of Normal Distribution: from scipy.stats import norm  import matplotlib.pyplot as mpl  import numpy as np  def normalDist() -> None:      fig, ax = mpl.subplots(1, 1)      mean, var, skew, kurt = norm.stats(moments = 'mvsk')      x = np.linspace(norm.ppf(0.01),  norm.ppf(0.99), 100)      ax.plot(x, norm.pdf(x),          'r-', lw = 5, alpha = 0.6, label = 'norm pdf')      ax.plot(x, norm.cdf(x),          'b-', lw = 5, alpha = 0.6, label = 'norm cdf')      vals = norm.ppf([0.001, 0.5, 0.999])      np.allclose([0.001, 0.5, 0.999], norm.cdf(vals))      r = norm.rvs(size = 1000)      ax.hist(r, normed = True, histtype = 'stepfilled', alpha = 0.2)      ax.legend(loc = 'best', frameon = False)      mpl.show()  normalDist() Output: Bernoulli Distribution: It is the simplest type of probability distribution. It is a particular case of Binomial distribution, where n=1. It means a binomial distribution takes 'n' number of trials, where n > 1 whereas, the Bernoulli distribution takes only a single trial.   Probability Mass Function of a Bernoulli’s Distribution is:  where p = probability of success and q = probability of failureHere is a code example showing the use of Bernoulli Distribution: from scipy.stats import bernoulli  import seaborn as sb    def bernoulliDist():      data_bern = bernoulli.rvs(size=1200, p = 0.7)      ax = sb.distplot(          data_bern,           kde = True,           color = 'g',           hist_kws = {'alpha' : 1},          kde_kws = {'color': 'y', 'lw': 3, 'label': 'KDE'})      ax.set(xlabel = 'Bernouli Values', ylabel = 'Frequency Distribution')  bernoulliDist() Output:Continuous Uniform Distribution: In this type of continuous distribution, all outcomes are equally possible; each variable gets the same probability of hit as a consequence. This symmetric probabilistic distribution has random variables at an equal interval, with the probability of 1/(b-a). Here is a code example showing the use of Uniform Distribution: from numpy import random  import matplotlib.pyplot as mpl  import seaborn as sb  def uniformDist():      sb.distplot(random.uniform(size = 1200), hist = True)      mpl.show()  uniformDist() Output: Log-Normal Distribution: A Log-Normal distribution is another type of continuous distribution of logarithmic values that form a normal distribution. We can transform a log-normal distribution into a normal distribution. Here is a code example showing the use of Log-Normal Distribution import matplotlib.pyplot as mpl  def lognormalDist():      muu, sig = 3, 1      s = np.random.lognormal(muu, sig, 1000)      cnt, bins, ignored = mpl.hist(s, 80, normed = True, align ='mid', color = 'y')      x = np.linspace(min(bins), max(bins), 10000)      calc = (np.exp( -(np.log(x) - muu) **2 / (2 * sig**2))             / (x * sig * np.sqrt(2 * np.pi)))      mpl.plot(x, calc, linewidth = 2.5, color = 'g')      mpl.axis('tight')      mpl.show()  lognormalDist() Output: Pareto Distribution: It is one of the most critical types of continuous distribution. The Pareto Distribution is a skewed statistical distribution that uses power-law to describe quality control, scientific, social, geophysical, actuarial, and many other types of observable phenomena. The distribution shows slow or heavy-decaying tails in the plot, where much of the data reside at its extreme end. Here is a code example showing the use of Pareto Distribution – import numpy as np  from matplotlib import pyplot as plt  from scipy.stats import pareto  def paretoDist():      xm = 1.5        alp = [2, 4, 6]       x = np.linspace(0, 4, 800)      output = np.array([pareto.pdf(x, scale = xm, b = a) for a in alp])      plt.plot(x, output.T)      plt.show()  paretoDist() Output:Exponential Distribution: It is a type of continuous distribution that determines the time elapsed between events (in a Poisson process). Let’s suppose, that you have the Poisson distribution model that holds the number of events happening in a given period. We can model the time between each birth using an exponential distribution.Here is a code example showing the use of Pareto Distribution – from numpy import random  import matplotlib.pyplot as mpl  import seaborn as sb  def expDist():      sb.distplot(random.exponential(size = 1200), hist = True)      mpl.show()   expDist()Output:Types of the Discrete probability distribution – There are various types of Discrete Probability Distribution a Data science aspirant should know about. Some of them are – Binomial Distribution: It is one of the popular discrete distributions that determine the probability of x success in the 'n' trial. We can use Binomial distribution in situations where we want to extract the probability of SUCCESS or FAILURE from an experiment or survey which went through multiple repetitions. A Binomial distribution holds a fixed number of trials. Also, a binomial event should be independent, and the probability of obtaining failure or success should remain the same. Here is a code example showing the use of Binomial Distribution – from numpy import random  import matplotlib.pyplot as mpl  import seaborn as sb    def binomialDist():      sb.distplot(random.normal(loc = 50, scale = 6, size = 1200), hist = False, label = 'normal')      sb.distplot(random.binomial(n = 100, p = 0.6, size = 1200), hist = False, label = 'binomial')      plt.show()    binomialDist() Output:Geometric Distribution: The geometric probability distribution is one of the crucial types of continuous distributions that determine the probability of any event having likelihood ‘p’ and will happen (occur) after 'n' number of Bernoulli trials. Here 'n' is a discrete random variable. In this distribution, the experiment goes on until we encounter either a success or a failure. The experiment does not depend on the number of trials. Here is a code example showing the use of Geometric Distribution – import matplotlib.pyplot as mpl  def probability_to_occur_at(attempt, probability):      return (1-p)**(attempt - 1) * probability  p = 0.3  attempt = 4  attempts_to_show = range(21)[1:]  print('Possibility that this event will occur on the 7th try: ', probability_to_occur_at(attempt, p))  mpl.xlabel('Number of Trials')  mpl.ylabel('Probability of the Event')  barlist = mpl.bar(attempts_to_show, height=[probability_to_occur_at(x, p) for x in attempts_to_show], tick_label=attempts_to_show)  barlist[attempt].set_color('g')  mpl.show() Output:Poisson Distribution: Poisson distribution is one of the popular types of discrete distribution that shows how many times an event has the possibility of occurrence in a specific set of time. We can obtain this by limiting the Bernoulli distribution from 0 to infinity. Data analysts often use the Poisson distributions to comprehend independent events occurring at a steady rate in a given time interval. Here is a code example showing the use of Poisson Distribution from scipy.stats import poisson  import seaborn as sb  import numpy as np  import matplotlib.pyplot as mpl  def poissonDist():       mpl.figure(figsize = (10, 10))      data_binom = poisson.rvs(mu = 3, size = 5000)      ax = sb.distplot(data_binom, kde=True, color = 'g',                       bins=np.arange(data_binom.min(), data_binom.max() + 1),                       kde_kws={'color': 'y', 'lw': 4, 'label': 'KDE'})      ax.set(xlabel = 'Poisson Distribution', ylabel='Data Frequency')      mpl.show()      poissonDist() Output:Multinomial Distribution: A multinomial distribution is another popular type of discrete probability distribution that calculates the outcome of an event having two or more variables. The term multi means more than one. The Binomial distribution is a particular type of multinomial distribution with two possible outcomes - true/false or heads/tails. Here is a code example showing the use of Multinomial Distribution – import numpy as np  import matplotlib.pyplot as mpl  np.random.seed(99)   n = 12                      pvalue = [0.3, 0.46, 0.22]     s = []  p = []     for size in np.logspace(2, 3):      outcomes = np.random.multinomial(n, pvalue, size=int(size))        prob = sum((outcomes[:,0] == 7) & (outcomes[:,1] == 2) & (outcomes[:,2] == 3))/len(outcomes)      p.append(prob)      s.append(int(size))  fig1 = mpl.figure()  mpl.plot(s, p, 'o-')  mpl.plot(s, [0.0248]*len(s), '--r')  mpl.grid()  mpl.xlim(xmin = 0)  mpl.xlabel('Number of Events')  mpl.ylabel('Function p(X = K)') Output:Negative Binomial Distribution: It is also a type of discrete probability distribution for random variables having negative binomial events. It is also known as the Pascal distribution, where the random variable tells us the number of repeated trials produced during a specific number of experiments.  Here is a code example showing the use of Negative Binomial Distribution – import matplotlib.pyplot as mpl   import numpy as np   from scipy.stats import nbinom    x = np.linspace(0, 6, 70)   gr, kr = 0.3, 0.7        g = nbinom.ppf(x, gr, kr)   s = nbinom.pmf(x, gr, kr)   mpl.plot(x, g, "*", x, s, "r--") Output: Apart from these mentioned distribution types, various other types of probability distributions exist that data science professionals can use to extract reliable datasets. In the next topic, we will understand some interconnections & relationships between various types of probability distributions. Relationship between various Probability distributions – It is surprising to see that different types of probability distributions are interconnected. In the chart shown below, the dashed line is for limited connections between two families of distribution, whereas the solid lines show the exact relationship between them in terms of transformation, variable, type, etc. Conclusion  Probability distributions are prevalent among data analysts and data science professionals because of their wide usage. Today, companies and enterprises hire data science professionals in many sectors, namely, computer science, health, insurance, engineering, and even social science, where probability distributions appear as fundamental tools for application. It is essential for Data analysts and data scientists. to know the core of statistics. Probability Distributions perform a requisite role in analyzing data and cooking a dataset to train the algorithms efficiently. If you want to learn more about data science - particularly probability distributions and their uses, check out KnowledgeHut's comprehensive Data science course https://www.knowledgehut.com/data-science-courses. 
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Types of Probability Distributions Every Data Scie...

Data Science has become one of the most popular in... Read More

Role of Unstructured Data in Data Science

Data has become the new game changer for businesses. Typically, data scientists categorize data into three broad divisions - structured, semi-structured, and unstructured data. In this article, you will get to know about unstructured data, sources of unstructured data, unstructured data vs. structured data, the use of structured and unstructured data in machine learning, and the difference between structured and unstructured data. Let us first understand what is unstructured data with examples. What is unstructured data? Unstructured data is a kind of data format where there is no organized form or type of data. Videos, texts, images, document files, audio materials, email contents and more are considered to be unstructured data. It is the most copious form of business data, and cannot be stored in a structured database or relational database. Some examples of unstructured data are the photos we post on social media platforms, the tagging we do, the multimedia files we upload, and the documents we share. Seagate predicts that the global data-sphere will expand to 163 zettabytes by 2025, where most of the data will be in the unstructured format. Characteristics of Unstructured DataUnstructured data cannot be organized in a predefined fashion, and is not a homogenous data model. This makes it difficult to manage. Apart from that, these are the other characteristics of unstructured data. You cannot store unstructured data in the form of rows and columns as we do in a database table. Unstructured data is heterogeneous in structure and does not have any specific data model. The creation of such data does not follow any semantics or habits. Due to the lack of any particular sequence or format, it is difficult to manage. Such data does not have an identifiable structure. Sources of Unstructured Data There are various sources of unstructured data. Some of them are: Content websites Social networking sites Online images Memos Reports and research papers Documents, spreadsheets, and presentations Audio mining, chatbots Surveys Feedback systems Advantages of Unstructured Data Unstructured data has become exceptionally easy to store because of MongoDB, Cassandra, or even using JSON. Modern NoSQL databases and software allows data engineers to collect and extract data from various sources. There are numerous benefits that enterprises and businesses can gain from unstructured data. These are: With the advent of unstructured data, we can store data that lacks a proper format or structure. There is no fixed schema or data structure for storing such data, which gives flexibility in storing data of different genres. Unstructured data is much more portable by nature. Unstructured data is scalable and flexible to store. Database systems like MongoDB, Cassandra, etc., can easily handle the heterogeneous properties of unstructured data. Different applications and platforms produce unstructured data that becomes useful in business intelligence, unstructured data analytics, and various other fields. Unstructured data analysis allows finding comprehensive data stories from data like email contents, website information, social media posts, mobile data, cache files and more. Unstructured data, along with data analytics, helps companies improve customer experience. Detection of the taste of consumers and their choices becomes easy because of unstructured data analysis. Disadvantages of Unstructured data Storing and managing unstructured data is difficult because there is no proper structure or schema. Data indexing is also a substantial challenge and hence becomes unclear due to its disorganized nature. Search results from an unstructured dataset are also not accurate because it does not have predefined attributes. Data security is also a challenge due to the heterogeneous form of data. Problems faced and solutions for storing unstructured data. Until recently, it was challenging to store, evaluate, and manage unstructured data. But with the advent of modern data analysis tools, algorithms, CAS (content addressable storage system), and big data technologies, storage and evaluation became easy. Let us first take a look at the various challenges used for storing unstructured data. Storing unstructured data requires a large amount of space. Indexing of unstructured data is a hectic task. Database operations such as deleting and updating become difficult because of the disorganized nature of the data. Storing and managing video, audio, image file, emails, social media data is also challenging. Unstructured data increases the storage cost. For solving such issues, there are some particular approaches. These are: CAS system helps in storing unstructured data efficiently. We can preserve unstructured data in XML format. Developers can store unstructured data in an RDBMS system supporting BLOB. We can convert unstructured data into flexible formats so that evaluating and storage becomes easy. Let us now understand the differences between unstructured data vs. structured data. Unstructured Data Vs. Structured Data In this section, we will understand the difference between structured and unstructured data with examples. STRUCTUREDUNSTRUCTUREDStructured data resides in an organized format in a typical database.Unstructured data cannot reside in an organized format, and hence we cannot store it in a typical database.We can store structured data in SQL database tables having rows and columns.Storing and managing unstructured data requires specialized databases, along with a variety of business intelligence and analytics applications.It is tough to scale a database schema.It is highly scalable.Structured data gets generated in colleges, universities, banks, companies where people have to deal with names, date of birth, salary, marks and so on.We generate or find unstructured data in social media platforms, emails, analyzed data for business intelligence, call centers, chatbots and so on.Queries in structured data allow complex joining.Unstructured data allows only textual queries.The schema of a structured dataset is less flexible and dependent.An unstructured dataset is flexible but does not have any particular schema.It has various concurrency techniques.It has no concurrency techniques.We can use SQL, MySQL, SQLite, Oracle DB, Teradata to store structured data.We can use NoSQL (Not Only SQL) to store unstructured data.Types of Unstructured Data Do you have any idea just how much of unstructured data we produce and from what sources? Unstructured data includes all those forms of data that we cannot actively manage in an RDBMS system that is a transactional system. We can store structured data in the form of records. But this is not the case with unstructured data. Before the advent of object-based storage, most of the unstructured data was stored in file-based systems. Here are some of the types of unstructured data. Rich media content: Entertainment files, surveillance data, multimedia email attachments, geospatial data, audio files (call center and other recorded audio), weather reports (graphical), etc., comes under this genre. Document data: Invoices, text-file records, email contents, productivity applications, etc., are included under this genre. Internet of Things (IoT) data: Ticker data, sensor data, data from other IoT devices come under this genre. Apart from all these, data from business intelligence and analysis, machine learning datasets, and artificial intelligence data training datasets are also a separate genre of unstructured data. Examples of Unstructured Data There are various sources from where we can obtain unstructured data. The prominent use of this data is in unstructured data analytics. Let us now understand what are some examples of unstructured data and their sources – Healthcare industries generate a massive volume of human as well as machine-generated unstructured data. Human-generated unstructured data could be in the form of patient-doctor or patient-nurse conversations, which are usually recorded in audio or text formats. Unstructured data generated by machines includes emergency video camera footage, surgical robots, data accumulated from medical imaging devices like endoscopes, laparoscopes and more.  Social Media is an intrinsic entity of our daily life. Billions of people come together to join channels, share different thoughts, and exchange information with their loved ones. They create and share such data over social media platforms in the form of images, video clips, audio messages, tagging people (this helps companies to map relations between two or more people), entertainment data, educational data, geolocations, texts, etc. Other spectra of data generated from social media platforms are behavior patterns, perceptions, influencers, trends, news, and events. Business and corporate documents generate a multitude of unstructured data such as emails, presentations, reports containing texts, images, presentation reports, video contents, feedback and much more. These documents help to create knowledge repositories within an organization to make better implicit operations. Live chat, video conferencing, web meeting, chatbot-customer messages, surveillance data are other prominent examples of unstructured data that companies can cultivate to get more insights into the details of a person. Some prominent examples of unstructured data used in enterprises and organizations are: Reports and documents, like Word files or PDF files Multimedia files, such as audio, images, designed texts, themes, and videos System logs Medical images Flat files Scanned documents (which are images that hold numbers and text – for example, OCR) Biometric data Unstructured Data Analytics Tools  You might be wondering what tools can come into use to gather and analyze information that does not have a predefined structure or model. Various tools and programming languages use structured and unstructured data for machine learning and data analysis. These are: Tableau MonkeyLearn Apache Spark SAS Python MS. Excel RapidMiner KNIME QlikView Python programming R programming Many cloud services (like Amazon AWS, Microsoft Azure, IBM Cloud, Google Cloud) also offer unstructured data analysis solutions bundled with their services. How to analyze unstructured data? In the past, the process of storage and analysis of unstructured data was not well defined. Enterprises used to carry out this kind of analysis manually. But with the advent of modern tools and programming languages, most of the unstructured data analysis methods became highly advanced. AI-powered tools use algorithms designed precisely to help to break down unstructured data for analysis. Unstructured data analytics tools, along with Natural language processing (NLP) and machine learning algorithms, help advanced software tools analyze and extract analytical data from the unstructured datasets. Before using these tools for analyzing unstructured data, you must properly go through a few steps and keep these points in mind. Set a clear goal for analyzing the data: It is essential to clear your intention about what insights you want to extract from your unstructured data. Knowing this will help you distinguish what type of data you are planning to accumulate. Collect relevant data: Unstructured data is available everywhere, whether it's a social media platform, online feedback or reviews, or a survey form. Depending on the previous point, that is your goal - you have to be precise about what data you want to collect in real-time. Also, keep in mind whether your collected details are relevant or not. Clean your data: Data cleaning or data cleansing is a significant process to detect corrupt or irrelevant data from the dataset, followed by modifying or deleting the coarse and sloppy data. This phase is also known as the data-preprocessing phase, where you have to reduce the noise, carry out data slicing for meaningful representation, and remove unnecessary data. Use Technology and tools: Once you perform the data cleaning, it is time to utilize unstructured data analysis tools to prepare and cultivate the insights from your data. Technologies used for unstructured data storage (NoSQL) can help in managing your flow of data. Other tools and programming libraries like Tableau, Matplotlib, Pandas, and Google Data Studio allows us to extract and visualize unstructured data. Data can be visualized and presented in the form of compelling graphs, plots, and charts. How to Extract information from Unstructured Data? With the growth in digitization during the information era, repetitious transactions in data cause data flooding. The exponential accretion in the speed of digital data creation has brought a whole new domain of understanding user interaction with the online world. According to Gartner, 80% of the data created by an organization or its application is unstructured. While extracting exact information through appropriate analysis of organized data is not yet possible, even obtaining a decent sense of this unstructured data is quite tough. Until now, there are no perfect tools to analyze unstructured data. But algorithms and tools designed using machine learning, Natural language processing, Deep learning, and Graph Analysis (a mathematical method for estimating graph structures) help us to get the upper hand in extracting information from unstructured data. Other neural network models like modern linguistic models follow unsupervised learning techniques to gain a good 'knowledge' about the unstructured dataset before going into a specific supervised learning step. AI-based algorithms and technologies are capable enough to extract keywords, locations, phone numbers, analyze image meaning (through digital image processing). We can then understand what to evaluate and identify information that is essential to your business. ConclusionUnstructured data is found abundantly from sources like documents, records, emails, social media posts, feedbacks, call-records, log-in session data, video, audio, and images. Manually analyzing unstructured data is very time-consuming and can be very boring at the same time. With the growth of data science and machine learning algorithms and models, it has become easy to gather and analyze insights from unstructured information.  According to some research, data analytics tools like MonkeyLearn Studio, Tableau, RapidMiner help analyze unstructured data 1200x faster than the manual approach. Analyzing such data will help you learn more about your customers as well as competitors. Text analysis software, along with machine learning models, will help you dig deep into such datasets and make you gain an in-depth understanding of the overall scenario with fine-grained analyses.
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Role of Unstructured Data in Data Science

Data has become the new game changer for busines... Read More

What Is Statistical Analysis and Its Business Applications?

Statistics is a science concerned with collection, analysis, interpretation, and presentation of data. In Statistics, we generally want to study a population. You may consider a population as a collection of things, persons, or objects under experiment or study. It is usually not possible to gain access to all of the information from the entire population due to logistical reasons. So, when we want to study a population, we generally select a sample. In sampling, we select a portion (or subset) of the larger population and then study the portion (or the sample) to learn about the population. Data is the result of sampling from a population.Major ClassificationThere are two basic branches of Statistics – Descriptive and Inferential statistics. Let us understand the two branches in brief. Descriptive statistics Descriptive statistics involves organizing and summarizing the data for better and easier understanding. Unlike Inferential statistics, Descriptive statistics seeks to describe the data, however, it does not attempt to draw inferences from the sample to the whole population. We simply describe the data in a sample. It is not developed on the basis of probability unlike Inferential statistics. Descriptive statistics is further broken into two categories – Measure of Central Tendency and Measures of Variability. Inferential statisticsInferential statistics is the method of estimating the population parameter based on the sample information. It applies dimensions from sample groups in an experiment to contrast the conduct group and make overviews on the large population sample. Please note that the inferential statistics are effective and valuable only when examining each member of the group is difficult. Let us understand Descriptive and Inferential statistics with the help of an example. Task – Suppose, you need to calculate the score of the players who scored a century in a cricket tournament.  Solution: Using Descriptive statistics you can get the desired results.   Task – Now, you need the overall score of the players who scored a century in the cricket tournament.  Solution: Applying the knowledge of Inferential statistics will help you in getting your desired results.  Top Five Considerations for Statistical Data AnalysisData can be messy. Even a small blunder may cost you a fortune. Therefore, special care when working with statistical data is of utmost importance. Here are a few key takeaways you must consider to minimize errors and improve accuracy. Define the purpose and determine the location where the publication will take place.  Understand the assets to undertake the investigation. Understand the individual capability of appropriately managing and understanding the analysis.  Determine whether there is a need to repeat the process.  Know the expectation of the individuals evaluating reviewing, committee, and supervision. Statistics and ParametersDetermining the sample size requires understanding statistics and parameters. The two being very closely related are often confused and sometimes hard to distinguish.  StatisticsA statistic is merely a portion of a target sample. It refers to the measure of the values calculated from the population.  A parameter is a fixed and unknown numerical value used for describing the entire population. The most commonly used parameters are: Mean Median Mode Mean :  The mean is the average or the most common value in a data sample or a population. It is also referred to as the expected value. Formula: Sum of the total number of observations/the number of observations. Experimental data set: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20  Calculating mean:   (2 + 4 + 6 + 8 + 10 + 12 + 14 + 16 + 18 + 20)/10  = 110/10   = 11 Median:  In statistics, the median is the value separating the higher half from the lower half of a data sample, a population, or a probability distribution. It’s the mid-value obtained by arranging the data in increasing order or descending order. Formula:  Let n be the data set (increasing order) When data set is odd: Median = n+1/2th term Case-I: (n is odd)  Experimental data set = 1, 2, 3, 4, 5  Median (n = 5) = [(5 +1)/2]th term      = 6/2 term       = 3rd term   Therefore, the median is 3 When data set is even: Median = [n/2th + (n/2 + 1)th] /2 Case-II: (n is even)  Experimental data set = 1, 2, 3, 4, 5, 6   Median (n = 6) = [n/2th + (n/2 + 1)th]/2     = ( 6/2th + (6/2 +1)th]/2     = (3rd + 4th)/2      = (3 + 4)/2      = 7/2      = 3.5  Therefore, the median is 3.5 Mode: The mode is the value that appears most often in a set of data or a population. Experimental data set= 1, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4,4,5, 6  Mode = 3 (Since 3 is the most repeated element in the sequence.) Terms Used to Describe DataWhen working with data, you will need to search, inspect, and characterize them. To understand the data in a tech-savvy and straightforward way, we use a few statistical terms to denote them individually or in groups.  The most frequently used terms used to describe data include data point, quantitative variables, indicator, statistic, time-series data, variable, data aggregation, time series, dataset, and database. Let us define each one of them in brief: Data points: These are the numerical files formed and organized for interpretations. Quantitative variables: These variables present the information in digit form.  Indicator: An indicator explains the action of a community's social-economic surroundings.  Time-series data: The time-series defines the sequential data.  Data aggregation: A group of data points and data set. Database: A group of arranged information for examination and recovery.  Time-series: A set of measures of a variable documented over a specified time. Step-by-Step Statistical Analysis ProcessThe statistical analysis process involves five steps followed one after another. Step 1: Design the study and find the population of the study. Step 2: Collect data as samples. Step 3: Describe the data in the sample. Step 4: Make inferences with the help of samples and calculations Step 5: Take action Data distributionData distribution is an entry that displays entire imaginable readings of data. It shows how frequently a value occurs. Distributed data is always in ascending order, charts, and graphs enabling visibility of measurements and frequencies. The distribution function displaying the density of values of reading is known as the probability density function. Percentiles in data distributionA percentile is the reading in a distribution with a specified percentage of clarifications under it.  Let us understand percentiles with the help of an example.  Suppose you have scored 90th percentile on a math test. A basic interpretation is that merely 4-5% of the scores were higher than your scores. Right? The median is 50th percentile because the assumed 50% of the values are higher than the median. Dispersion Dispersion explains the magnitude of distribution readings anticipated for a specific variable and multiple unique statistics like range, variance, and standard deviation. For instance, high values of a data set are widely scattered while small values of data are firmly clustered. Histogram The histogram is a pictorial display that arranges a group of data facts into user detailed ranges. A histogram summarizes a data series into a simple interpreted graphic by obtaining many data facts and combining them into reasonable ranges. It contains a variety of results into columns on the x-axis. The y axis displays percentages of data for each column and is applied to picture data distributions. Bell Curve distribution Bell curve distribution is a pictorial representation of a probability distribution whose fundamental standard deviation obtained from the mean makes the bell, shaped curving. The peak point on the curve symbolizes the maximum likely occasion in a pattern of data. The other possible outcomes are symmetrically dispersed around the mean, making a descending sloping curve on both sides of the peak. The curve breadth is therefore known as the standard deviation. Hypothesis testingHypothesis testing is a process where experts experiment with a theory of a population parameter. It aims to evaluate the credibility of a hypothesis using sample data. The five steps involved in hypothesis testing are:  Identify the no outcome hypothesis.  (A worthless or a no-output hypothesis has no outcome, connection, or dissimilarities amongst many factors.) Identify the alternative hypothesis.  Establish the importance level of the hypothesis.  Estimate the experiment statistic and equivalent P-value. P-value explains the possibility of getting a sample statistic.  Sketch a conclusion to interpret into a report about the alternate hypothesis. Types of variablesA variable is any digit, amount, or feature that is countable or measurable. Simply put, it is a variable characteristic that varies. The six types of variables include the following: Dependent variableA dependent variable has values that vary according to the value of another variable known as the independent variable.  Independent variableAn independent variable on the other side is controllable by experts. Its reports are recorded and equated.  Intervening variableAn intervening variable explicates fundamental relations between variables. Moderator variableA moderator variable upsets the power of the connection between dependent and independent variables.  Control variableA control variable is anything restricted to a research study. The values are constant throughout the experiment. Extraneous variableExtraneous variable refers to the entire variables that are dependent but can upset experimental outcomes. Chi-square testChi-square test records the contrast of a model to actual experimental data. Data is unsystematic, underdone, equally limited, obtained from independent variables, and a sufficient sample. It relates the size of any inconsistencies among the expected outcomes and the actual outcomes, provided with the sample size and the number of variables in the connection. Types of FrequenciesFrequency refers to the number of repetitions of reading in an experiment in a given time. Three types of frequency distribution include the following: Grouped, ungrouped Cumulative, relative Relative cumulative frequency distribution. Features of FrequenciesThe calculation of central tendency and position (median, mean, and mode). The measure of dispersion (range, variance, and standard deviation). Degree of symmetry (skewness). Peakedness (kurtosis). Correlation MatrixThe correlation matrix is a table that shows the correlation coefficients of unique variables. It is a powerful tool that summarises datasets points and picture sequences in the provided data. A correlation matrix includes rows and columns that display variables. Additionally, the correlation matrix exploits in aggregation with other varieties of statistical analysis. Inferential StatisticsInferential statistics use random data samples for demonstration and to create inferences. They are measured when analysis of each individual of a whole group is not likely to happen. Applications of Inferential StatisticsInferential statistics in educational research is not likely to sample the entire population that has summaries. For instance, the aim of an investigation study may be to obtain whether a new method of learning mathematics develops mathematical accomplishment for all students in a class. Marketing organizations: Marketing organizations use inferential statistics to dispute a survey and request inquiries. It is because carrying out surveys for all the individuals about merchandise is not likely. Finance departments: Financial departments apply inferential statistics for expected financial plan and resources expenses, especially when there are several indefinite aspects. However, economists cannot estimate all that use possibility. Economic planning: In economic planning, there are potent methods like index figures, time series investigation, and estimation. Inferential statistics measures national income and its components. It gathers info about revenue, investment, saving, and spending to establish links among them. Key TakeawaysStatistical analysis is the gathering and explanation of data to expose sequences and tendencies.   Two divisions of statistical analysis are statistical and non-statistical analyses.  Descriptive and Inferential statistics are the two main categories of statistical analysis. Descriptive statistics describe data, whereas Inferential statistics equate dissimilarities between the sample groups.  Statistics aims to teach individuals how to use restricted samples to generate intellectual and precise results for a large group.   Mean, median, and mode are the statistical analysis parameters used to measure central tendency.   Conclusion Statistical analysis is the procedure of gathering and examining data to recognize sequences and trends. It uses random samples of data obtained from a population to demonstrate and create inferences on a group. Inferential statistics applies economic planning with potent methods like index figures, time series investigation, and estimation.  Statistical analysis finds its applications in all the major sectors – marketing, finance, economic, operations, and data mining. Statistical analysis aids marketing organizations in disputing a survey and requesting inquiries concerning their merchandise. 
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What Is Statistical Analysis and Its Business Appl...

Statistics is a science concerned with collection,... Read More