Basic Fundamentals of Statistics for Data Science

If you’re an aspiring Data Scientist, being familiar with the core concepts of Statistics for Data Science. You need not be a Ph.D. in Statistics to excel at Data Science, but you need to know enough to perhaps describe a couple of basic algorithms at a dinner party.

Going forward, we’ll walk you through some of the prerequisites in basics of Statistics for Data Science.

If you’ve just entered the world of Data Science, you might have come across people stating “Maths” as a prerequisite to Data Science. In all honesty, it’s not Maths, per se, but you have to learn Statistics for Data Science.

These days, libraries like Tensorflow hide almost all the complex Mathematics away from the user. Good for us, but it’s still good to have a basic understanding of the underlying principles on which these things work. Having a good understanding of data analytics can help you understand everything better.

This article will help arm you with some theorems, concepts, and equations that will not only help your cause as a Data Scientist but will also make you sound like you aced the course on Advanced Statistical Computing big time.

Basics of Statistics for Data Science

Statistical Significance: Differentiating between Random and Meaningful Results

Data analysis requires the ability to discern between random fluctuations in data and relevant patterns or consequences. This is where the statistical significance idea comes into play. Statistical significance assists academics and data scientists in determining whether observed results are due to chance or indicate a true link or impact.

Hypothesis testing, a commonly used statistical approach, is frequently used to determine statistical significance. The procedure begins with the formulation of a null hypothesis, which asserts that the data has no significant impact or link. In contrast, the alternative hypothesis implies the presence of a substantial impact or link.

Factual tests, such as the t-test or chi-square test, are used to determine quantitative relevance depending on the type of material and the review topic. If the faulty hypothesis is correct, these tests provide a p-value, which expresses the likelihood of achieving the specified outcomes by chance alone. A truly big p-value is one that is less than a defined limit, which is often 0.05.

It is critical to remember that factual significance does not always correspond to reasonable pertinence or the magnitude of the impact. Depending on the precise scenario and purposes of the assessment, a very crucial consequence may have little commonsense worth, although a non-significant finding may.

Understanding and using statistical significance is critical for obtaining trustworthy results from data analysis. Researchers may make educated judgments, support hypotheses, and discover significant results that contribute to the progress of knowledge and decision-making processes by distinguishing between random fluctuations and meaningful patterns.

Data Visualization: Communicating Insights through Graphs and Charts

Data visualization plays a crucial role in data analysis by transforming raw data into intuitive and visually appealing representations. Graphs and charts provide a powerful means of communicating insights, patterns, and trends hidden within complex datasets.

• Bar Charts: Bar charts are commonly used to display categorical data and compare values across different categories. They are effective in visualizing frequency counts, market shares, and other discrete data. Bar charts allow for quick comparisons and help identify the most significant categories or trends within the data.
• Line Charts: Line charts are ideal for visualizing trends and changes over time. They are commonly used to display time series data, such as stock prices or temperature fluctuations. Line charts allow data scientists to observe patterns, seasonality, and long-term trends, making them invaluable for forecasting and monitoring purposes.
• Scatter Plots: Scatter plots are useful for examining relationships between two continuous variables. By plotting data points on a Cartesian plane, data scientists can identify correlations, clusters, and outliers. Scatter plots help in understanding the nature of the relationship between variables and can aid in decision-making processes.
• Pie Charts: Pie charts are effective for illustrating the proportions or percentages of a whole. They are commonly used to display market shares, survey responses, or the distribution of categorical data. Pie charts provide a visual snapshot of relative proportions and make it easy to compare different categories at a glance.
• Heatmaps: Heatmaps are graphical representations of data where the values are encoded using colors. They are particularly useful for displaying large matrices or tabular data. Heatmaps help identify patterns, clusters, and relationships within datasets, making them valuable for tasks like correlation analysis and gene expression analysis.

Statistical Distributions

This is probably one of the most important things you need to know while arming yourself with prerequisite Statistics for Data Science.

• Poisson Distribution

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• The Poisson distribution is one of the most essential tools in statistics. It’s used for to calculate the number of events that are likely to occur in a time interval. For instance, how many phone calls are likely to occur in any particular period of time.
  The funny looking symbol in this equation (λ) is known as lambda. It is used to represent the average number of events occurring per time interval.

  Another good example where Poisson distribution finds use is to calculate the loss in manufacturing. Suppose a machine produces sheets of metal and has X flaws per yard. Suppose, for instance, the error rate was 2 per yard of the sheet – then using Poisson distribution, we can calculate the probability that exactly two errors will occur in a yard.

• Binomial Distribution

• If you’ve ever encountered basic Statistics, you might have come across Binomial Distribution.

  Let’s say you had an experiment of flipping an unbiased coin thrice.
  Can you tell the probability of the coin showing heads on all three flips?

  First, from basic combinatorics, we can find out that there are eight possible combinations of results when flipping a coin thrice. Now, we can plot the probabilities of having 0,1,2, or 3 heads. That plot will give us our required binomial distribution for this problem. When graphed, you’ll notice that it looks very similar to a typical normal distribution curve, in theory, both are very similar. While Binomial Distribution is for discrete values (a limited number of coin flips), Normal Distribution takes care of continuous values.

  There are a number of distributions other than the ones we talked about above. If you’re an interested soul and also want to arm yourself better with the needed Statistics for Data Science, we suggest you to read up about the following distributions as well:

• Geometric Distribution
• Hypergeometric Distribution
• Discrete Uniform Distribution
• Negative Binomial Distribution

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Some Theorems and Algorithms

When we talk about Statistics for Data Science, we just can’t ignore the basic theorems and algorithms that are the foundation of many libraries that you’ll be working on as a Data Scientist. There are a number of classification algorithms, clustering algorithms, neural network algorithms, decision trees, so on and so forth. In this section, we’ll talk about a few basic theorems that you should know – it’ll also help you understand other complex theorems with ease.

Bayes Theorem

This is one of the common theorems that you’ll come across if you’ve had any formal education in Computer Science. There have been numerous books over the years that excessively discuss Bayes Theorem and its concepts in an elaborate manner.

Bayes Theorem greatly simplifies complex concepts. It explains a lot of statistical facts using a few simple variables. It supports the concept of  “conditional probability”(e.g., If A occurred, it played in role in the occurrence of B). The most appreciable thing about this is the fact that you can predict the probability of any hypothesis using just the given data points.

Bayes can help you predict the probability of someone having cancer just by knowing their age. It can also let you know if an email is spam based on the number of words. This theorem is in essence used to remove uncertainty.

Fun fact: Bayes Theorem helped predict locations of U-boats as well as predicting the configuration of the Enigma machine to translate the German codes, in WW2. Even in modern Data Science Bayes finds extensive applications in many algorithms.
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K-Nearest Neighbor Algorithm

This is a very easy algorithm both in terms of understanding and implementation. So much so that it’s referred to as the “lazy algorithm”. Its simplicity lies in the fact that it’s based on logical deductions than any fundamental of statistics, per se. In layman terms, this algorithm looks to find groups closest to each other.

K-NN uses the concept of Euclidean Distance. It searches for local groups in and around a specified number of focal points. That number is represented by “k”. There are many approaches to finding out how large the value of ‘k’ should be as this is a user-decided value.

This concept is great for feature clustering, basic market segmentation, and seeking out outliers from a group of data entries. Most modern programming languages implement the K-NN algorithm in just two lines of code.

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Bagging (Bootstrap aggregating)

Bagging essentially refers to creating more than one models of a single algorithm – like a decision tree. Each of the models is trained on a different sample data (this is called bootstrap sample).

Therefore, each decision tree is made using different sample data – this solves the problem of overfitting to the sample size. Grouping decision trees like this essentially help in reducing the total error, as the overall variance decreases with each new tree added. A bag of such decision trees is known as a random forest.

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ROC Curve Analysis

The term ROC stands for Receiver Operating Characteristic. The ROC analysis curve finds extensive use in Data Science. It predicts how well a test is likely to perform by measuring its overall sensitivity vs. its fall-out rate. ROC Analysis is extremely important when determining the viability of any model.

How does it work?

Your machine learning model might give you some inaccurate predictions. Some of them are because a particular value should’ve been ‘true’ but is instead set ‘false’, or vice-versa.

What is the probability of you being correct then?

Using the ROC curve, you can see how accurate your prediction is. With the two different parables, you can also figure out where to put your threshold value. The threshold is where you decide if the binary classification is positive or negative – true or false.

As the two parables get closer to each other, the area under the curve will tend to zero. This essentially means that your model is tending to inaccuracy. Greater the area, greater is the accuracy of your model. This is one of the first tests used when testing any modeling, as it helps detect problems early on by telling whether or not the model is correct.

A real-life example of ROC curves – They are used to depict the connection/trade-off between clinical sensitivity and specificity for cut-off for a particular test or a combination of tests – in a graphical way. To add to that, the area under the ROC curve also gives a fair idea of the benefits of using the tests mentioned above. Hence, ROC curves find extensive use in Biochemistry for choosing an appropriate cut-off. Ideally, the best cut-off is the one that has the lowest false positive rate with the highest true positive rate together.  

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Importance of Statistics in Data Science

From the above discussion now that you are aware of the basic concepts of Statistics and fundamentals of Statistics, let’s talk about the importance to learn Statistics for Data Science. The crucial tools and technologies to organize and find deep insights in the data, to analyze and quantify data are provided by Statistics for Data Analytics.

We have given you an overview of Statistics basic concepts and the impact of Statistics on data exploration, analysis, modelling, and representation. We also indicate to the problem if their is an inconsistency while neglecting the basics of Statistics. If you are interested in joining the fastest growing industry, come straight to our website at UpGrad to follow our Statistics for Data Science tutorial as we provide both online and offline courses in the same. Once you ace up your game in atleast the fundamentals of Statistics and the Basics of Statistics, you will job ready.

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In Conclusion…
The above list of topics is by no means a comprehensive list of everything you need to know in Statistics. This list is just to give you a flavor of what all you might encounter in your journey of Data Science, and how can you be prepared for it.

All in all, this article introduces to some of the core concepts of Statistics for Data Science. A deep understanding of the concepts explained coupled will help you understand the other concepts easily. If you would like to explore more and master data science, find our best online data science courses.