# Statistical Thinking in Python (Part 1)

Build the foundation you need to think statistically and to speak the language of your data.

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## Course Description

After all of the hard work of acquiring data and getting them into a form you can work with, you ultimately want to make clear, succinct conclusions from them. This crucial last step of a data analysis pipeline hinges on the principles of statistical inference. In this course, you will start building the foundation you need to think statistically, speak the language of your data, and understand what your data is telling you. The foundations of statistical thinking took decades to build, but can be grasped much faster today with the help of computers. With the power of Python-based tools, you will rapidly get up-to-speed and begin thinking statistically by the end of this course.

- 1
### Graphical Exploratory Data Analysis

**Free**Before diving into sophisticated statistical inference techniques, you should first explore your data by plotting them and computing simple summary statistics. This process, called exploratory data analysis, is a crucial first step in statistical analysis of data.

Introduction to Exploratory Data Analysis50 xpTukey's comments on EDA50 xpAdvantages of graphical EDA50 xpPlotting a histogram50 xpPlotting a histogram of iris data100 xpAxis labels!100 xpAdjusting the number of bins in a histogram100 xpPlot all of your data: Bee swarm plots50 xpBee swarm plot100 xpInterpreting a bee swarm plot50 xpPlot all of your data: ECDFs50 xpComputing the ECDF100 xpPlotting the ECDF100 xpComparison of ECDFs100 xpOnward toward the whole story!50 xp - 2
### Quantitative Exploratory Data Analysis

In this chapter, you will compute useful summary statistics, which serve to concisely describe salient features of a dataset with a few numbers.

Introduction to summary statistics: The sample mean and median50 xpMeans and medians50 xpComputing means100 xpPercentiles, outliers, and box plots50 xpComputing percentiles100 xpComparing percentiles to ECDF100 xpBox-and-whisker plot100 xpVariance and standard deviation50 xpComputing the variance100 xpThe standard deviation and the variance100 xpCovariance and the Pearson correlation coefficient50 xpScatter plots100 xpVariance and covariance by looking50 xpComputing the covariance100 xpComputing the Pearson correlation coefficient100 xp - 3
### Thinking Probabilistically-- Discrete Variables

Statistical inference rests upon probability. Because we can very rarely say anything meaningful with absolute certainty from data, we use probabilistic language to make quantitative statements about data. In this chapter, you will learn how to think probabilistically about discrete quantities: those that can only take certain values, like integers.

Probabilistic logic and statistical inference50 xpWhat is the goal of statistical inference?50 xpWhy do we use the language of probability?50 xpRandom number generators and hacker statistics50 xpGenerating random numbers using the np.random module100 xpThe np.random module and Bernoulli trials100 xpHow many defaults might we expect?100 xpWill the bank fail?100 xpProbability distributions and stories: The Binomial distribution50 xpSampling out of the Binomial distribution100 xpPlotting the Binomial PMF100 xpPoisson processes and the Poisson distribution50 xpRelationship between Binomial and Poisson distributions100 xpHow many no-hitters in a season?50 xpWas 2015 anomalous?100 xp - 4
### Thinking Probabilistically-- Continuous Variables

It’s time to move onto continuous variables, such as those that can take on any fractional value. Many of the principles are the same, but there are some subtleties. At the end of this final chapter, you will be speaking the probabilistic language you need to launch into the inference techniques covered in the sequel to this course.

Probability density functions50 xpInterpreting PDFs50 xpInterpreting CDFs50 xpIntroduction to the Normal distribution50 xpThe Normal PDF100 xpThe Normal CDF100 xpThe Normal distribution: Properties and warnings50 xpGauss and the 10 Deutschmark banknote50 xpAre the Belmont Stakes results Normally distributed?100 xpWhat are the chances of a horse matching or beating Secretariat's record?100 xpThe Exponential distribution50 xpMatching a story and a distribution50 xpWaiting for the next Secretariat50 xpIf you have a story, you can simulate it!100 xpDistribution of no-hitters and cycles100 xpFinal thoughts50 xp

Datasets

2008 election results (all states)2008 election results (swing states)Belmont StakesSpeed of lightCollaborators

Prerequisites

Python Data Science Toolbox (Part 2)#### Justin Bois

Lecturer at the California Institute of Technology

Justin Bois is a Teaching Professor in the Division of Biology and Biological Engineering at the California Institute of Technology. He teaches nine different classes there, nearly all of which heavily feature Python. He is dedicated to empowering students in the biological sciences with quantitative tools, particularly data analysis skills. Beyond biologists, he is thrilled to develop courses for DataCamp, whose students are an excited bunch of burgeoning data scientists!

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