A/B testing

The A/B test (also known as a randomised controlled trial, or RCT, in the other sciences) is a powerful tool for product development. some motivations: With the rise of digital marketing led by tools including Google Analytics, Google Adwords, and Facebook Ads, a key competitive advantage for businesses is using A/B testing to determine effects…

Binomial Random Variables: Introduction

Binomial Random Variables So far, in our discussion about discrete random variables, we have been introduced to: The probability distribution, which tells us which values a variable takes, and how often it takes them. The mean of the random variable, which tells us the long-run average value that the random variable takes. The standard deviation…

Introduction to Normal Random Variables: Overview

In the Exploratory Data Analysis sections of this course, we encountered data sets, such as lengths of human pregnancies, whose distributions naturally followed a symmetric unimodal bell shape, bulging in the middle and tapering off at the ends. Many variables, such as pregnancy lengths, shoe sizes, foot lengths, and other human physical characteristics exhibit these properties: symmetry…

The Big Picture: Inference

Recall again the Big Picture, the four-step process that encompasses statistics: data production, exploratory data analysis, probability, and inference. We are about to start the fourth part of the process and the final section of this course, where we draw on principles learned in the other units (exploratory data analysis, producing data, and probability) in order…

Conditional Probability and Independence Introduction

Introduction In the last section, we established the five basic rules of probability, which include the two restricted versions of the Addition Rule and Multiplication Rule: The Addition Rule for Disjoint Events and the Multiplication Rule for Independent Events. We have also established a General Addition Rule for which the events need not be disjoint. In order to complete…

How To Distribute Sample

Sampling Distributions Introduction Already on several occasions we have pointed out the important distinction between a population and a sample. In Exploratory Data Analysis, we learned to summarize and display values of a variable for a sample, such as displaying the blood types of 100 randomly chosen U.S. adults using a pie chart, or displaying the heights of 150…

Probability A short story

Sample Spaces As we saw in the previous section, probability questions arise when we are faced with a situation that involves uncertainty. Such a situation is called a random experiment, an experiment that produces an outcome that cannot be predicted in advance (hence the uncertainty). Here are a few examples of random experiments: Toss a coin…

Producing Data From Population

Recall “The Big Picture,” the four-step process that encompasses statistics: data production, exploratory data analysis, probability, and inference. In the previous posts, we considered exploratory data analysis—the discovery of patterns in the raw data. First we need to choose the individuals from the population that will be included in the sample. Then, once we have…

Causation and Lurking Variables With simpson’s paradox

The one and only principle rule in statistics is Principle:Association does not imply causation! The scatterplot below illustrates how the number of firefighters sent to fires (X) is related to the amount of damage caused by fires (Y) in a certain city. The scatterplot clearly displays a fairly strong (slightly curved) positive relationship between the two variables. Would it,…

Relations A statistical Approach

In most studies involving two variables, each of the variables has a role. We distinguish between: the explanatory variable (also commonly referred to as the independent variable)-—the variable that claims to explain, predict or affect the response; and the response variable (also commonly referred to as the dependent variable)-—the outcome of the study. Typically the explanatory (or independent) variable is denoted by X, while the response (or…