Statistics: A Step-By-Step Introduction

Lessons and examples from a former Google data scientist to master hypothesis tests, confidence intervals, and more

What you'll learn
Build a strong statistical vocabulary and foundation in probability
Learn to tests hypotheses for proportions and means
Learn how to create confidence intervals, and their connection to hypothesis tests
Learn how to perform chi-square tests for categorical data
Requirements
Basic arithmetic skills
Basic algebra (ability to understand equations with variables)
Description
This 51 lesson course teaches the foundational material of statistics covered in an introductory college course, with a focus on mastering hypothesis testing for proportions, means, and categorical data.The course includes:51 video lectures, using the innovative lightboard technology to deliver face-to-face lectures157 pages of lecture notes covering important vocabulary, examples and explanations from the 51 lessons19 quizzes to check your understanding9 assignments with solutions to practice what you have learnedYou will learn about:Common terminology to describe different types of data and learn about commonly used graphsBasic probability, including the concept of a random variable, probability mass functions, cumulative distribution functions, and the binomial distributionWhat is the normal distribution, why it is so important, and how to use z-scores and z-tables to compute probabilitiesType I errors, alpha, critical values, and p-valuesHow to conduct hypothesis tests for one and two proportions using a z-testHow to conduct hypothesis tests for one and two means using a t-testConfidence Intervals for proportions and means, and the connection between hypothesis testing and confidence intervalsHow to conduct a chi-square goodness-of-fit testHow to conduct a chi-square test of homogeneity and independence.This course is ideal for many types of students:Anyone who wants to learn the foundations of statistics and understand concepts like p-values and confidence intervalsStudents taking an introductory college or high school statistics class who would like further explanations and detailed examplesData science professionals who would like to refresh and expand their statistics knowledge to prepare for job interviews

Overview

Section 1: Introduction, Data, and Graphs

Lecture 1 Introduction (Download Lecture Notes and Assignments here!)

Lecture 2 Statistics, data, and variables

Lecture 3 Categorical Variables, Frequency and Proportion, Bar Charts

Lecture 4 Discrete and Continuous Variables, Dot Plots

Lecture 5 Stem-and-leaf plots and Histograms

Lecture 6 Shape, Skewness. and Symmetry

Lecture 7 Central Tendency: Mean, Median, Mode

Lecture 8 Spread: Range, IQR, Boxplots

Lecture 9 Spread: Variance and Standard Deviation

Section 2: Probability

Lecture 10 Observed vs. Expected

Lecture 11 Outcomes, Events, Sample Space, Complements

Lecture 12 Probability of A or B: Unions of Events

Lecture 13 Probability of A and B: Intersections and Conditional Probability

Lecture 14 Random Variables, PDF/PMF, CDF

Lecture 15 Binomial distribution

Lecture 16 Expected value

Section 3: Normal distributions

Lecture 17 The Standard Normal Distribution and the Empirical Rule

Lecture 18 More on the Empirical Rule

Lecture 19 Z-table

Lecture 20 Normal distribution parameters: mu and sigma

Lecture 21 Z-scores

Lecture 22 The Central Limit Theorem

Section 4: One Proportion: Z-test

Lecture 23 The Null and Alternative Hypothesis

Lecture 24 Critical values and Decision Rules

Lecture 25 P-values

Lecture 26 P-values with normal approximation

Lecture 27 Type I errors and Alpha

Lecture 28 One proportion z-test example

Section 5: Two Proportions:: Z-test

Lecture 29 Hypothesis testing for two proportions

Lecture 30 Hypothesis testing for two proportion example

Section 6: One Mean: Z-test, t-test

Lecture 31 One sample z-test

Lecture 32 One sample t-test

Lecture 33 One sample t-test example

Section 7: Two Means: T-test

Lecture 34 Two sample t-test

Lecture 35 Two sample t-test example

Lecture 36 Pooled and Unpooled

Lecture 37 Paired t-tests

Section 8: Confidence Intervals

Lecture 38 Confidence Intervals

Lecture 39 (Optional) Pivoting a test statistic to make a CI

Lecture 40 Performing a hypothesis test based on a confidence interval

Lecture 41 All Four CI Formulas

Lecture 42 Confidence Interval One Proportion Example

Lecture 43 Confidence Interval Two Proportion Example

Lecture 44 Confidence Interval One Mean Example

Lecture 45 Confidence Interval Two Mean Example

Section 9: Chi-Square Tests

Lecture 46 Chi-square Goodness of Fit Test: Die

Lecture 47 Chi-square Goodness of Fit example

Lecture 48 Two way tables and expected counts

Lecture 49 Chi-square test for two way table

Lecture 50 Independence vs Homogeneity

Lecture 51 Chi Square Two way Example

Self-learners who want a strong college-level foundational course in statistics,College and high school students who need to supplement their course with high-quality lectures and example problems,Data science professionals looking to refresh or expand their knowledge to prepare for job interviews