Statistics With R: Core Concepts & Applications

Discovering Statistical Analysis: Exploring Essential Skills and Concepts

What you'll learn

Learn the essentials of R programming, including installation, setup, and exploring datasets for effective data analysis.

Understand the concept of subjects within a population and their relevance in statistical analysis.

Explore five types of statistical questions and their applications in summarizing, comparing, and predicting data.

Differentiate between categorical and quantitative data and understand their significance in statistical analysis.

Gain insights into both descriptive and inferential statistics and their usage in analyzing sample and population data.

Explore variable distribution and frequency tables to gain insights into data patterns.

Learn to visualize categorical and quantitative data distributions using various graphical representations.

Understand the different shapes of distributions for quantitative variables and their implications.

Learn methods to describe the center of quantitative data, including mean, median, and mode.

Explore measures of variability, including range and standard deviation, to understand data spread.

Gain insights into the empirical rule for understanding data distribution and identifying outliers.

Understand percentiles and quartiles and their significance in summarizing data variability.

Explore the relationship between different variables, including categorical and quantitative variables, and understand correlation analysis.

Learn predictive analysis techniques to make informed predictions based on data patterns and trends.

Requirements

The prerequisites for taking this course include a willingness to learn. No prior experience with statistical analysis or programming is required. Whether you're a beginner or seeking to enhance your skills, this course offers a solid foundation in statistical analysis techniques using R programming.

Description

Discover the world of statistical analysis in our comprehensive course, designed to cover key concepts and skills. Starting with R programming, we'll explore its significance and how to set it up for statistical computing. Then, we'll delve into understanding subjects within populations and different types of statistical questions. Moving forward, we'll learn about descriptive and inferential statistics, data types, and visualization techniques. We'll explore the distribution of variables, visualize distributions using graphs, and understand the shape of distributions. We'll also cover topics such as measuring the center and variability of quantitative data, empirical rules, percentiles, quartiles, and their graphical representation using box plots. Additionally, we'll explore the relationship between variables, including categorical and quantitative variables, and delve into correlation analysis. Through engaging modules, you'll gain practical skills and knowledge essential for effective statistical analysis in various settings.Course Outline:1: R ProgrammingIn this section, we'll explore the world of statistical computing with R, an essential tool in data science. We'll learn why R is a fantastic choice—it's free and widely used in machine learning. We'll cover how to download and set up R and RStudio on different operating systems, ensuring everyone can follow along. Then, we'll explore the RStudio interface and learn how to create a new project. We'll also discuss R packages, which extend R's capabilities, and how to install and load them. In this section, we'll start by installing R and RStudio., and then we will learn the basics of R programming.we'll delve into R comments and datasets. We'll explore datasets stored in data frames, covering variables like integers, numerics, and factors (categorical). Understanding these concepts will aid in effective data analysis in R.By the end, you'll be ready to embark on your statistical journey using R!2: Subjects in the population.In this section, the data outlines the concept of subjects within a population for statistical analysis. Subjects can range from people to various objects, such as orange trees, cars, or chickens, depending on the research focus. Examples illustrate the diverse nature of subjects in statistical studies.3: Statistical QuestionStatistical questions are categorized into five types: Descriptive, Comparative, Relationship, Causal, and Predictive. Descriptive questions aim to summarize data, while Comparative questions compare groups. Relationship questions explore connections between variables, while Causal questions investigate direct causation. Predictive questions use data summaries to make predictions. Examples illustrate each question type's purpose and application4: Types of Data.In this section, we will look at how the answers to our statistical questions can be divided into two types of data: categorical data and quantitative data. We will also explore their subtypes and understand why it is essential to classify data into these two categories.5: Descriptive and inferential statistics.Here We will discuss when we have a sample from the population, we need both descriptive and inferential statistics.However, if we have data for the entire population, we only need to use descriptive statistics. There's no need for inferential statistics in such cases.We'll use real-life examples, like surveys from the General Social Survey website and the UK age pyramid from the 2020 census, to understand these concepts.7: Distribution of a variable and frequency tableAfter that We're going to explore the concept of variable distribution and how frequency tables can help us see this distribution clearly. To understand this, we'll use survey data from the General Social Survey website, look at an age pyramid based on UK census data, and analyze information from the Titanic dataset on Wikipedia.8: Visualize the distribution of a variable using graphs.we will create bar graphs and pie charts to show the distribution of categorical variables using the Titanic dataset. For the discrete variable, we will make a histogram using the GSS survey data. Lastly, we will create a histogram for a continuous variable using the Titanic dataset.9: The shape of the distribution.We're going to talk about different shapes of distributions for quantitative variables. Imagine distributions like hills or valleys. There are three types: one with a single hill in the middle, another where one side stretches out longer than the other, and one where there are two hills. We'll learn about these using examples like heights of people, survey results, and how people rate products. It's like looking at different patterns in numbers.10: Center of Quantitative Data.There are three ways to describe the center of quantitative data: mean, median, and mode. We will examine the population mean and median using a hypothetical population of female heights, and then we'll explore the sample mean and median using a simulated sample from this same hypothetical female height population.11: Measuring the variability of Quantitative data.The simplest way of describing the variability of the quantitative data is range which is easily affected by outliers. The more robust measure for variability is standard deviation. We will discuss how most of the times sample variability underestimates the population variability that’s why we tweak the sample standard deviation formula a little bit.We will also learn how we can generate a hypothetical normal distribution just by using two values mean and standard deviation.12: Empirical Rule.Then we will discuss empirical rule that tells us using standard deviation we can find out how much data falls at different standard deviations away from the mean in a normal distribution. Then we will find out what makes an observation an outlier. At the end we will see what could be the plausible values of the standard deviation.13: Percentiles and quartiles.In this section we will discuss percentiles and quartiles using growth charts, Growth charts are special kinds of charts that help us understand how kids are growing by comparing their height and weight to other children of the same age and gender.We will also discuss sat exam scores, which is another good example of using percentiles to compare how well students perform as compared to each other.Then we will summaries the entire dataset using 5 number which is called a 5 number summary. At the end we will see another way of measuring variability which is called interquartile range which does not get effected by outliers like range and standard deviation and also its graphical representation box plot.14: Relationship Between VariablesUp until now, we've focused on individual variables, examining their types, distributions, and methods for visual representation using graphs. However, it's time to explore how two variables relate to each other.There are three primary types of relationships:The relationship between two categorical variables.The relationship between two quantitative variables.The relationship between a categorical variable and a quantitative variable.Furthermore, we will delve into the concept of correlation, which not only reveals the direction but also measures the strength of the relationship between two quantitative variables.

Overview

Section 1: Introduction

Lecture 1 Introduction

Lecture 2 What you will learn in this tutorial

Section 2: R Programming

Lecture 3 Why Do We Need R?

Lecture 4 What Is R and R Studio?

Lecture 5 R Installation

Lecture 6 RStudio Installation

Lecture 7 R Studio Interface (Console and Help Tab)

Lecture 8 R Studio Interface (File, Packages, Plot, and Environment Tabs)

Lecture 9 Create a New Project in R

Lecture 10 Download Code and Data Files for This Project

Lecture 11 R Packages

Lecture 12 Install a Package in R

Lecture 13 Load a Package in R

Lecture 14 R Data Sets

Lecture 15 Broom in R Studio

Lecture 16 Get the Feel of the Data

Lecture 17 Get the Feel of the Data: View()

Lecture 18 Get the Feel of the Data: glimpse()

Lecture 19 Types of Variables in R

Lecture 20 Types of Variables in R: Integers

Lecture 21 Types of Variables in R: Numerics

Lecture 22 Types of Variables in R: Factors or Categorical Variables

Lecture 23 Types of Variables in R: Types of Factors or Categorical Variables

Lecture 24 Errors, Warnings, and Messages

Lecture 25 Error, Warning, and Messages: Errors

Lecture 26 Error, Warning, and Messages: Information Messages

Lecture 27 Error, Warning, and Messages: Warning Messages

Lecture 28 Error, Warning, and Messages: A Quick Recap

Section 3: Subjects in the Population

Lecture 29 Subjects in a Population

Section 4: Statistical Questions

Lecture 30 Statistical Questions

Lecture 31 Types of Statistical Questions

Lecture 32 Descriptive Questions

Lecture 33 Comparative Questions

Lecture 34 Relationship Questions

Lecture 35 Causal Questions

Lecture 36 Predictive Questions

Section 5: Types of Data

Lecture 37 Types of Data

Lecture 38 Categorical Data

Lecture 39 Nominal Categorical Data

Lecture 40 Ordinal Categorical Data

Lecture 41 Dichotomous Categorical Data

Lecture 42 Quantitative Data

Lecture 43 Discrete Quantitative Data

Lecture 44 Continuous Quantitative Data

Lecture 45 Why It Is Important to Classify Variables

Section 6: Descriptive and Inferential Statistics

Lecture 46 Descriptive and Inferential Statistics

Lecture 47 Descriptive Statistics

Lecture 48 General Social Survey

Lecture 49 Real World Example of Descriptive Statistics: GSS Survey

Lecture 50 Descriptive Statistics for the Entire Population

Lecture 51 Inferential Statistics

Lecture 52 Sample Statistics and Population Parameters

Section 7: Distribution of a Variable and Frequency Table

Lecture 53 Distribution of a variable and Frequency table

Lecture 54 Distribution of a Categorical Variable

Lecture 55 Frequency Table for Categorical Variables

Lecture 56 Understanding Relative Frequency: Proportions and Percentages

Lecture 57 Distribution of Quantitative Variables

Lecture 58 Frequency Table for Discrete Quantitative Variables

Lecture 59 Frequency table for discrete Var: Hours Per Day Watching TV (Limited Outcomes)

Lecture 60 Frequency table for discrete Var: Ideal Number of Kids (Limited Outcomes)

Lecture 61 Frequency table for discrete Var: Math Exam Scores (Wide Range of Outcomes)

Lecture 62 Frequency Table: Continuous Quantitative Variables

Lecture 63 Frequency Table for Continuous Variables: Age in Census

Lecture 64 Calculate Proportion and Percentages in Excel

Lecture 65 Task 1: Frequency Table for Discrete Quantitative Variable in Excel

Lecture 66 Task 2: Frequency Table for Categorical Variable in Excel

Lecture 67 Titanic Dataset

Lecture 68 Loading Titanic Data Set from Excel into R

Lecture 69 Getting to Know the Titanic Dataset: Exploring Variables

Lecture 70 Frequency Table for Categorical Variables in R

Lecture 71 Proportions and Percentages in Frequency Table in R

Lecture 72 Pipe Operator

Lecture 73 Discrete Data

Lecture 74 General Social Survey: Number of Kids

Lecture 75 Recreating GSS Survey Data in Excel: Ideal Number of Kids

Lecture 76 Frequency Table for Discrete Data 1: Loading Number of Kids Data in R

Lecture 77 Frequency Table for Discrete Data 2: Creating a Frequency Table

Lecture 78 Frequency Table for Continuous Data 1: Loading Titanic Data In R

Lecture 79 Frequency Table for Continuous Data 2: Calculating Range

Lecture 80 Frequency Table for Continuous Data 3: Grouping Passengers by Age Group

Lecture 81 Frequency Table for Continuous Data 4: Left-Closed and Right-Open Intervals

Lecture 82 Frequency Table for Continuous Data 5: Creating a Frequency Table

Lecture 83 Frequency Table for Continuous Data 6: Missing Values NAs

Section 8: Visualizing the Distribution of a Variable Using Graphs

Lecture 84 Graphs

Lecture 85 Bar Graph

Lecture 86 Pie Chart

Lecture 87 Pie Chart in R

Lecture 88 Bar graph or Pie chart (Article )

Lecture 89 Histogram for a Discrete Variable

Lecture 90 Histogram for a Discrete Variable in R

Lecture 91 Histogram for a Continuous Variable

Lecture 92 Histogram for a Continuous Variable

Lecture 93 Histogram for a Continuous Var: Left-Closed, Right-Open: Adjusting Intervals

Lecture 94 Histogram for a Continuous Var: Dealing with Missing Values

Lecture 95 Histogram for a Continuous Var: Setting Interval Lengths in a Histogram

Section 9: The Shape of the Distribution

Lecture 96 The Shape of a Distribution

Lecture 97 Unimodal Distribution

Lecture 98 Symmetric Distribution

Lecture 99 Symmetric Distribution of Male Height: An Example

Lecture 100 Simulating Hypothetical Normal Distribution in R (Male Heights)

Lecture 101 Symmetric Distribution Histogram in R

Lecture 102 Skewed Distributions

Lecture 103 Left-Skewed Distribution

Lecture 104 Left-Skewed Distribution Histogram in R

Lecture 105 Right-Skewed Distribution

Lecture 106 Right-Skewed Distribution Histogram in R

Lecture 107 Bimodal Distributions

Lecture 108 Histogram for Bimodal Distribution

Lecture 109 Another Example of Bimodal Distribution

Lecture 110 Histogram for Bimodal Distribution 2

Lecture 111 Uniform Distribution

Lecture 112 Simulating Hypothetical Uniform Distribution in R (Dice Output)

Lecture 113 Histogram for Uniform Distribution

Section 10: Center of Quantitative Data

Lecture 114 Center of Quantitative Data

Lecture 115 Mode

Lecture 116 Mode in Symmetric Discrete Distribution

Lecture 117 Mode in Left Skewed Discrete Distribution

Lecture 118 Mode in Right Skewed Discrete Distribution

Lecture 119 Mode in Uniform Discrete Distribution

Lecture 120 Mode in Categorical Variables

Lecture 121 Mean

Lecture 122 Calculating Mean in Excel

Lecture 123 Impact of Outliers on the Mean

Lecture 124 Formula for the Mean(Article)

Lecture 125 Compute Population Mean in R

Lecture 126 Compute Sample Mean in R (Part 1)

Lecture 127 Compute Sample Mean in R (Part 2)

Lecture 128 Median

Lecture 129 Impact of Outliers on the Median

Lecture 130 Formula for Median (Article)

Lecture 131 Compute Population Median in R

Lecture 132 Compute Sample Median in R

Lecture 133 Outliers and Skewed Distributions (Article)

Lecture 134 Mean and Median in Symmetric Distribution

Lecture 135 Mean and Median in Symmetric Distribution In R

Lecture 136 Mean, Median in Skewed Distribution (Article)

Lecture 137 Mean, Median in Right Skewed Distribution In R

Lecture 138 Mean, Median in Left Skewed Distribution In R

Lecture 139 The Mean or Median? (Article)

Section 11: Measuring the Variability of Quantitative Data

Lecture 140 What is the Variability

Lecture 141 Range

Lecture 142 Standard Deviation

Lecture 143 Compute Standard Deviation Manually in Excel(Part 1)

Lecture 144 Compute Standard Deviation Manually in Excel(Part 2)

Lecture 145 Formula for Population Standard Deviation (Article)

Lecture 146 Formula for the Sample Standard Deviation (Article)

Lecture 147 Population Standard Deviation In R

Lecture 148 Sample Standard Deviation In R

Lecture 149 Sample Standard Deviation Formula Recap

Lecture 150 Calculate Standard Deviation Manually in R Using n-1 (Part 1)

Lecture 151 Calculate Standard Deviation Manually in R Using n-1 (Part 2)

Lecture 152 Sample Standard Deviation vs. Population Standard Deviation (Article)

Lecture 153 "n" versus "n-1" Mathematically (Article)

Lecture 154 Hypothetical Normal Distribution

Lecture 155 Hypothetical Normal Distribution In R

Lecture 156 Z-Score (Article)

Section 12: Empirical Rule

Lecture 157 Empirical Rule

Lecture 158 Empirical Rule in R (Part 1)

Lecture 159 Empirical Rule in R (Part 2)

Lecture 160 Understanding Data Distribution with the Empirical Rule

Lecture 161 Outliers in Normal Distributions (Article)

Lecture 162 Plausible Value of Standard Deviation (Article)

Section 13: Percentiles and Quartiles

Lecture 163 Percentiles and Quartiles

Lecture 164 Percentiles and Quartiles in R

Lecture 165 Real-Life Usage of Percentiles: Growth Charts

Lecture 166 Real-Life Usage of Percentiles: SAT Exams

Lecture 167 Making Sense of SAT Scores: The Scaling Process Simplified (Article)

Lecture 168 5-Number Summary Using Quartiles (Article)

Lecture 169 Measuring Variability Using Interquartile Range (IQR)

Lecture 170 Identifying Outliers Using Interquartile Range (IQR)

Lecture 171 Boxplot in R

Lecture 172 Creating Side-by-Side Box Plots

Lecture 173 Comparing Two Distributions Using Box Plots

Section 14: Relationship Between Variables

Lecture 174 Relationship Between Variables

Lecture 175 Response and Explanatory Variables (Article)

Lecture 176 Types of Relationship

Lecture 177 Relationship Between Two Categorical Variables

Lecture 178 Contingency Table

Lecture 179 Contingency Table In R

Lecture 180 Stacked Bar Plot (Article)

Lecture 181 Stacked Bar Plot In R

Lecture 182 Relationship between Categorical and Quantitative Variables

Lecture 183 Relationship between Two Quantitative Variables

Lecture 184 Positive Relationship (Article)

Lecture 185 Negative Relationship (Article)

Lecture 186 No Relationship (Article)

Lecture 187 Scatterplot in R

Lecture 188 Correlation (Article)

Lecture 189 Correlation In R

Section 15: Summary

Lecture 190 Summary

This course is suitable for anyone interested in learning statistical analysis techniques using R programming. Whether you're a beginner looking to acquire new skills or someone already familiar with statistical concepts seeking to deepen your knowledge, this course provides valuable insights and practical guidance.