Table of Contents - Relaxed Statistics
Introduction
This is Relaxed Statistics.
Let's learn statistics together!
Using the official CBT problem collection for the Statistics Grade 2 exam as a starting point, we will delve into statistical topics!
I am writing this so that anyone can read it (or at least, that is my intention 😉).
If you have the problem collection, please start reading from "Solving Problems."
If you don't have the problem collection but are interested in statistics, please read "Learning" and "Practicing," which cover general statistical topics.
There are also articles that provide sample files for Python and EXCEL.
You can also learn by listening with "Radio Outline," which provides audio summaries of the blog!
🍀🍀🍀
Overview & Text
The menu article summarizes the general structure of the blog, the problem collection, and reference books.
Please be sure to read 🔽this article🔽.
Table of Contents
The article titles are linked to the titles in the official Statistics Grade 2 [CBT Edition] problem collection.
Underlined titles are links to the articles.
Please feel free to jump over to the articles 🚀
2025/05/12 Notice: "Addition of Radio Outline"
We have added "Radio Outline," which introduces the overview of each section in a radio-talk style audio format.
This was created using Google's Notebook LM for AI-based article summarization and audio generation.
1. Field of Univariate Descriptive Statistics
📻️ Click here for Radio Outline
1.1 Calculating Relative Frequency
📈Creating Frequency Distribution Tables, Histograms, and Box Plots
1.2 Classes Containing the Median
📈Calculating Quartiles, Creating Frequency Distribution Tables and Histograms
1.3 Box Plots and Frequency Distribution
📈Creating and Interpreting Box Plots, Deep Dive into Quartiles
1.4 Reading Stem-and-Leaf Plots
📈Creating Stem-and-Leaf Plots
1.5 Characteristics of Time Series Fluctuations
📈Visualizing Trend, Seasonal, and Irregular Fluctuations
1.6 Formula for Average Rate of Change
📈Calculating Average Rate of Change Using Geometric Mean
1.7 Mean and Standard Deviation via Linear Transformation
📈Linearly Transforming Temperature Data from Celsius to Fahrenheit
📈Calculating Mean, Variance, and Standard Deviation Using Bread Weight Data
1.8 Explanation of Lorenz Curve and Gini Coefficient
📈Creating Lorenz Curve Graphs, Calculating Gini Coefficients
1.9 Selecting a Correlogram
📈Calculating Autocorrelation Coefficients for Time Series Data, Deep Dive into Reading Correlograms
1.10 Formula for Laspeyres Index
📈Calculating Fruit Price Indices Using Laspeyres, Paasche, and Fisher Formulas
2. Field of Bivariate Descriptive Statistics
2.1 Scatter Plots and Frequency Distributions
📈 Creating scatter plots, deep dive into the relationship with frequency distribution tables and histograms
2.2 Reading Scatter Plots
📈 Creating and interpreting scatter plots, creating pair plots
2.3 Selecting Scatter Plots
📈 Calculating correlation coefficients, interpreting the relationship between correlation coefficients and scatter plots
2.4 Scatter Plots, Correlation, and Range
📈 Quiz on estimating correlation coefficients from scatter plots
2.5 Calculating Covariance from Correlation Coefficients
📈 Calculating covariance, data analysis using scatter plots, box plots, and histograms
2.6 Describing Correlations
📈 Changes in scatter plots and correlation coefficients due to various sampling methods
3. Data Collection Field
3.1 Properties of Each Sampling Method
📈 Selecting representative sampling methods
3.2 Forms of Research
📈 Identifying experimental research and observational research
3.3 Fisher's Three Principles
📈 Judging whether it conforms to Fisher's three principles (with a story)
3.4 Non-sampling Errors
📈 Identifying sampling errors and non-sampling errors
4. Probability Field
4.1 Probability of Intersection Events
📈 Calculate the probability of intersection events using the definition of conditional probability and the multiplication rule of probability
4.2 Bayes' Theorem
📈 Calculate the probability of drawing a rare cookie and the probability of a positive test result using Bayes' theorem
4.3 Conditional Expectation
📈 Calculate the probability of getting a win for the first time using a geometric distribution, and visualize the geometric distribution
4.4 Mutually Exclusive and Independent Events
📈 Determine whether events are mutually exclusive or independent using the addition rule of probability and Venn diagrams
4.5 Expectation of Two-Stage Experimental Random Variables
📈 Calculate the "expectation of two-stage random variables" where a bag is chosen by rolling a die, and a red ball is drawn from multiple balls in the bag
4.6 Correctness of Match Order Explanation + Monty Hall Problem
📈 Challenge two probabilities that defy intuition!
Probability of two consecutive wins, Monty Hall problem (Bayes' theorem)
5. Field of Probability Distributions
5.1 Determining Constants for Probability Distributions
📈 Definite Integration of Continuous Distribution Probabilities with Google Colab!
5.2 Calculating Normal Probabilities
📈 Probability Calculation and Visualization of Normal Distributions
5.3 Expected Values of Functions of Random Variables
📈 Solving Continuous Probability Distribution Probabilities via 1) Definite Integration, 2) Geometry, and 3) Mathematical Solvers
5.4 Normal Approximation of Binomial Distributions
📈 Learn Binomial Distributions and Calculate the Probability of Differences Between Exit Poll Percentages and Population Proportions!
5.5 Ratio of Binomial Probabilities
📈 A Mysterious Journey to Find Probability Ratios by Setting Random Variables to x and x+1
5.6 Distribution Shape, Skewness, and Kurtosis
📈 Visualizing Skewness and Kurtosis of Probability Distributions, and Their Relationship with Moment Generating Functions
5.7 Probability Calculation of X-Y
📈 Variable Transformation and Linear Combinations of Random Variables, Reproducibility of Normal Distributions, and Simulations
5.8 Linear Variable Transformation, Covariance, and Correlation Coefficient
📈 [Special Feature] Transformation Formulas for Random Variables, and Calculation Formulas for Expected Value, Variance, Covariance, and Correlation Coefficient
6. Field of Sampling Distributions
6.1 Sampling Distribution of Sample Proportion
📈 Interval estimation of population proportion, exit polls, meaning of 95% confidence interval, and experiments
6.2 Median of Sampling Distribution, etc.
📈 Experiments on sample median, mode, and the Central Limit Theorem
6.3 Variance of Estimators
📈 Estimators and estimates, precision of weight measurement using a balance scale
6.4 Properties of Random Variables of Sums and Differences
📈 Two random variables, bivariate normal distribution, 3D graphs
6.5 Probability Calculation of t-distribution
📈 Probability of $${t}$$ distribution, relationship between sampling distribution and $${t}$$ distribution, statistical estimation and statistical hypothesis testing
6.6 Variance, Covariance, and Correlation Coefficient
📈 Correlation coefficient of three random variables and their means, linear combination of random variables, experiments using Python
6.7 Expected Value of X squared
📈 Finding $${E[X^2]}$$ from the variance formula $${V[X]=E[X^2]-(E[X])^2}$$
6.8 Characterization of F-distribution
📈 Standard normal distribution, $${{\chi^2}}$$ distribution, $${t}$$ distribution, and $${F}$$ distribution are connected through three random variables
7. Field of Estimation
7.1 Estimates and Standard Errors
📈 Point estimation of population proportion, standard error, and sports participation by prefecture
7.2 Unbiased Estimator of the Square of the Population Mean
📈 Expected value and variance of sample mean, variance formula, and expanding the formula for unbiased estimators
7.3 Sample Size when Population Proportion p is Unknown
📈 Interval estimation of population proportion and calculation of minimum sample size
7.4 Capture-Recapture Method Confidence Intervals
📈 Catch fish → mark → release → recapture → estimate fish population in the basin
7.5 Confidence Intervals for Population Mean in Non-Normal Populations
📈 Normal distribution approximation, visualizing distributions with graphs, and searching for approximating distributions with Fitter
7.6 Confidence Intervals and Tests for the Difference in Population Proportions
📈 Confidence intervals for the difference in population proportions, tests for the difference in population proportions, and public opinion polls on sports
8. Field of Hypothesis Testing
8.1 Concepts of Population Mean Testing
📈 Experience the general procedure of statistical hypothesis testing, one-sample population mean testing
8.2 Type I Error and Probability
📈 Type I and Type II errors in statistical hypothesis testing, thumbtack tossing simulation
8.3 One-tailed t-test for Population Mean
📈 One-sample population mean t-test, statistical hypothesis testing using manual calculation, Excel, and Python
8.4 Procedure for Population Proportion Testing
📈 One-sample population proportion z-test, coin toss experiment, Yates' correction
8.5 Testing Using Normal Approximation
📈 One-sample population proportion z-test, defect rate, test statistic Z
8.6 Testing for Difference in Population Means
📈 Two-sample independent t-test for difference in population means, performing t-tests with various tools
8.7 Testing for Paired Differences
📈 Paired two-sample t-test for difference in population means, one-tailed test
8.8 Testing for Difference in Population Proportions
📈 Paired two-sample t-test for difference in population means, defect rate, statsmodels
8.9 Testing for Homogeneity of Variance
📈 F-test for ratio of two-sample population variances, lower-tail probability of F-distribution
8.10 Graph of (β, 1-α)
📈 Type I error α, Type II error β, advanced problems
9. Field of Chi-Square Testing
9.1 Field of Goodness-of-Fit Testing
9.1.1 Basics of Goodness-of-Fit Test
📈 Get used to the elements of goodness-of-fit tests: "observed frequency," "expected frequency," and "number of categories"
9.1.2 Goodness-of-Fit Test for Uniformity
📈 In the case of uniformity, the denominator can be aggregated into one; standardization of the calculation procedure for goodness-of-fit tests
9.1.3 Test of Homogeneity
📈 Test of homogeneity, two-dimensional cross-tabulation, chi-square test
9.1.4 Fitting a Poisson Distribution
📈 The assumed distribution is a Poisson distribution, and the parameter $${\lambda}$$ of the Poisson distribution is known
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9.2 Field of Independence Tests
9.2.1 Expected Frequency and Degrees of Freedom
📈 Get used to the elements of independence tests: "expected frequency" and "degrees of freedom of the $${\chi^2}$$ distribution"
9.2.2 Expected Frequency and Independence Test
📈 Get used to the elements of independence tests: "$${\chi^2}$$ test statistic"
9.2.3 Expected Frequency and Independence Test
📈 Get used to the "expected frequency" and "$${\chi^2}$$ test statistic" of a 2x2 cross-tabulation
9.2.4 Correctness Regarding Test Results
📈 2x2 cross-tabulation and independence test
10. Field of Linear Models
[Special Feature] Simple Linear Regression Model
Part 1: Overview
📈 Summary of topics on simple linear regression models
Part 2: Utilizing Tools
📈 Practical examples of simple linear regression models using EXCEL, R, Python, and College Analysis
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10.1 Field of Regression Analysis
10.1.1 Least Squares Method and Slope Testing
📈 Linear simple regression model, differences from correlation coefficients, properties of regression lines, and testing of regression coefficients
10.1.2 Interpretation of Multiple Regression Results and Simple Regression Analysis
📈 Linear multiple regression model, linear simple regression model, partial regression coefficients, and main properties of regression
10.1.3 Interpretation of Output Results, Residuals, and Confidence Intervals
📈 Linear simple regression model, detailed analysis of statistical software output results
10.1.4 Dummy Variables and Properties of Simple Regression Coefficients
📈 Regression analysis including qualitative variables, trends in starting salaries
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10.2 Field of Analysis of Variance
10.2.1 Basics of One-Way Analysis of Variance
📈 Let's get used to the terminology, symbols, and tables specific to analysis of variance
10.2.2 Sum of Squares, Degrees of Freedom, and Explanation of Results
📈 We will perform time-series analysis on convenience store sales data used for analysis of variance!
10.2.3 Testing the Difference in Population Means and One-Way Analysis of Variance
📈 Simultaneous practice of (1) t-test for the difference in population means of two independent samples and (2) one-way analysis of variance using two-group data
10.2.4 Analysis of Variance for Multiple Regression Models
📈 Relationship between linear regression models and one-way analysis of variance; we will perform regression analysis using rent data!
Extra Edition
Part 1: The Balance Between Type I and Type II Errors
📈 Visualization of the null hypothesis $${H_0}$$, alternative hypothesis $${H_1}$$, probability of Type I error $${{\alpha}}$$, and probability of Type II error $${{\beta}}$$
Conclusion
I will do my best to write in a way that helps you feel comfortable with statistics in a relaxed mood!
Please be sure to read the articles 🌸
Relaxed~, relaxed~ 🍊
Blog Introduction
I am writing eight series of articles on note.
Please take a look!
1. Relaxed Statistics
This is a blog that roughly explores probability and statistics using the Statistics Certification Grade 2 problem collection as a guide.
Casual conversation style is fine. Please feel free to take a look.
It corresponds to the Statistics Certification Grade 2 Official Problem Collection CBT Edition.
Sample code for Python and EXCEL is also available.
2. Connecting with Statistics and Data Analysis
The series "Connecting with Statistics and Data Analysis" is a blog series that uncovers "connections" to statistics and data analysis and presents them in a column style.
With the help of generative AI, I wrote these freely, imagining the gateway to statistics and data analysis.
For example...
・Connections between daily life and statistics
・Connections from Statistics Certification Grade 2 to what lies beyond
I would be happy if you could read them at your leisure 🍀
3. Experiment! Fun Bayesian Modeling 1 & 2 with PyMC Ver. 5
I will draw and analyze the Bayesian models used in psychological research from the books "Fun Bayesian Modeling" and "Fun Bayesian Modeling 2" using PyMC Ver. 5.
Like this book, many Bayesian models are written in R language + Stan.
I will strive to explore the possibilities of PyMC and make Bayesian modeling easy to practice.
Since these are familiar and easy-to-visualize themes, please run them with PyMC and let's enjoy them together!
4. Experiment! Iwanami Data Science 1 Bayesian Modeling with PyMC Ver. 5
I will draw and analyze the Bayesian models by four Bayesians from the book "Experiment! Iwanami Data Science Vol. 1" using PyMC Ver. 5.
This book is a great resource for learning the basics of Bayesian programming.
I feel like I've become friends with Bayesian methods by happily running PyMC models.
Everyone, please run them with PyMC and let's play and learn together!
5. Fun Transcription: Bayesian, Python, etc.
I will blog about the results of my "book transcription activities" for Bayesian, Python, and others.
I am mainly working on translations into Python.
I hope this will serve as sample code for fellow transcribers 🍀
6. Introduction to Time Series Analysis for Psychology with R and Stan, using Python and PyMC Ver. 5
I will practice the time series analysis from the book "Introduction to Time Series Analysis for Psychology with R and Stan" using Python and PyMC Ver. 5.
This book is packed with time series analysis themes!
I realized the depth of time series analysis.
I will enjoy learning time series analysis with my favorite language, Python.
7. Writing about things that seem like data science
I write columns on statistics, data analysis, AI, machine learning, and Python on an irregular basis.
There are many articles related to statistics and data science books.
Series on "Statistics," "Python," "Mathematics and Python," and "R" have been created.
8. Practical Notes on Python Machine Learning Programming
I have written articles about my various thoughts while studying the book "Python Machine Learning Programming: PyTorch & scikit-learn Edition."
This book is a textbook for scikit-learn and PyTorch.
Please feel free to give it a try if you like.
Thank you very much for reading until the end.
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