Bayes’ Theorem
Subje ctive Proba
bility
n Neyman-Pearson statistics is well-suited to make decisions using hypothesis testing, to
evaluate the consistency of models with observed sample data, and to make
inferences (e.g., about what population or universe a sample represents).
Curriculum Framework for Statistical Thinking on InMside
NEYMAN-PEARSON STATISTICS BAYES
IAN STA
TISTICS
Likelihood
DATA SCIENCE
Coding Data
Statistics
Formal and
Informal Inference Modeling Probability of Variability
Subjects
n In all school subjects, there is a need to integrate, to a lesser or greater degree, data handling, data
collection and data analysis into regular school routines and activities.
NEYMAN-PEARSON STATISTICS
n Bayesian statistics is well-suited to deal with population forecasting, missing and noisy data, comparison of multiple hypotheses, addressing multiple levels of uncertainty, and analyzing large numbers of variables to predict outcomes.
BAYES
IAN STA
TISTICS
Bayes’ Theorem
Subje ctive Proba
bility
n Neyman-Pearson statistics is well-suited to make decisions using hypothesis testing, to
evaluate the consistency of models with observed sample data, and to make
inferences (e.g., about what population or universe a sample represents).
Curriculum Framework for Statistical Thinking on InMside
NEYMAN-PEARSON STATISTICS BAYES
IAN STA
TISTICS
Likelihood
DATA SCIENCE
Coding Data
Statistics
Formal and
Informal Inference Modeling Probability of Variability
Subjects
n In all school subjects, there is a need to integrate, to a lesser or greater degree, data handling, data
collection and data analysis into regular school routines and activities.
NEYMAN-PEARSON STATISTICS
n Bayesian statistics is well-suited to deal with population forecasting, missing and noisy data, comparison of multiple hypotheses, addressing multiple levels of uncertainty, and analyzing large numbers of variables to predict outcomes.
BAYES
IAN STA
TISTICS
Bayes’ Theorem
Subje ctive Proba
bility
n Neyman-Pearson statistics is well-suited to make decisions using hypothesis testing, to
evaluate the consistency of models with observed sample data, and to make
inferences (e.g., about what population or universe a sample represents).
Curriculum Framework for Statistical Thinking on InMside
NEYMAN-PEARSON STATISTICS BAYES
IAN STA
TISTICS
Likelihood
DATA SCIENCE
Coding Data
Statistics
Formal and
Informal Inference Modeling Probability of Variability
Subjects
n In all school subjects, there is a need to integrate, to a lesser or greater degree, data handling, data
collection and data analysis into regular school routines and activities.
NEYMAN-PEARSON STATISTICS
n Bayesian statistics is well-suited to deal with population forecasting, missing and noisy data, comparison of multiple hypotheses, addressing multiple levels of uncertainty, and analyzing large numbers of variables to predict outcomes.
BAYES
IAN STA
TISTICS DATA SCIENCE
n Data science is well-suited to discover patterns or latent structure in large volumes of unstructured data, to transform big data into actionable insights.
Curriculum Framework for Statistical Thinking on InMside
n Probability of variability (i.e., the p-value returned by a significance test) is the probability of obtaining the same or more extreme data given both a hypothesis and a decision procedure.
NEYMAN-PEARSON STATISTICS BAYES
IAN STA
TISTICS
Likelihood
Bayes’ Theorem
Subje ctive Proba
bility
DATA SCIENCE
Coding Data
Statistics
Formal and
Informal Inference Modeling Probability of Variability
Subjects
NEYMAN-PEARSON STATISTICS Formal and
Informal Inference Modeling Probability of Variability
n Neyman-Pearson statistics (i.e., frequentist, classical, or orthodox statistics) is currently the common approach to statistical practice at school level.
n Inference is a probabilistic prediction or generalization about an unknown quantity, based on information contained in a sample, using (formal) or not (informal) significance tests and formal probabilistic statements.
n Modeling is the process of generating a mathematical model (e.g., simple or multiple linear regression models) to best describe and provide evidence of the relationship
relationship between an outcome and one or more explanatory variables.
Curriculum Framework for Statistical Thinking on InMside
n Bayesian statistics is about assessing the subjective probability of hypotheses and unknown parameters, using the rules of probability to combine data with prior information to yield inferences.
NEYMAN-PEARSON STATISTICS BAYES
IAN STA
TISTICS
Likelihood
Bayes’ Theorem
Subje ctive Proba
bility
DATA SCIENCE
Coding Data
Statistics
Formal and
Informal Inference Modeling Probability of Variability
Subjects
BAYES
IAN STA
TISTICS
Likelihood
Bayes’ Theorem
Subje ctive Proba
bility
n Likelihood is the probability of obtaining the exact evidence or data obtained given a hypothesis, P(E|H).
n Bayes’ theorem is an application of conditional probability to calculate the probability that an event has to happen, in given circumstances.
n Subjective probability is a person’s perception of the likelihood of an event
toto occur, P(H), based on personal beliefs, preferences and experience.
DATA SCIENCE
Coding Data
Statistics
Curriculum Framework for Statistical Thinking on InMside
n Coding in a script language (e.g., R, Python or SQL) is essential for feeding the computer with the appropriate commands to handle and analyze data.
NEYMAN-PEARSON STATISTICS BAYES
IAN STA
TISTICS
Likelihood
Bayes’ Theorem
Subje ctive Proba
bility
Formal and
Informal Inference Modeling Probability of Variability
Subjects
DATA SCIENCE
Coding Data
Statistics
n Data science is a multi-disciplinary field that uses scientific methods, processes, algorithms, and computational infrastructure to extract knowledge and insights from structured and unstructured data.
n Statistics allows data scientists to distinguish between causation and correlation; to establish methods for diagnosis, prediction, estimation and decision-making; and to quantify their degree of certainty.
n Data science requires the processing, analysis and visualization of very large amounts of data through engagement in the five phases of Statistical Thinking in the Era of Big Data for the Digital Economy.
Curriculum Framework for Statistical Thinking on InMside
Curriculum Framework for Statistical Thinking on InMside
n We must help our students to develop their statistical thinking beyond the boundaries of traditional analytics (e.g., PPDAC), and provide them with opportunities to engage in big data analytics (i.e., patterns and relationships from data, questions, objectives, data mining, and designing).
Curriculum Framework for Statistical Thinking on InMside
EXEMPLAR APPLICATIONS
High School
Curriculum Middle School
Curriculum Primary School Curriculum
n This conceptual framework identifies what statistical fundamental ideas, thinking processes and competencies Society 4.0 (and the upcoming Society 5.0) demands from people.
n Statistical education must continue to evolve to prepare the next generation of statistical users with skills that cross the boundaries of traditional statistics.
n Based on these considerations, we would like to propose the following curriculum framework model to foster in our students Statistical Thinking for the Era of Digital Society.
Conceptual Frameworkvelopment Framework
