– Statistical Thinking

Patient clustering, often described as the finding of new phenotypes, is being used with increasing frequency in the medical literature. Most of the applications of clustering of observations are not well thought out, not even considering whether observation clustering aligns with the clinical goals. And the resulting clusters are not validated even in a statistical way. This article describes some of the challenges of observation clustering, and challenges researchers to carefully check that found clusters are compact and contain the important statistical information in the variables on which clustering is based.

The Burden of Demonstrating Statistical Validity of Clusters

classification

data-reduction

diagnosis

medicine

personalized-medicine

subgroup

2024

Oct 6, 2024

This article is about lessons I’ve learned in building and maintaining web sites, with hopefully helpful recommendations.

Hosting Web Content

computing

2024

Sep 29, 2024

Considering a simple fixed sample-size non-adaptive design in which standard frequentist inference agrees with non-informative prior-based Bayesian inference, it is argued that the implied assumption about the unknown effect made by frequentist inference (and Bayesian inference if the non-informative prior is actually used) is quite unrealistic.

Traditional Frequentist Inference Uses Unrealistic Priors

bayes

design

inference

hypothesis-testing

RCT

multiplicity

2024

Jun 10, 2024

In randomized clinical trials, power can be greatly increased and sample size reduced by using an ordinal outcome instead of a binary one. The proportional odds model is the most popular model for analyzing ordinal outcomes, and it borrows treatment effect information across outcome levels to obtain a single overall treatment effect as an odds ratio. When deaths can occur, it is logical to have death as one of the ordinal categories. Consumers of the results frequently seek evidence of a mortality reduction even though they were not willing to fund a study large enough to be able to detect this with decent power. The same goes when assessing whether there is an increase in mortality, indicating a severe safety problem for the new treatment. The partial proportional odds model provides a continuous bridge between standalone evidence for a mortality effect and obtaining evidence using statistically richer information on the combination of nonfatal and fatal endpoints. A simulation demonstrates the relationship between the amount of borrowing of treatment effect across outcome levels and the Bayesian power for finding evidence for a mortality reduction.

Borrowing Information Across Outcomes

bayes

design

RCT

accuracy-score

inference

ordinal

2024

Apr 30, 2024

This article has detailed examples with complete R code for computing frequentist power for ordinal, continuous, and mixed ordinal/continuous outcomes in two-group comparisons with equal sample sizes. Mixed outcomes allow one to easily handle clinical event overrides of continuous response variables. The proportional odds model is used throughout, and care is taken to convert odds ratios to differences in medians or means to aid in understanding effect sizes. Since the Wilcoxon test is a special case of the proportional odds model, the examples also show how to tailor sample size calculations to the Wilcoxon test, at least when there are no covariates.

18 min

Proportional Odds Model Power Calculations for Ordinal and Mixed Ordinal/Continuous Outcomes

inference

hypothesis-testing

regression

ordinal

change-scores

design

endpoints

medicine

sample-size

2024

Apr 22, 2024

It is well known that the score test for comparing survival distributions between two groups without covariate adjustment, using a Cox proportional hazards (PH) model, is identical to the log-rank \(\chi^2\) test when there are no tied failure times. Yet there persists a belief that the log-rank test is somehow completely nonparametric and does not assume PH. Log-rank and Cox approaches can only disagree if the more commonly used likelihood ratio (LR) statistic from the Cox model disagrees with the log-rank statistic (and the Cox score statistic). This article shows that in fact the log-rank and Cox LR statistics agree to a remarkable degree, and furthermore the hazard ratio arising from the log-rank test also has remarkable agreement with the Cox model counterpart. Since both methods assume PH and the log-rank test assumes within-group heterogeneity (because it doesn’t allow for covariate adjustment), the Cox model actually makes fewer assumptions than log-rank.

The log-rank Test Assumes More Than the Cox Model

inference

hypothesis-testing

regression

2024

Mar 28, 2024

Sometimes it is unclear exactly what a specific statistical estimator or analysis method is assuming. This is especially true for methods that at first glance appear to be nonparametric when in reality they are semiparametric. This article attempts to explain what it means to make different types of assumptions, and how to tell when a certain type of assumption is being made. It also describes the assumptions made by various commonly used statistical procedures.

9 min

What Does a Statistical Method Assume?

inference

hypothesis-testing

regression

2024

Mar 23, 2024

Traditionally trained statisticians have much difficulty in accepting the absence of multiplicity issues with Bayesian sequential designs, i.e., that Bayesian posterior probabilities do not change interpretation or become miscalibrated just because a stopping rule is in effect. Most statisticians are used to dealing with backwards-information-flow probabilities which do have multiplicity issues, because they must deal with opportunities for data to be extreme. This leads them to believe that Bayesian methods must have some kind of hidden multiplicity problem. The chasm between forward and backwards probabilities is explored with a simple example involving continuous data looks where the ultimate truth is known. The stopping rule is the home NFL team having ≥ 0.9 probability of ultimately winning the game, and the correctness of the Bayesian-style forecast is readily checked.

22 min

Football Multiplicities

bayes

design

sequential

RCT

accuracy-score

backward-probability

decision-making

forward-probability

inference

multiplicity

prediction

probability

2024

Mar 10, 2024

Frank Harrell, Stephen Ruberg

Random intercepts in a model induce a compound symmetric correlation structure in which the correlation between two responses on the same subject have the same correlation…

How Does a Compound Symmetric Correlation Structure Translate to a Markov Model?

ordinal

prediction

regression

2023

Dec 3, 2023

Historical data (HD) are being used increasingly in Bayesian analyses when it is difficult to randomize enough patients to study effectiveness of a treatment. Such analyses summarize observational studies’ posterior effectiveness distribution (for two-arm HD) or standard-of-care outcome distribution (for one-arm HD) then turn that into a prior distribution for an RCT. The prior distribution is then flattened somewhat to discount the HD. Since Bayesian modeling makes it easy to fit multiple models at once, incorporation of the raw HD into the RCT analysis and discounting HD by explicitly modeling bias is perhaps a more direct approach than lowering the effective sample size of HD. Trust the HD sample size but not what the HD is estimating, and realize several benefits from using raw HD in the RCT analysis instead of relying on HD summaries that may hide uncertainties.

Incorporating Historical Control Data Into an RCT

drug-evaluation

bayes

design

drug-development

inference

observational

posterior

prior

2023

Nov 4, 2023

This article describes a real example in which use of a hybrid Bayesian-frequentist RCT design resulted in an analytical mess after overly successful participant recruitment.

18 min

Wedding Bayesian and Frequentist Designs Created a Mess

2023

inference

RCT

bayes

design

evidence

multiplicity

posterior

prior

sequential

Aug 22, 2023

This article briefly discusses why the rank difference test is better than the Wilcoxon signed-rank test for paired data, then shows how to generalize the rank difference test using the proportional odds ordinal logistic semiparametric regression model. To make the regression model work for non-independent (paired) measurements, the robust cluster sandwich covariance estimator is used for the log odds ratio. Power and type I assertion \(\alpha\) probabilities are compared with the paired \(t\)-test for \(n=25\). The ordinal model yields \(\alpha=0.05\) under the null and has power that is virtually as good as the optimum paired \(t\)-test. For non-normal data the ordinal model power exceeds that of the parametric test.

Ordinal Models for Paired Data

2023

ordinal

hypothesis-testing

inference

regression

Aug 16, 2023

This article provides resources to assist researchers in understanding and using ordinal regression models, and provides arguments for their wider use.

10 min

Resources for Ordinal Regression Models

2022

2023

2024

endpoints

ordinal

regression

May 1, 2023

I describe seven common errors in decision curve analysis. Avoidance of such errors will make decision curve analysis more reliable and useful.

20 min

Seven Common Errors in Decision Curve Analysis

decision-making

diagnosis

medicine

2023

Mar 18, 2023

Andrew Vickers

Randomized clinical trials are successful because they do not mimic clinical practice. They remain highly clinically relevant despite this.

Randomized Clinical Trials Do Not Mimic Clinical Practice, Thank Goodness

generalizability

design

medicine

RCT

drug-evaluation

personalized-medicine

evidence

2017

2023

Feb 14, 2023

This is an example statistical plan for project proposals where the goal is to develop a biostatistical model for prediction, and to do external or strong internal validation of the model.

20 min

Biostatistical Modeling Plan

2023

accuracy-score

endpoints

ordinal

collaboration

data-reduction

design

medicine

prediction

regression

validation

bootstrap

Jan 26, 2023

This article covers some of the bad statistical practices that have crept into biomarker research, including setting the bar too low for demonstrating that biomarker information is new, believing that winning biomarkers are really “winners”, and improper use of continuous variables. Step-by-step guidance is given for ensuring that a biomarker analysis is not reproducible and does not provide clinically useful information.

12 min

How to Do Bad Biomarker Research

2022

big-data

bioinformatics

biomarker

bootstrap

data-science

decision-making

dichotomization

forward-probability

generalizability

medical-literature

multiplicity

personalized-medicine

prediction

principles

reporting

reproducible

responder-analysis

sample-size

sensitivity

Oct 6, 2022

An overview of R Workflow, which covers how to use R effectively all the way from importing data to analysis, and making use of Quarto for reproducible reporting.

R Workflow

2022

data-science

graphics

reproducible

Jun 25, 2022

This article examines the benefits of decision curve analysis for assessing model performance when adding a new marker to an existing model. Decision curve analysis provides a clinically interpretable metric based on the number of events identified and interventions avoided.

Decision curve analysis for quantifying the additional benefit of a new marker

2022

biomarker

accuracy-score

decision-making

diagnosis

medicine

Apr 11, 2022

Emily Vertosick and Andrew Vickers

In this article I provide much more extensive simulations showing the near perfect agreement between the odds ratio (OR) from a proportional odds (PO) model, and the Wilcoxon two-sample test statistic. The agreement is studied by degree of violation of the PO assumption and by the sample size. A refinement in the conversion formula between the OR and the Wilcoxon statistic scaled to 0-1 (corcordance probability) is provided.

Equivalence of Wilcoxon Statistic and Proportional Odds Model

2022

2024

endpoints

ordinal

drug-evaluation

hypothesis-testing

RCT

regression

Apr 6, 2022

Most analysts automatically turn towards random effects models when analyzing longitudinal data. This may not always be the most natural, or best fitting approach.

26 min

Longitudinal Data: Think Serial Correlation First, Random Effects Second

drug-evaluation

endpoints

measurement

RCT

regression

2022

Mar 15, 2022

This article demonstrates how the proportional odds (PO) assumption and its impact can be assessed. General robustness to non-PO on either a main variable of interest or on an adjustment covariate are exemplified. Advantages of a continuous Bayesian blend of PO and non-PO are also discussed.

10 min

Assessing the Proportional Odds Assumption and Its Impact

2022

accuracy-score

dichotomization

endpoints

ordinal

Mar 9, 2022

We compare decision curve analysis and traditional decision analysis to illustrate their similarities and differences.

27 min

A Comparison of Decision Curve Analysis with Traditional Decision Analysis

decision-making

diagnosis

medicine

2021

Dec 27, 2021

Andrew Vickers

This is a commentary on the paper by Benkeser, Díaz, Luedtke, Segal, Scharfstein, and Rosenblum

Commentary on Improving Precision and Power in Randomized Trials for COVID-19 Treatments Using Covariate Adjustment, for Binary, Ordinal, and Time-to-Event Outcomes

bayes

covid-19

design

generalizability

inference

metrics

ordinal

personalized-medicine

RCT

regression

reporting

2021

Jul 17, 2021

Frank Harrell, Stephen Senn

25 min

Incorrect Covariate Adjustment May Be More Correct than Adjusted Marginal Estimates

2021

generalizability

RCT

regression

This article provides a demonstration that the perceived non-robustness of nonlinear models for covariate adjustment in randomized trials may be less of an issue than the non-transportability of marginal so-called robust estimators.

Jun 29, 2021

This article presents an argument that for RCTs with a binary outcome the primary result should be a distribution and not any single number summary. The GUSTO-I study is used to exemplify risk difference distributions.

17 min

Avoiding One-Number Summaries of Treatment Effects for RCTs with Binary Outcomes

2021

generalizability

RCT

regression

Jun 28, 2021

Since the Wilcoxon test is a special case of the proportional odds (PO) model, if one likes the Wilcoxon test, one must like the PO model. This is made more convincing by showing examples of how one may accurately compute the Wilcoxon statistic from the PO model’s odds ratio.

10 min

If You Like the Wilcoxon Test You Must Like the Proportional Odds Model

ordinal

hypothesis-testing

2021

accuracy-score

RCT

regression

metrics

Mar 10, 2021

The recent PATH (Predictive Approaches to Treatment effect Heterogeneity) Statement outlines principles, criteria, and key considerations for applying predictive approaches to clinical trials to provide patient-centered evidence in support of decision making. Here challenges in implementing the PATH Statement are addressed with the GUSTO-I trial as a case study.

Implementation of the PATH Statement

Nov 24, 2020

Ewout Steyerberg

19 min

Violation of Proportional Odds is Not Fatal

2020

ordinal

accuracy-score

RCT

regression

hypothesis-testing

metrics

Many researchers worry about violations of the proportional hazards assumption when comparing treatments in a randomized study. Besides the fact that this frequently makes them turn to a much worse approach, the harm done by violations of the proportional odds assumption usually do not prevent the proportional odds model from providing a reasonable treatment effect assessment.

Sep 20, 2020

This article discusses issues with unadjusted effect ratios such as odds ratios and hazard ratios, showing a simple example of non-generalizability of unadjusted odds ratios.

12 min

Unadjusted Odds Ratios are Conditional

2020

generalizability

RCT

regression

Sep 13, 2020

This article summarizes arguments for the claim that the primary analysis of treatment effect in a RCT should be with adjustment for baseline covariates. It reiterates some findings and statements from classic papers, with illustration on the GUSTO-I trial.

9 min

RCT Analyses With Covariate Adjustment

2020

drug-evaluation

generalizability

medicine

personalized-medicine

prediction

RCT

regression

Jul 19, 2020

Ewout Steyerberg
@ESteyerberg

The COVID-19 pandemic has elevated the challenge for designing and executing clinical trials with vaccines and drug/device combinations within a substantially shortened time frame. Numerous challenges in designing COVID-19 trials include lack of prior data for candidate interventions / vaccines due to the novelty of the disease, evolving standard of care and sense of urgency to speed up development programmes. We propose sequential and adaptive Bayesian trial designs to help address the challenges inherent in COVID-19 trials. In the Bayesian framework, several methodologies can be implemented to address the complexity of the primary endpoint choice. Different options could be used for the primary analysis of the WHO Severity Scale, frequently used in COVID-19 trials. We propose the longitudinal proportional odds mixed effects model using the WHO Severity Scale ordinal scale. This enables efficient utilization of all clinical information to optimize sample sizes and maximize the rate of acquiring evidence about treatment effects and harms.

Bayesian Methods to Address Clinical Development Challenges for COVID-19 Drugs and Biologics

bayes

RCT

design

drug-evaluation

medicine

responder-analysis

covid-19

May 29, 2020

Natalia Muhlemann MD, Rajat Mukherjee Phd, Frank Harrell PhD

This article explains how the generalizability of randomized trial findings depends primarily on whether and how patient characteristics modify (interact with) the treatment effect. For an observational study this will be related to overlap in the propensity to receive treatment.

Implications of Interactions in Treatment Comparisons

RCT

drug-evaluation

generalizability

medicine

observational

personalized-medicine

prediction

subgroup

2020

Mar 3, 2020

Reasons are given for why heterogeneity of treatment effect must be demonstrated, not assumed. An example is presented that shows that HTE must exceed a certain level before personalizing treatment results in better decisions than using the average treatment effect for everyone.

25 min

The Burden of Demonstrating HTE

RCT

generalizability

medicine

metrics

personalized-medicine

subgroup

2019

Apr 8, 2019

This article shows an example formally testing for heterogeneity of treatment effect in the GUSTO-I trial, shows how to use penalized estimation to obtain patient-specific efficacy, and studies variation across patients in three measures of treatment effect.

Assessing Heterogeneity of Treatment Effect, Estimating Patient-Specific Efficacy, and Studying Variation in Odds ratios, Risk Ratios, and Risk Differences

RCT

generalizability

medicine

metrics

personalized-medicine

prediction

subgroup

accuracy-score

2019

Mar 25, 2019

Researchers have used contorted, inefficient, and arbitrary analyses to demonstrated added value in biomarkers, genes, and new lab measurements. Traditional statistical measures have always been up to the task, and are more powerful and more flexible. It’s time to revisit them, and to add a few slight twists to make them more helpful.

16 min

Statistically Efficient Ways to Quantify Added Predictive Value of New Measurements

prediction

sample-size

validation

accuracy-score

biomarker

diagnosis

medicine

reporting

2018

Oct 17, 2018

The performance metrics chosen for prediction tools, and for Machine Learning in particular, have significant implications for health care and a penetrating understanding of the AUROC will lead to better methods, greater ML value, and ultimately, benefit patients.

19 min

In Machine Learning Predictions for Health Care the Confusion Matrix is a Matrix of Confusion

data-science

machine-learning

prediction

2018

Aug 28, 2018

Drew Griffin Levy
@DrewLevy

24 min

Data Methods Discussion Site

collaboration

teaching

2018

This article lays out the rationale and overall design of a new discussion site about quantitative methods.

Jun 19, 2018

This article provides my reflections after the PCORI/PACE Evidence and the Individual Patient meeting on 2018-05-31. The discussion includes a high-level view of heterogeneity of treatment effect in optimizing treatment for individual patients.

Viewpoints on Heterogeneity of Treatment Effect and Precision Medicine

RCT

biomarker

decision-making

drug-evaluation

generalizability

medicine

metrics

personalized-medicine

prediction

subgroup

2018

Jun 4, 2018

This article elaborates on Frank Harrell’s post providing guidance in choosing between machine learning and statistical modeling for a prediction project.

16 min

Navigating Statistical Modeling and Machine Learning

data-science

machine-learning

prediction

2018

May 14, 2018

Drew Griffin Levy
@DrewLevy

This article provides general guidance to help researchers choose between machine learning and statistical modeling for a prediction project.

Road Map for Choosing Between Statistical Modeling and Machine Learning

data-science

machine-learning

prediction

2018

Apr 30, 2018

This article discusses issues related to alpha spending, effect sizes used in power calculations, multiple endpoints in RCTs, and endpoint labeling. Changes in endpoint priority is addressed. Included in the the discussion is how Bayesian probabilities more naturally allow one to answer multiple questions without all-too-arbitrary designations of endpoints as “primary” and “secondary”. And we should not quit trying to learn.

Musings on Multiple Endpoints in RCTs

RCT

bayes

design

drug-evaluation

evidence

hypothesis-testing

medicine

multiplicity

p-value

posterior

endpoints

2018

Mar 26, 2018

What are the major elements of learning from data that should inform the research process? How can we prevent having false confidence from statistical analysis? Does a Bayesian approach result in more honest answers to research questions? Is learning inherently subjective anyway, so we need to stop criticizing Bayesians’ subjectivity? How important and possible is pre-specification? When should replication be required? These and other questions are discussed.

Improving Research Through Safer Learning from Data

design

evidence

generalizability

inference

judgment

measurement

prior

bayes

2018

Mar 8, 2018

Deep learning and other forms of machine learning are getting a lot of press in medicine. The reality doesn’t match the hype, and interpretable statistical models still have a lot to offer.

Is Medicine Mesmerized by Machine Learning?

machine-learning

accuracy-score

classification

data-science

decision-making

medicine

prediction

validation

2018

Feb 1, 2018

This article gives examples of information gained by using ordinal over binary response variables. This is done by showing that for the same sample size and power, smaller effects can be detected.

Information Gain From Using Ordinal Instead of Binary Outcomes

RCT

design

ordinal

dichotomization

inference

precision

responder-analysis

sample-size

2018

Jan 28, 2018

I prefer fractions and ratios over percents. Here are the reasons.

Why I Don’t Like Percents

metrics

2018

Jan 19, 2018

It is easy to compute the sample size N₁ needed to reliably estimate how one predictor relates to an outcome. It is next to impossible for a machine learning algorithm entertaining hundreds of features to yield reliable answers when the sample size < N₁.

How Can Machine Learning be Reliable When the Sample is Adequate for Only One Feature?

prediction

machine-learning

sample-size

validation

precision

accuracy-score

2018

Jan 11, 2018

Methodologic goals and wishes for research and clinical practice for 2018

New Year Goals

2018

2019

Dec 29, 2017

This article addresses data reduction, also called unsupervised learning.

Scoring Multiple Variables, Too Many Variables and Too Few Observations: Data Reduction

variability

data-reduction

2017

Nov 21, 2017

Criticism of medical journal articles is easy. I need to keep in mind that much good research is done even if there are some flaws in the design, analysis, or interpretation. I also need to remember that real people are involved.

Statistical Criticism is Easy; I Need to Remember That Real People are Involved

RCT

2017

Nov 5, 2017

This article describes the drastically different way that sequential data looks operate in a Bayesian setting compared to a classical frequentist setting.

Continuous Learning from Data: No Multiplicities from Computing and Using Bayesian Posterior Probabilities as Often as Desired

bayes

sequential

RCT

2017

Oct 9, 2017

This article contrasts language used when reporting a classical frequentist treatment comparison vs. a Bayesian one, and describes why Bayesian statements convey more actionable information.

Bayesian vs. Frequentist Statements About Treatment Efficacy

reporting

inference

p-value

RCT

bayes

drug-evaluation

evidence

hypothesis-testing

2017

Oct 4, 2017

In this article I seek recommendations for integrating various media for teaching long courses.

Integrating Audio, Video, and Discussion Boards with Course Notes

collaboration

teaching

reproducible

2017

Aug 1, 2017

Observational data from electronic health records may contain biases that large sample sizes do not overcome. Moderate confounding by indication may render an infinitely large observational study less useful than a small randomized trial for estimating relative treatment effectiveness.

EHRs and RCTs: Outcome Prediction vs. Optimal Treatment Selection

prediction

generalizability

drug-evaluation

evidence

subgroup

EHR

design

medicine

inference

big-data

RCT

personalized-medicine

2017

Jun 1, 2017

Frank Harrell, Laura Lazzeroni

16 min

Statistical Errors in the Medical Literature

prediction

logic

p-value

validation

bayes

evidence

subgroup

dichotomization

medicine

inference

change-scores

RCT

personalized-medicine

responder-analysis

hypothesis-testing

medical-literature

2017

This article catalogs several types of statistical problems that occur frequently in the medical journal articles.

Apr 8, 2017

This is a subjective ranking of topical areas by the typical quality of research published in the area. Keep in mind that top-quality research can occur in any area when the research team is multi-disciplinary, team members are at the top of their game, and peer review is functional.

32 min

Subjective Ranking of Quality of Research by Subject Matter Area

2017

Mar 16, 2017

Estimating tendencies is usually a more appropriate goal than classification, and classification leads to the use of discontinuous accuracy scores which give rise to misleading results.

Damage Caused by Classification Accuracy and Other Discontinuous Improper Accuracy Scoring Rules

prediction

machine-learning

accuracy-score

dichotomization

probability

bioinformatics

validation

classification

data-science

2017

Mar 1, 2017

This is the story of what influenced me to become a Bayesian statistician after being trained as a classical frequentist statistician, and practicing only that mode of statistics for many years.

5 min

My Journey from Frequentist to Bayesian Statistics

inference

p-value

likelihood

RCT

bayes

multiplicity

posterior

drug-evaluation

principles

evidence

hypothesis-testing

2017

Feb 19, 2017

With interactive graphics one can start by showing the most important data features, then drill down to see details.

24 min

Interactive Statistical Graphics: Showing More By Showing Less

survival-analysis

graphics

2017

Feb 5, 2017

p-values are very often misinterpreted. p-values and null hypothesis significant testing have hurt science. This article attempts to catalog all the ways in which these happen.

A Litany of Problems With p-values

decision-making

bayes

multiplicity

p-value

hypothesis-testing

2017

Feb 5, 2017

The error of the transposed conditional is rampant in research. Conditioning on what is unknowable to predict what is already known leads to a host of complexities and interpretation problems.

36 min

Clinicians’ Misunderstanding of Probabilities Makes Them Like Backwards Probabilities Such As Sensitivity, Specificity, and Type I Error

specificity

probability

backward-probability

forward-probability

p-value

bayes

conditioning

diagnosis

decision-making

dichotomization

medicine

bioinformatics

biomarker

sensitivity

posterior

accuracy-score

classification

2017

Jan 25, 2017

The many disadvantages of split-sample validation, including subtle ones, are discussed.

Split-Sample Model Validation

prediction

bootstrap

validation

2017

Jan 23, 2017

This brief note catalogs what I feel are some of the most important principles to guide statistical practice.

Fundamental Principles of Statistics

design

measurement

principles

2017

2023

Jan 18, 2017

Suggestions for future articles, by readers

Ideas for Future Articles

2017

Jan 16, 2017

Classification involves a forced-choice premature decision, and is often misused in machine learning applications. Probability modeling involves the quantification of tendencies and usually addresses the real project goals.

2 min

Classification vs. Prediction

prediction

decision-making

machine-learning

accuracy-score

classification

data-science

2017

Jan 15, 2017

This article explains why for decision making the original idea of null hypothesis testing never delivered on its goal.

Null Hypothesis Significance Testing Never Worked

logic

inference

bayes

p-value

hypothesis-testing

inductive-reasoning

2017

Jan 14, 2017

p-values are not what decision makers need, nor are they what most decision makers think they are getting.

p-values and Type I Errors are Not the Probabilities We Need

judgment

inference

likelihood

bayes

multiplicity

p-value

prior

hypothesis-testing

2017

Jan 14, 2017

Introducing the Statistical Thinking Blog

12 min

Introduction

2017

principles

Jan 13, 2017