Today, according to “Our World in Data”

Why?

Only 11.4% of people in low-income countries have been vaccinated

In rich countries we observe

*vaccine hesitance*

Political

Belief

Distrust of Science

Besides the Anti-vaccine people, we have

Climate change denial

Flat Earthers

and several others

In 2009, 2% of scientists admitted to falsifying studies at least once

14% admitted to personally knowing someone who did

**Most people do not lie**

A 2016 poll of 1,500 scientists reported that 70% of them had failed to reproduce at least one other scientist’s experiment

50% had failed to reproduce one of their own experiments

**There are problems with the experiments and their
analysis**

Repeated the top 100 studies in psychology

- Only 36% of the replications gave significant findings
- compared to 97% of the original studies

- The effect size in the replications was half of the effect size in the original studies, on average

Journal of the Royal Statistical Society and American Statistical Association

- Physicist
- Excellent professor
- Worked in the Manhattan Project at 25 years old
- Nobel Prize on Physics in 1965
- He was talking about USA in the 1970s

“the ritualistic miming of statistics rather than conscientious practice”

“practitioners go through the motions of fitting models, computing p-values or confidence intervals, or simulating posterior distributions”

“They invoke statistical terms and procedures as incantations, with scant understanding of the assumptions or relevance of the calculations, or even the meaning of the terminology”

“We believe that poor statistical education and practice are symptoms of and contributors to problems in science as a whole”

As someone who teaches maths and statistics, I say

**We are bad at teaching
maths**

We need to find better ways to teach math

(in particular to math teachers)

Math allow us to travel in time, and see the invisible

That is why people who knows do not want to teach math:

It gives power to the people

“They” do not want you to know math

We do an experiment *E*

We get some data *X*

We define null and alternative hypotheses *H _{0},
H_{1}*

We do an hypothesis test

The probability that the null hypothesis is true, given that we observed

*X*The probability of observing

*X*, assuming that the null hypothesis is true

**2. The probability of observing X, assuming that the
null hypothesis is true**

But many people believe it means the first option

*P*-values do not mean what many people thinks

Probabilities depend on two things

- The event we are evaluating
*A* - What we know about the state of the system
*B*

We say “probability of *A* given *B*”

They are not interchangeable

Imagine that you are randomly chosen for a test of COVID-19

The result is “positive”. It says that you have the virus

But this test fails 2% of times, giving a *false positive* or
a *false negative*

Then the question:

**What is the probability that you have COVID-19 given that the
test said “positive”?**

The test is correct 98% of times

That is, the probability of a positive test *given that you have
COVID*

But we really want to know the probability of COVID *given that
the test is positive*

They are not the same

To answer this question we must know the *prevalence* of
COVID

That is, what is the proportion of the population with COVID

There are 728,692 active cases in Turkey today

(only 1,128 are serious)

Population of Turkey is 85,828,516

Dividing both numbers we find that the prevalence is 0.86%

Test- | Test+ | Total | |
---|---|---|---|

COVID- |
. | . | . |

COVID+ |
. | . | . |

Total |
. | . | . |

COVID reality in the rows and test results in the columns

Test- | Test+ | Total | |
---|---|---|---|

COVID- |
. | . | . |

COVID+ |
. | . | . |

Total |
. | . | 1000000 |

We will fill this matrix in the following slides

Assuming one million people makes the math easier

Test- | Test+ | Total | |
---|---|---|---|

COVID- |
. | . | 991400 |

COVID+ |
. | . | 8600 |

Total |
. | . | 1000000 |

Prevalence is the percentage of the population that has COVID.

In other words, it is the probability of (COVID_{+})

Test- | Test+ | Total | |
---|---|---|---|

COVID- |
971572 | . | 991400 |

COVID+ |
. | 8428 | 8600 |

Total |
. | . | 1000000 |

*Precision* is the probability of a correct diagnostic

(Here we assumed that the error rates are the same for positive and negative. That may not be the case always)

Test- | Test+ | Total | |
---|---|---|---|

COVID- |
971572 | 19828 | 991400 |

COVID+ |
172 | 8428 | 8600 |

Total |
. | . | 1000000 |

(this error rate is only an example. Real tests are usually better)

Test- | Test+ | Total | |
---|---|---|---|

COVID- |
971572 | 19828 | 991400 |

COVID+ |
172 | 8428 | 8600 |

Total |
971744 | 28256 | 1000000 |

We sum and fill the empty boxes

28256 people got positive test, but only 8428 of them have COVID

Probability of having COVID if the text is positive: 29.83%

The same book with two names, for different markets

- Utilitarian
- To pay the bills and not be cheated
- To get the proper concentrations in the lab

- Practical
- To design the experiments
- To analyze the results of the experiment

- Philosophical
- Understand the meaning of the results
- Connect experiments with the rest of human knowledge

The universe […] cannot be understood unless one first learns […] the language and interpret the characters in which it is written. It is written in the language of mathematics, […] without these, one is wandering around in a dark labyrinth.

Galileo Galilei (1564 – 1642),

Italian astronomer, physicist, engineer, philosopher, and
mathematician

Mendel discovered genes using only math

Galton created the first Department of Genetics, and linear correlation

Fisher invented statistics while working at Agricultural research

“Student’s test” was invented by biotech working in beer

It has been invented and developed independently in several places:

- ancient Babylon, ancient Egypt,
- ancient Greece (all around Mediterranean and Aegean sea),
- China, India,
- Pre-hispanic Mexico, Golden Age Persia,
- European Renaissance, Industrial England, Soviet Union, etc.

We have mathematicians in Turkish money.

- We need to learn math to receive this cultural legacy
- We speak about “Universal literature”
- Architecture
- Painting and Sculptures
- Music
- Cinema

Mathematic belongs to all humanity

It is like moving in the city using only the metro:

easy, but you can only go to places that others have already prepared

These places are crowded, and it is hard to be noticed here.

It is like having your own car. Depending on your knowledge level, it can be

- a taxi (someone else drives),
- an sedan car (you drive on paved streets),
- a jeep (you can go to much more places, you can fix up when things break down), or
- an experimental autonomous car (you design a new car from the zero)

You need at least to understand enough mechanics to know

- when to put gasoline,
- When to change oil,
- maybe how to change a tire,
- How to talk to the mechanic so he does not cheat you.

To have correct answers we must ask the correct questions

This is the real reason we need math

Mathematicsis not about numbers, equations, computations or algorithms: it’s aboutunderstandingWilliam Paul Thurston (1946 – 2012),

American mathematician

It is easier to solve a problem when we discard irrelevant details

Abstract problems can correspond to several applied problems

Solving one solves all of them

These

*connections*help us to understand new problems by analogy to old ones

- It requires energy and willpower
- Everybody can run 10K … if trained correctly

Erika Check Hayden, Weak statistical standards implicated in scientific irreproducibility Nature, 11 November 2013

Open Science Collaboration, Estimating the reproducibility of psychological science. Science 28 Aug 2015: Vol. 349, Issue 6251, aac4716

Replications can cause distorted belief in scientific progress Behavioral and Brain Sciences, Volume 41, 2018, e122 DOI: https://doi.org/10.1017/S0140525X18000584. Published online by Cambridge University Press: 27 July 2018

Reproducibility of Scientific Results Stanford Encyclopedia of Philosophy

T.D. Stanley, Evan C. Carter and Hristos Doucouliagos What Meta-Analyses Reveal about the Replicability of Psychological Research Deakin Laboratory for the Meta-Analysis of Research, Working Paper, November 2017

Silas Boye Nissen, Tali Magidson, Kevin Gross Is a corresponding author, Carl T Bergstrom Research: Publication bias and the canonization of false facts eLife Dec 20, 2016; 5:e21451