Statistics

A Math? A Science? An Art? Or Something Else?

Isaac Quintanilla Salinas

Statistical Warning

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Chester from Linkin Park in "In the End" video with text saying: but in the end it doesn't even matter

Statistics

Statistics

An image cloud of different statistical plots, the word statistics is in the middle with capital letters.

  • With an increasing use of data to make decisions, Statistics has been essential for processing large amounts of data to byte-size information

  • Statistics is also known as

    • Data Science

    • Machine Learning

    • Artificial Intelligence

  • So for today, we’re asking: what is Statistics?

What does Google say?

UC Irvine

Statistics is the science concerned with developing and studying methods for collecting, analyzing, interpreting and presenting empirical data.

Wikipedia

Statistics is a mathematical body of science that pertains to the collection, analysis, interpretation or explanation, and presentation of data, or as a branch of mathematics.

What does AI say?

ChatGPT

Statistics is a branch of mathematics and a field of study that deals with the collection, analysis, interpretation, presentation, and organization of data.

Google Gemini

Statistics is the science of collecting, analyzing, interpreting, and presenting data.

What do researchers say?

Objectively interpreting data to make meaningful inferences about our predictions.

Whatever the statistician says.

Gathering the narratives of individuals, groups, or society and telling a story about their past, present, or future. The numbers paint a picture worth many words.

Using numbers to try to explain behaviors and/or patterns in our world.

Statistics is the way to make sense of the natural world by taking data we collect to identify patterns between variables, and applying statistical theory to make sure we are taking the right approach to data collection and analysis. Also, assess patterns to see if they are reproducible and provide a logical explanation that makes biological sense.

Statistics is the study of data, patterns, and trends.

What is it?

Math

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Science

Bill Nye, waving up dramatically with words Science!!! on image.

What does a Statistician say?

It is the study of variation and randomness!

Using mathematics, we model randomness to characterizes commonality and variation!

Using science, we systematically refine models to better fit randomness in data!

Using art, when it all eventually fails!

When it fails?!?!

Professor Farmsworth from futurama doing a 'yes yes' motion with hand and looking away. Text include Yes, Yes

Statistics Mantra - George Box

An image of George Box

All models are wrong,

some are useful!

What is the formal definition of Statistics?

Statistics is both the development of mathematical models to be used in real-world data and the analysis of data using existing models.

Probability Models

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  • Model observations that follow a new data generating process

  • Understand its properties

  • Develop new probability distributions

  • Known as Probability Theory

  • Researcher is a Probabilist or Mathematical Statistician

Data Analysis

  • Model data with a known probability model

  • Account for sources of variation and bias

  • Account for violations of independence and randomness

  • Known as Statistician or Data Scientist

A cat working on a laptop hissing angrily.

What’s the goal of a Statistician?

INFERENCE

Use our sample data to understand the larger population.

The data will tell us how the population generally behaves.

The data will guide us in the differences in units.

Data will tell us if there is a signal or just noise.

Word Cloud

A word cloud about statistics. main words are data, variation, probability, and difficult

Conducting Inference

A population of people is displayed. then pointing to a sample with individuals being sampled from population. Afterwards, there is an arrow pointing back to the population with the words inference.

Are we seeing something or is it just noise???

Are we seeing something different from what was expected? Or is it due to random chance?

Hypothesis Testing

  1. Set up the Null and Alternative Hypothesis
  2. Construct a test statistic based on the null hypothesis
  3. Construct a distribution of the test statistic based on probability theory
  4. Compute the probability of observing the test statistic
  5. Make a decision based on the probability

What if we cannot construct the distribution?!?!

An image showing the Monte Carlo car pulling out from a garage.

We bring out the Monte Carlo methods!

Monte Carlo Methods

  • Monte Carlo Methods are used to construct a distribution function of an obscure test statistic
  • We simulate a large number of data sets based on the null hypothesis
  • We construct a test statistic for each fake data set and the real one
  • We count how many data sets produce a test statistic that is more extreme than the real test statistic
  • \(p=\#\ of\ extreme\ data\ sets\ /\ all\ data\ sets\)

Overview of Research

  1. Ask a question about a population
  2. Collect data from a sample
  3. Construct and test a hypothesis
  4. Draw conclusion about the population
  5. Refine your question and methodology

So, what is Statistics?

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For you, I’ll be anything

But Wait! There’s More!

What’s Statistics without a little …

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Train of Thoughts

There are two train of thoughts on how to interpret estimates and probability.

One approach is the Frequentist approach.

The other approach is the Bayesian approach.

Both sides hate each other.

Frequentists

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Frequentists

A frequentist, in the context of statistics, is an individual who adheres to the frequentist interpretation of probability and statistical inference.

Meaning probability is obtained by the repetition of multiple experiments.

Bayesians

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Bayesians

A Bayesians, in the context of statistics, is an individual who adheres to the Bayesian interpretation of probability and statistical inference.

Probability is obtained by likelihood of an event to occur, given data and prior knowledge.

What am I (and people that have lives)?

Bart Simpson and Nelson rolling bowling balls, then ralph places a banana. Words Appear in the following order: Go Team Mystic, Go Team Valor, then Go team Instinct.

Whatever gets the job done!

There is more, much more, but I will say this, in my statistical journey

Shows Frank Sinatra singing with the words: I did it my way