3.01 Randomness

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來自 University of Amsterdam 的課程

统计基础

1796 個評分

University of Amsterdam

统计基础

1796 個評分

課程 3（共 5 門，Specialization 社会科学的方法和统计）

Understanding statistics is essential to understand research in the social and behavioral sciences. In this course you will learn the basics of statistics; not just how to calculate them, but also how to evaluate them. This course will also prepare you for the next course in the specialization - the course Inferential Statistics. In the first part of the course we will discuss methods of descriptive statistics. You will learn what cases and variables are and how you can compute measures of central tendency (mean, median and mode) and dispersion (standard deviation and variance). Next, we discuss how to assess relationships between variables, and we introduce the concepts correlation and regression. The second part of the course is concerned with the basics of probability: calculating probabilities, probability distributions and sampling distributions. You need to know about these things in order to understand how inferential statistics work. The third part of the course consists of an introduction to methods of inferential statistics - methods that help us decide whether the patterns we see in our data are strong enough to draw conclusions about the underlying population we are interested in. We will discuss confidence intervals and significance tests. You will not only learn about all these statistical concepts, you will also be trained to calculate and generate these statistics yourself using freely available statistical software.

從本節課中

Probability

This module introduces concepts from probability theory and the rules for calculating with probabilities. This is not only useful for answering various kinds of applied statistical questions but also to understand the statistical analyses that will be introduced in subsequent modules. We start by describing randomness, and explain how random events surround us. Next, we provide an intuitive definition of probability through an example and relate this to the concepts of events, sample space and random trials. A graphical tool to understand these concepts is introduced here as well, the tree-diagram.Thereafter a number of concepts from set theory are explained and related to probability calculations. Here the relation is made to tree-diagrams again, as well as contingency tables. We end with a lesson where conditional probabilities, independence and Bayes rule are explained. All in all, this is quite a theoretical module on a topic that is not always easy to grasp. That's why we have included as many intuitive examples as possible.

3.01 Randomness4:43

3.02 Probability4:42

與講師見面

Matthijs Rooduijn
Dr.
Department of Political Science
Emiel van Loon
Assistant Professor
Institute for Biodiversity and Ecosystem Dynamics

Recognizing and understanding randomness as well as the ability to reason

about it are important skills, not only to apply statistical analysis but

also to make sense of things happening around us every day.

Here, I will explain that humans are pathologically bad at

dealing with randomness.

I will use an example along the way.

Imagine you're on a beach watching the waves roll in.

And then your attention is caught by a beautiful shell

which is distinctive in shape and larger than it's neighboring shells.

So you start to search for another one.

This will be an unpredictable enterprise.

The shells may be distributed at random at this huge beach.

Hence, the time it will take you to find another will be uncertain.

You may not be able to find a similar at all.

The more you think about it,

the more you'll realize that randomness is pervasive in everyday life.

It is therefore not surprising that we have a rich vocabulary to communicate it,

with terms like uncertainty, chance, risk and likelihood.

Also, degrees of variability and uncertainty can expressed quite subtly.

Consider for example this sequence.

Rarely.

Seldom.

Sometimes.

Common.

Frequent. Often.

Importantly, whether something is random is not just a property of that phenomenon,

but very much also a consequence of our knowledge about it.

If you'd have been at this beach before, you might have spotted

this special shell previously, so that this may change your search strategy and

increase your chance of finding more of them.

Also the scale of your search matters.

While you may not be very certain about finding another shell

within a few minutes at a short stretch of beach, the chance to find one

when you take a bit more time and cover a larger stretch of beach will increase.

But in spite of many words, our ability to memorize in our daily experience

with randomness, we are not very good at assessing it quantitatively at all.

On one hand, we see all sorts of patterns in what is really random data.

There's a word for it, apophenia.

And on the other hand, we are unable to make up random data ourselves.

An example of a failed attempt to create random data is this fabricated map

of random shell locations which turn out to be spaced too regular.

This is how a realistic random point pattern looks like

with much more clusters.

Another example of over interpreting randomness is the so

called gambler's fallacy, the false idea that a random phenomenon

can be predicted from a series of preceding random phenomena.

And who doesn't recognize this.

If you have thrown a six four times in a row with a die, it feels

as if it's going to be very unlikely to throw a six again the fifth time.

Yet, the probability of this outcome was and continues to be one sixth.

The reason that we have a bad head for randomness is that

our brain tends to measure randomness in the effort it takes to memorize a pattern.

And it turns out that memorizing frequently changing short sequences

is harder than longer sequences.

Given this state of affairs it's really important to learn about formal ways for

quantifying randomness, reasoning about it and generating realistic random patterns.

It will help to avoid mistakes, predict more accurate and

be more efficient when you try to make sense of the world around you.

Let me summarize what I hope you understood from this video.

Randomness is not an intrinsic property of a phenomenon.

It also depends amongst others of prior knowledge, observation method, and

a scale at which the phenomenon is considered.

While there are many words to express aspects of randomness,

humans are not very good in assessing it quantitatively.

We suffer from apophenia, the over interpretation of what are purely random

patterns and are also bad in constructing randomness.

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