Statistical Thinking for the 21st Century

Data Science







Learning Progress: 7.21%.


  • This book focuses on understanding the basic ideas of statistical thinking – a systematic way of thinking about how we describe the world and use data make decisions and predictions, all in the context of the inherent uncertainty that exists in the real world.


  • The only way to really learn statistics is to do statistics.

1 Introduction

  • Statistical thinking will one day be as necessary for efficient citizenship as the ability to read and write. — H.G. Wells

  • Statistical thinking provides us with the tools to more accurately understand the world and overcome the biases of human judgment.

  • One way to think of statistics is as a set of tools that enable us to learn from data. In any situation, we start with a set of ideas or hypotheses about what might be the case. Another way to think of statistic is as “the science of throwing away data”.

  • Statistics provides us with a way to describe how new data can be best used to update our beliefs, and in this way there are deep links between statistic and psychology. In fact, many theories of human and animal learning from psychology are closely aligned with ideas from the new field of machine learning. Machine learning is a field at the interface of statistics and computer science that focuses on how to build computer algorithms that can learn from experience. While statistics and machine learning often try to solve the same problems, researchers from these fields often take very different approaches; the famous statistician Leo Breiman once referred to them as “The Two Cultures” to reflect how different their approaches can be. In this book I will try to blend the two cultures together because both approaches provide useful tools for thinking about data.

    统计学为我们提供了一种描述新数据如何最好地用于更新我们信仰的方法,这样统计学与心理学之间存在深刻的联系。事实上,许多心理学中关于人类和动物学习的理论与新兴的机器学习领域的思想密切相关。机器学习是统计学和计算机科学交界处的一个领域,重点研究如何构建能够从经验中学习的计算机算法。虽然统计学和机器学习通常试图解决相同的问题,但来自这些领域的研究人员通常采取非常不同的方法;著名的统计学家 Leo Breiman 曾将它们称为“两种文化”,以反映它们的方法之间有多么不同。在本书中,我将尝试将这两种文化融合在一起,因为两种方法都为思考数据提供了有用的工具。

  • Statistics provides us with the tools to characterize uncertainty, to make decisions under uncertainty, and to make predictions whose uncertainty we can quantify.


  • Statistics can provide us with evidence, but it’s always tentative and subject to the uncertainty that is always present in the real world.


  • In fact, the rate at which the benefit of larger samples decreases follows a simple mathematical rule, growing as the square root of the sample size, such that in order to double the precision of our estimate we need to quadruple the size of our sample.


  • Although observational research cannot conclusively demonstrate causal relations, we generally think that causation can be demonstrated using studies that experimentally control and manipulate a specific factor. In medicine, such a study is referred to as a randomized controlled trial (RCT).


  • Researchers often try to address these confounds using statistical analyses, but removing the influence of a confound from the data can be very difficult.


2 Working with data

  • The first important point about data is that data are – meaning that word “data” is plural (though some people disagree with me on this).

  • In many fields such as psychology, the thing that we are measuring is not a physical feature, but instead is an unobservable theoretical concept, which we usually refer to as a construct. It is usually impossible to measure a construct without some amount of error.

  • When we think about what makes a good measurement, we usually distinguish two different aspects of a good measurement: it should be reliable, and it should be valid.

  • Reliability refers to the consistency of our measurements. One common form of reliability, known as “test-retest reliability”, measures how well the measurements agree if the same measurement is performed twice.

  • Reliability is important if we want to compare one measurement to another, because the relationship between two different variables can’t be any stronger than relationship between either of the variables and itself (i.e., its reliability). This means that unreliable measure can never have a strong statistical relationship with any other measure. For this reason, researchers developing a new measurement (such as a new survey) will often go to great lengths to establish and improve its reliability.


  • We want our measurements to also be valid — that is, we want to make sure that we actually measuring the construct that we think we are measuring.

    • Face validity. Does the measurement make sense on its face?

    • Construct validity. Is the measurement related to other measurements in an appropriate way?

    • Predictive validity. If our measurements are truly valid, then they should be predictive of other outcomes.

3 Summarizing data

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