#statistical literacy

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There's always a chance you'll get hit by a car on any given day.

Tomorrow I may get hit with a car, or I may not

There are two options

100% ÷ 2 = 50%

There is a 50% chance I'll be hit by a car tomorrow

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What's going on, what's going on?

What’s going on, what’s going on?

For many high school teachers here in New Zealand, the teaching year is over and it’s now a six-week summer break before school starts again next year. Despite the well-deserved break, some teachers are already thinking about ideas for next year. I’ve been amazed (and inspired) by the teachers who have signed up to spend a day with Liza and I on Friday 15th December to learn more about working…

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Children need to be taught health literacy in school so they can analyse, interpret and question pseudoscience

Science and health education that teaches students to analyse health and wellness blogs, reports and advice would do a great service promoting a healthy literate community and keeping the anti-science crowd at bay.

Health literacy is being able to make informed decisions about your own health based on a critical look at the evidence. It’s the ability to take a health recommendation and ask the right questions, rather than taking advice without question.

When reading health recommendations on wellness blogs or in media reports people need to ask themselves: where was this research published? What was the sample size for the study, and what makes a strong sample size? Was this an observational or intervention study? What are the flaws in the study design, who was it funded by, and have the findings been replicated? Was it carried out in animals or humans? What’s the difference?

Relying on studies in peer-reviewed medical journals and advice from doctors and nurses is a good start but it’s not perfect. Of course, dodgy studies slip through the cracks and are published in respected journals. . . An increasing push for open science and transparency is helping identify flawed and unethical studies so they are picked apart and retracted faster.

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Given the timing, with all the talk about fake news, alternative facts, concern over misinformation and propaganda-by-numbers, [Hans] Rosling stood for the exact opposite – the idea we can have debates about what could or should be done, but that facts and an open mind are needed before informed discussions can begin.

Claire Provost, former Guardian journalist who interviewed Rosling in 2013

Read more:

Hans Rosling dies aged 68

[bookfre]

Using Real Life Examples to Teach Abstract Statistical Concepts

Summary

This article provides real life examples that can be used to explain statistical concepts. It does not attempt to be exhaustive, but rather, provide a few examples for selected concepts based on what students should know after taking a statistics course.

INTRODUCTION

Efforts in statistics education reform have focused on statistical thinking and conceptual understanding rather than mere knowledge of procedure.

Statistics is not an easy subject to teach. Almost every statistics beginner experiences difficulties understanding the topic. There is a consensus among statisticians that statistics education should focus on data and on statistical reasoning rather than on either the presentation of as many methods as possible or the mathematical theory of inference. Generally, the goal of statistics education is to answer ‘real world’ questions. The student should develop sufficient competence to understand and draw accurate meaning from a statistical argument. Examples, therefore, should be presented in the context of real-world problems. Recommendations for statistics courses from the GAISE (Guidelines for Assessment and Instruction in Statistics Education) Report (Garfield et al. 2005) include the following:

Emphasize statistical literacy and develop statistical thinking.

Use real data.

Stress conceptual understanding rather than mere knowledge of procedures.

Foster active learning in the classroom.

Use technology for developing conceptual understanding and analyzing data.

Use assessments to improve and evaluate student learning.

Furthermore, the guidelines are given in the GAISE

The report suggests designing statistics courses that teach students to communicate results of a statistical analysis and do so in context. In addition, students should develop skills to read and critique news stories and journal articles that include statistical information. That is, they should have statistical reasoning skills as well as statistical understanding.

This goal of applying statistics to everyday life is reiterated by Gal and Ginsburg (1994).

It is sometimes difficult for students to relate statistical concepts presented in class to real world problems and everyday situations. Therefore, teaching introductory statistics requires the instructor not only to transmit knowledge but also to enhance students’ motivation and attention (Symanzik and Vukasinovic 2006). From our experiences in teaching statistics, what we have found helpful is to relate the statistical concepts to real life situations. In most cases, this strategy helps lower the students’ statistical anxiety. The impact of statistics anxiety on student learning is well documented (e.g. Benson

1989; Dillon 1982; Roberts and Bilderback 1980; Roberts and Saxe 1982).

Researchers (e.g. Everson et al. 2008) have provided some ideas for putting the GAISE guidelines into practice in the statistics classroom. Interactivity, hands-on exercises, visualization of statistical concepts and well-documented real-life examples are some of the features of a statistical course that help stimulate the student’s activity in class, ease understanding of statistical concepts and make the whole course more attractive and fun for the student.

In this article, we discuss certain real life examples that we normally use to explain statistical concepts.

We do not attempt to cover all the statistical concepts, but rather, we just provide a few examples that are popular with students. Each of the concepts discussed can be linked directly to the goals suggested in the GAISE Report.

REAL LIFE EXAMPLES:

If the field of statistics could be described in one word, that word would be variability. In almost all cases we are attempting to explain variance or apportion variance. We use models (samples) as a representation of the real world so it should not be surprising that there is variability in whatever characteristics we study. As the GAISE Report suggests, students should understand that variability is natural and is also predictable and quantifiable.

The weather reports we hear on the news every day provide an illustration of the value of variability. While two regions can have the same average temperature of, say, 55°F, we get a better understanding of the weather in these regions by considering the variation in temperature. For instance, a region that is near the coast is more likely to have a narrower range than one further inland. That is, the average temperature of 55°F for the inland region may have highs of 75°F and lows of 35°F, while in the coastal region the highs might be 60°F with lows of 50°F. Although the regions have the same average temperature, the higher standard deviation means that predictions are less reliable for the temperature of the inland region.

A similar phenomenon can be found in sports. In sports, trying to predict which teams will win, on any given day, may include looking at the standard deviations of the team ratings in various categories.

In such ratings, anomalies can match strengths versus weaknesses in an attempt to understand which factors are the stronger indicators of eventual scoring outcomes. For instance, there will be teams that excel in some aspects of the sport and perform poorly in others. Teams may have a great offense and a weak defense or vice versa. Furthermore, teams with higher standard deviations will be more unpredictable. It is important, of course, to consider the mean with the standard deviation in making predictions. A team that is constantly good in most categories will have a low standard deviation but so will a team that is consistently bad.

It is important that students understand the concept of a sampling distribution and how it applies to making statistical inferences. Sampling distributions are important because inferential statistics is based on them. Inferential statistics is about drawing conclusions about the population based on sample data.

An example of this is the polling done prior to elections. At the end of August 2008, two of the polls conducted to predict the winner of the US presidential race provided somewhat different results (see table 1). Looking at these results provides an opportunity to discuss what happens when different samples are drawn from the same population.

Although the samples may have been drawn from the same population they may provide different estimates. Furthermore, individual sample statistics do not always match the true population value but vary around it. At this point, the instructor can discuss the distribution of sample statistics

(e.g. means being approximately normal).

This demonstration can also naturally lead to a discussion of the margin of error as it is computed in political polls and to confidence intervals (Baumann and Danielson 1997). Examining the formula for the margin of error can also lead to a discussion of the effect of sample size and variability in the sampling statistics. Students can see that larger samples correspond to smaller sampling variation and smaller margins of error and that population size is not a factor in the margin of error. With these ideas clarified, students can turn to applications such as projecting winners in elections or comparing the responses of subgroups such as men and women.

Download original “Using Real Life Examples to Teach Abstract Statistical Concepts” file 

The paper published by:

Nyaradzo Mvududu Seattle Pacific University, Washington, USA. e-mail: [email protected]

Gibbs Y. Kanyongo Duquesne University, Pittsburgh, Pennsylvania, USA. e-mail: [email protected]

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The Royal Statistical Society's _Data Manifesto_ has called on the UK government to recognise the value of data and the importance that we, as a country, have the capability to use it.

Statistics is a technical and creative discipline. . . Rather than just providing abstract numbers, statistics as taught in school should relate to real situations that pupils should have an interest in. This can help to resolve number-phobia by making numbers part of everyday problem solving.

[W]e advocate statistical enquiry as a way of understanding the world that is transferable across a range of subjects and situations. In the statistical enquiry cycle, students learn to state a problem and to plan their own statistical or analytical approach. They then collect their data, or source existing appropriate datasets. They process, analyse and present their data, and then they interpret and communicate their findings to address the stated problem.

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Trump is a masterful troll, and trolls – and aspiring authoritarians – can thrive in environments where there’s a lot of confusing information.

“Why I Support An Election Audit, Even Though It’s Unlikely To Change The Outcome” by Nate Silver @ fivethirtyeight.com