Statistical literacy

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Statistical literacy is the ability to understand and reason with statistics and data. The abilities to understand and reason with data, or arguments that use data, are necessary for citizens to understand material presented in publications such as newspapers, television, and the Internet. However, scientists also need to develop statistical literacy so that they can both produce rigorous and reproducible research and consume it. Numeracy is an element of being statistically literate and in some models of statistical literacy, or for some populations (e.g., students in kindergarten through 12th grade/end of secondary school), it is a prerequisite skill. Being statistically literate is sometimes taken to include having the abilities to both critically evaluate statistical material and appreciate the relevance of statistically-based approaches to all aspects of life in general [1] [2] [3] or to the evaluating, design, and/or production of scientific work. [4]

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Promoting statistical literacy

Each day people are inundated with statistical information from advertisements ("4 out of 5 dentists recommend"), news reports ("opinion poll show the incumbent leading by four points"), and even general conversation ("half the time I don't know what you're talking about"). Experts and advocates often use numerical claims to bolster their arguments, and statistical literacy is a necessary skill to help one decide what experts mean and which advocates to believe. This is important because statistics can be made to produce misrepresentations of data that may seem valid. The aim of statistical literacy proponents is to improve the public understanding of numbers and figures.

Health decisions are often manifest as statistical decision problems but few doctors or patients are well equipped to engage with these data. [5]

Results of opinion polling are often cited by news organizations, but the quality of such polls varies considerably. Some understanding of the statistical technique of sampling is necessary in order to be able to correctly interpret polling results. Sample sizes may be too small to draw meaningful conclusions, and samples may be biased. The wording of a poll question may introduce a bias, and thus can even be used intentionally to produce a biased result. Good polls use unbiased techniques, with much time and effort being spent in the design of the questions and polling strategy. Statistical literacy is necessary to understand what makes a poll trustworthy and to properly weigh the value of poll results and conclusions.

For these reasons, and others, many programs around the world have been created to promote or improve statistical literacy. For example, many official statistical agencies such as Statistics Canada and the Australian Bureau of Statistics have programs to educate students in schools about the nature of statistics. A project [6] of the International Statistical Institute is the only international organization whose focus is to promote national programs and drives to increase the statistical literacy of all members of society. Numerous resources and activities, as well as a body of international experts help maintain a very successful campaign across the continents. The United Nations Economic Commission for Europe has taken the notion of statistical literacy as the subject for its fourth guide to making data meaningful. Recognising the obligation of its royal charter to promote the public understanding of statistics, in 2010 the Royal Statistical Society launched a ten-year statistical literacy campaign. [7]

Models of statistical literacy

Experiments in the sciences, business models and reports, use statistics. People involved in these fields generally have studied the meaning of statistical quantities, such as averages and standard deviation. Many colleges and universities require an introductory course in statistics as part of a professional program.

Data visualization can contribute to either understanding or misunderstanding of the data or of the argument being made with the data. [8] [9] [10] [11] [12]

Studies have shown that human beings’ estimations of probabilities are heavily influenced by context and wording. Statistical reasoning may be difficult to develop and refine, which has led to labeling this type of reasoning as not intuitive. For example, people typically underestimate the probability of being involved in a car accident because their everyday interaction with vehicles gives the impression that they are safer than they actually are. Likewise, they tend to overestimate the probability of being attacked by a shark because of media or other influences. [13]

Gambling is one setting in which a lack of statistical literacy can be costly.[ citation needed ] Simple probability theory helps the individual either estimate or calculate the probabilities involved with games of chance. However, most individuals fail to approximate, for example, the probability of being dealt a full-house in a game of poker. Not understanding these probabilities causes the individual to wager more or less than they would knowing at least an estimate of the probability.[ citation needed ] Increasing individuals’ statistical literacy and knowledge of probability through classroom applications, textbook examples, and other methods, would lead to more informed citizens, capable of making more informed decisions, or perhaps not. [13]

The definition of statistical literacy and opinions about it have been somewhat historically variable. Before 1940 some statistical skills passed to the sciences. Some statistics was then taught in grade school, "So a degree of statistical literacy will be universal in the future...". [14] More recently, expectations have been higher. "'Statistical Literacy' is the ability to understand and critically evaluate statistical results that permeate our lives...". [2] Those statistical results often originate from inferential methods which reached college statistics textbooks in about 1940. Statistics continues to advance. A lack of statistical literacy has long been condemned under many labels. [15] [16] [17] [18] H.G. Wells has been cited as saying that statistical understanding will one day be as important as being able to read or write [2] but he may have been referring more to the older idea of political arithmetic than modern statistics.

See also

Related Research Articles

In statistics, sampling bias is a bias in which a sample is collected in such a way that some members of the intended population have a lower or higher sampling probability than others. It results in a biased sample of a population in which all individuals, or instances, were not equally likely to have been selected. If this is not accounted for, results can be erroneously attributed to the phenomenon under study rather than to the method of sampling.

<span class="mw-page-title-main">Statistics</span> Study of the collection, analysis, interpretation, and presentation of data

Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a scientific, industrial, or social problem, it is conventional to begin with a statistical population or a statistical model to be studied. Populations can be diverse groups of people or objects such as "all people living in a country" or "every atom composing a crystal". Statistics deals with every aspect of data, including the planning of data collection in terms of the design of surveys and experiments.

<span class="mw-page-title-main">Simpson's paradox</span> Probability and statistics phenomenon

Simpson's paradox is a phenomenon in probability and statistics in which a trend appears in several groups of data but disappears or reverses when the groups are combined. This result is often encountered in social-science and medical-science statistics, and is particularly problematic when frequency data are unduly given causal interpretations. The paradox can be resolved when confounding variables and causal relations are appropriately addressed in the statistical modeling.

<span class="mw-page-title-main">Sampling (statistics)</span> Selection of data points in statistics.

In statistics, quality assurance, and survey methodology, sampling is the selection of a subset or a statistical sample of individuals from within a statistical population to estimate characteristics of the whole population. Statisticians attempt to collect samples that are representative of the population. Sampling has lower costs and faster data collection compared to recording data from the entire population, and thus, it can provide insights in cases where it is infeasible to measure an entire population.

<span class="mw-page-title-main">Information design</span> Communication and graphic design

Information design is the practice of presenting information in a way that fosters an efficient and effective understanding of the information. The term has come to be used for a specific area of graphic design related to displaying information effectively, rather than just attractively or for artistic expression. Information design is closely related to the field of data visualization and is often taught as part of graphic design courses. The broad applications of information design along with its close connections to other fields of design and communication practices have created some overlap in the definitions of communication design, data visualization, and information architecture.

<span class="mw-page-title-main">Edward Tufte</span> American statistician (b.1942) noted for his writings on information design

Edward Rolf Tufte, sometimes known as "ET", is an American statistician and professor emeritus of political science, statistics, and computer science at Yale University. He is noted for his writings on information design and as a pioneer in the field of data visualization.

Sampling is the use of a subset of the population to represent the whole population or to inform about (social) processes that are meaningful beyond the particular cases, individuals or sites studied. Probability sampling, or random sampling, is a sampling technique in which the probability of getting any particular sample may be calculated. In cases where external validity is not of critical importance to the study's goals or purpose, researchers might prefer to use nonprobability sampling. Nonprobability sampling does not meet this criterion. Nonprobability sampling techniques are not intended to be used to infer from the sample to the general population in statistical terms. Instead, for example, grounded theory can be produced through iterative nonprobability sampling until theoretical saturation is reached.

An opinion poll, often simply referred to as a survey or a poll, is a human research survey of public opinion from a particular sample. Opinion polls are usually designed to represent the opinions of a population by conducting a series of questions and then extrapolating generalities in ratio or within confidence intervals. A person who conducts polls is referred to as a pollster.

<span class="mw-page-title-main">Numeracy</span> Ability to apply numerical concepts

Numeracy is the ability to understand, reason with, and to apply simple numerical concepts. The charity National Numeracy states: "Numeracy means understanding how mathematics is used in the real world and being able to apply it to make the best possible decisions...It’s as much about thinking and reasoning as about 'doing sums'". Basic numeracy skills consist of comprehending fundamental arithmetical operations like addition, subtraction, multiplication, and division. For example, if one can understand simple mathematical equations such as 2 + 2 = 4, then one would be considered to possess at least basic numeric knowledge. Substantial aspects of numeracy also include number sense, operation sense, computation, measurement, geometry, probability and statistics. A numerically literate person can manage and respond to the mathematical demands of life.

<span class="mw-page-title-main">Chartjunk</span>

Chartjunk consists of all visual elements in charts and graphs that are not necessary to comprehend the information represented on the graph, or that distract the viewer from this information.

<span class="mw-page-title-main">Infographic</span> Graphic visual representation of information

Infographics are graphic visual representations of information, data, or knowledge intended to present information quickly and clearly. They can improve cognition by utilizing graphics to enhance the human visual system's ability to see patterns and trends. Similar pursuits are information visualization, data visualization, statistical graphics, information design, or information architecture. Infographics have evolved in recent years to be for mass communication, and thus are designed with fewer assumptions about the readers' knowledge base than other types of visualizations. Isotypes are an early example of infographics conveying information quickly and easily to the masses.

Statistics, when used in a misleading fashion, can trick the casual observer into believing something other than what the data shows. That is, a misuse of statistics occurs when a statistical argument asserts a falsehood. In some cases, the misuse may be accidental. In others, it is purposeful and for the gain of the perpetrator. When the statistical reason involved is false or misapplied, this constitutes a statistical fallacy.

This glossary of statistics and probability is a list of definitions of terms and concepts used in the mathematical sciences of statistics and probability, their sub-disciplines, and related fields. For additional related terms, see Glossary of mathematics and Glossary of experimental design.

<span class="mw-page-title-main">Data and information visualization</span> Visual representation of data

Data and information visualization is the practice of designing and creating easy-to-communicate and easy-to-understand graphic or visual representations of a large amount of complex quantitative and qualitative data and information with the help of static, dynamic or interactive visual items. Typically based on data and information collected from a certain domain of expertise, these visualizations are intended for a broader audience to help them visually explore and discover, quickly understand, interpret and gain important insights into otherwise difficult-to-identify structures, relationships, correlations, local and global patterns, trends, variations, constancy, clusters, outliers and unusual groupings within data. When intended for the general public to convey a concise version of known, specific information in a clear and engaging manner, it is typically called information graphics.

<i>Innumeracy</i> (book) 1988 book by John Allen Paulos

Innumeracy: Mathematical Illiteracy and its Consequences is a 1988 book by mathematician John Allen Paulos about innumeracy as the mathematical equivalent of illiteracy: incompetence with numbers rather than words. Innumeracy is a problem with many otherwise educated and knowledgeable people. While many people would be ashamed to admit they are illiterate, there is very little shame in admitting innumeracy by saying things like "I'm a people person, not a numbers person", or "I always hated math", but Paulos challenges whether that widespread cultural excusing of innumeracy is truly worthy of acceptability.

Statistical graphics, also known as statistical graphical techniques, are graphics used in the field of statistics for data visualization.

Statistics education is the practice of teaching and learning of statistics, along with the associated scholarly research.

Data literacy is the ability to read, understand, create, and communicate data as information. Much like literacy as a general concept, data literacy focuses on the competencies involved in working with data. It is, however, not similar to the ability to read text since it requires certain skills involving reading and understanding data.

Intuitive statistics, or folk statistics, is the cognitive phenomenon where organisms use data to make generalizations and predictions about the world. This can be a small amount of sample data or training instances, which in turn contribute to inductive inferences about either population-level properties, future data, or both. Inferences can involve revising hypotheses, or beliefs, in light of probabilistic data that inform and motivate future predictions. The informal tendency for cognitive animals to intuitively generate statistical inferences, when formalized with certain axioms of probability theory, constitutes statistics as an academic discipline.

<span class="mw-page-title-main">Graphical perception</span>

Graphical perception is the human capacity for visually interpreting information on graphs and charts. Both quantitative and qualitative information can be said to be encoded into the image, and the human capacity to interpret it is sometimes called decoding. The importance of human graphical perception, what we discern easily versus what our brains have more difficulty decoding, is fundamental to good statistical graphics design, where clarity, transparency, accuracy and precision in data display and interpretation are essential for understanding the translation of data in a graph to clarify and interpret the science.

References

  1. ↑ Dodge, Y. (2003) The Oxford Dictionary of Statistical Terms, OUP. ISBN   0-19-920613-9
  2. 1 2 3 Wallman, Katherine K. (1993). "Enhancing statistical literacy: Enriching our society". Journal of the American Statistical Association. 88 (421): 1–8. doi:10.1080/01621459.1993.10594283. Wallman was president of the American Statistical Association and Chief of Statistical Policy, United States Office of Management and Budget.
  3. ↑ Gal, I. (2002). Adults’ statistical literacy: Meaning, components, responsibilities (with Discussion). International Statistical Review, 70(1), 1–51.
  4. ↑ Tractenberg, Rochelle E. (2016-12-24). "How the Mastery Rubric for Statistical Literacy Can Generate Actionable Evidence about Statistical and Quantitative Learning Outcomes". Education Sciences. 7 (1): 3. doi: 10.3390/educsci7010003 .
  5. ↑ Gerd Gigerenzer et al. (2008) "Helping doctors and patients make sense of health statistics" Psychological Science in the Public Interest8 (2), pp.53-96
  6. ↑ The International Statistical Literacy Project
  7. ↑ getstats.org.uk
  8. ↑ Tufte, Edward R. (1997). Visual explanations : images and quantities, evidence and narrative. Cheshire, Conn.: Graphics Press. ISBN   9780961392123. OCLC   36234417.
  9. ↑ Tufte, Edward R. (2001). The visual display of quantitative information (2nd ed.). Cheshire, Conn.: Graphics Press. ISBN   9780961392147. OCLC   46932988.
  10. ↑ Tufte, Edward R. Envisioning information . Graphics Press. Cheshire, Connecticut. ISBN   9780961392116. OCLC   21270160.
  11. ↑ Heiberger, R.M., Holland, B. (2004) Statistical Analysis and Data Display. Springer. ISBN   0-387-40270-5
  12. ↑ Tufte, Edward R. (2006). Beautiful evidence. Cheshire, Conn.: Graphics Press. ISBN   9780961392178. OCLC   70203994.
  13. 1 2 Kahneman, Daniel (2013). Thinking, fast and slow . New York: Farrar, Straus and Giroux. ISBN   9780374533557. The book is about how people actually think, decide and remember (based on psychological experimentation). "Why is it so difficult for us to think statistically? We easily think associatively, we think metaphorically, we think causally, but statistics requires thinking about many things at once, which is something that [intuition] is not designed to do." p 13 "Even statisticians were not good intuitive statisticians." p 5 "The lesson is clear: estimates of causes of death are warped by media coverage. The coverage is biased toward novelty and poignancy." p 138 "When people were favorably disposed toward a technology, they rated it as offering large benefits and imposing little risk; when they disliked a technology, they could think only of its disadvantages, and few advantages came to mind." p 139 "[M]y intuitive thinking is just as prone to overconfidence, extreme predictions, and the planning fallacy as it was before I made a study of these issues. I have improved only my ability to recognize situations in which errors are likely..." p 417
  14. ↑ Ogburn, William Fielding (1940). "Statistical Trends". Journal of the American Statistical Association. 35 (209b): 252–260. doi:10.1080/01621459.1940.10500563.
  15. ↑ Huff, Darrell (1993). How to lie with statistics. New York: Norton. ISBN   978-0393310726. First published in 1954.
  16. ↑ Hopkins, Harry (1973). The numbers game: the bland totalitarianism. Boston: Little, Brown. ISBN   978-0316372701.
  17. ↑ Paulos, John (1988). Innumeracy : mathematical illiteracy and its consequences . New York: Hill and Wang. ISBN   0-8090-7447-8.
  18. ↑ Seife, Charles (2011). Proofiness : how you're being fooled by the numbers. New York: Penguin. ISBN   9780143120070.
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