Eye colour and reaction time: an opportunity for critical statistical reasoning.Eye colour is a variable that is often used in classroom data collection activities. It is relatively easy to document, subject to the occasional argument, and provides an example of a categorical That which is unqualified or unconditional.
A categorical imperative is a rule, command, or moral obligation that is absolutely and universally binding.
Categorical is also used to describe programs limited to or designed for certain classes of people. variable other than gender to be used for graphing purposes. Figure 1 shows a pie graph produced by some students in a grade 5/6 classroom (Chick chick
abbreviation for chicken (1). & Watson, 2001). Detailing the relative presence of the colours in the class is about as far as the use of the variable extends. As the students who worked with Chick and Watson found, attempts to show associations of eye colour with other variables such as weight, age, or number of fast foods eaten per week, are usually fruitless fruit·less
1. Producing no fruit.
2. Unproductive of success: a fruitless search. See Synonyms at futile. . In fact by grade 7 most students have dismissed eye colour as an "interesting" attribute to explore.
It was hence surprising to read a short article in The Mercury newspaper in Hobart Hobart, city, Australia
Hobart, city (1990 pop. 127,134), capital and principal port of Tasmania, SE Australia, at the foot of Mt. Wellington (4,166 ft/1,270 m high). Hobart's harbor is one of the finest in the world. about blue-eyed Blue´-eyed`
a. 1. Having blue eyes.
Adj. 1. blue-eyed - favorite; "the fair-haired boy of the literary set"
fair-haired, white-haired people being more intelligent and brown-eyed people having faster reaction times (see Figure 2). Such an article invites immediate scepticism scep·ti·cism
Variant of skepticism.
a personal disposition toward doubt or incredulity of facts, persons, or institutions. See also 312. PHILOSOPHY. — skeptic, n. from the statistically literate. The lack of data in the article should lead the interested reader to a search for further information, most likely through an internet search. Although the first claim might be considered too contentious for investigation in the classroom, the second one about brown eyes Brown Eyes (브라운 아이즈) was a Korean musical duo, specializing in ballads. Although both members have powerful voices, they were initially disregarded because of their physical looks. and reaction times seems quite harmless The term harmless may be taken in several ways:
tr.v. re·fut·ed, re·fut·ing, re·futes
1. To prove to be false or erroneous; overthrow by argument or proof: refute testimony.
2. the claim.
[FIGURE 1 OMITTED]
This article progresses through the steps that could be followed in a middle school classroom to explore the question and develop critical statistical reasoning skills (Watson, 2006). Students should first consider their initial reaction to the claims in the article and what questions they would like to have answered before accepting the claims. Second, students should undertake as much research on the topic as possible, probably through the Internet. Next students have the opportunity to collect data from their own class and see what their sample suggests about the claim. Finally students can collect larger random samples, such as from the Australian Australian
pertaining to or originating in Australia.
Australian bat lyssavirus disease
see Australian bat lyssavirus disease.
Australian cattle dog
a medium-sized, compact working dog used for control of cattle. Bureau of Statistics' (ABS (Automatic Backup System) See backup program. ) CensusAtSchool website to check out the eye colour and reaction time claim. All of these steps should then contribute to a report that supplies evidence for and/or and/or
Used to indicate that either or both of the items connected by it are involved.
Usage Note: And/or is widely used in legal and business writing. against the claim and reaches a tentative tentative,
adj not final or definite, such as an experimental or clinical finding that has not been validated. conclusion about its validity.
Figure 2. Newspaper article. The Mercury(Hobart), 21 August 2007 Eye colour achievements The colour of your eyes could determine your achievements in life, say scientists. Those with blue eyes are more likely to sparkle academically than those with brown. In reaction time trials in the US, brown eyes performed better, making them more likely to succeed at things like football, hockey and rugby. But those with lighter eyes appeared to be better strategic thinkers.
Questioning the article
Of interest from a critical literacy Critical literacy is an instructional approach that advocates the adoption of critical perspectives toward text. Critical literacy encourages readers to actively analyze texts and it offers strategies for uncovering underlying messages. perspective is how the news media chose to report on the study. The article in The Mercury reproduced in Figure 2 is quite short but a search of the Internet produces reports of varying length. Students should collect a few of these and compare and contrast them. Some, such as the much longer one in Figure 3, include examples of well-known well-known
1. Widely known; familiar or famous: a well-known performer.
2. Fully known: well-known facts. people with blue eyes Blue eyes are eyes that have blue irises (see eye color), and may also refer to:
1. Not constituting a vital element or part.
2. Inessential or unrelated to the topic or matter at hand; irrelevant. See Synonyms at irrelevant.
3. ? Another extract from The Times of India India, officially Republic of India, republic (2005 est pop. 1,080,264,000), 1,261,810 sq mi (3,268,090 sq km), S Asia. The second most populous country in the world, it is also sometimes called Bharat, its ancient name. India's land frontier (c. (see Figure 4) adds a few more details, for example noting that black eyes were not considered. Students could consider why this would be a significant addition in India. The use of language is also interesting in comparing the reports in Figure 3 and Figure 4. In the latter, the "brown-eyed people succeeded," whereas in the former they were "more likely to succeed" at activities such as football and hockey. One statement claims a fact whereas the other is a probabilistic (probability) probabilistic - Relating to, or governed by, probability. The behaviour of a probabilistic system cannot be predicted exactly but the probability of certain behaviours is known. Such systems may be simulated using pseudorandom numbers. statement. This raises other questions about the study itself. A few of these are finally answered in the extract in Figure 5, which provides the sample size and the explanations of the "forehand forehand
the head, neck, shoulders, withers and forelimbs of the horse. rally" activity that was carried out.
At this point is it important to get students to speculate about what the data might have looked like to produce the claims in the media reports. Without the information in Figure 5, many general comments can be made and graphs drawn. A task such as shown in Figure 6 would be highly relevant to building critical statistical literacy Statistical literacy is a term used to describe an individual's or group's ability to understand statistics. Statistical literacy is considered by many to be necessary for citizens to understand material presented in publications such as newspapers, television and the internet. . Depending on how the classroom activity progressed, it could be used both before and after information such as in Figure 5 was available. Questions about the sample size may emerge when students begin to consider the subgroups with different coloured eyes. A careful reading of the results reported in Figure 5 should also raise some questions about which subgroups were compared with each other. As well, the use of the terms dark-eyed and light-eyed may address the question raised by The Times of India about black-eyed Black´-eyed`
a. 1. Having black eyes. individuals. Finally, although reaction time is the phrase used in the first three reports, the Medline report suggests counting rather than time measurement. How this experiment was carried out to find that more rallies correspond to faster reaction time would lead to further interesting and relevant discussion.
Figure 3. Longer report from the Internet (Clerkin, 2007). Why Blue-eyed boys (and girls) are so brilliant Scientists discover what may have made Stephen Hawking--and Lily Cole--so intelligent By BEN CLERKIN - Last updated at 11:33am on 20th August 2007 The colour of your eyes could determine your achievements in life, say scientists. They claim those with blue eyes are more likely to sparkle academically than those with brown. They are more intelligent and gain more qualifications because they study more effectively and perform better in exams. The discovery might help explain the success of such disparate individuals as Stephen Hawking, Alexander Fleming, Marie Curie, Stephen Fry and Lily Cole. In reaction time trials conducted by U.S. scientists, the brown-eyed performed better, making them more likely to succeed at activities such as football, hockey and rugby. But the researchers concluded that those with lighter eyes appeared to be better strategic thinkers. Blue-eyed boys and girls proved to be more successful in activities that required them to plan and structure their time, such as golf, cross-country running and studying for exams. [ILLUSTRATION OMITTED] Those highly intelligent Stephens (Hawking and Fry): New research has revealed that blue-eyed individuals may study more effectively and perform better in exams than those with dark eyes. Stephen Hawking, author of A Brief History Of Time, is Britain's most eminent physicist. Writer and actor Stephen Fry gained a scholarship to Cambridge. Joanna Rowe, professor emeritus at the University of Louisville in Kentucky, who conducted the tests, said the results suggested a hitherto unexplored link between eye colour and academic achievement. "It is just observed, rather than explained," she said. "There's no scientific answer yet." Dr Tony Fallone, senior psychology lecturer at the University of Bedfordshire, who has also studied eye colour, believes it should be taken more seriously as an indicator or personality and ability. Most babies have blue eyes but they usually darken as the pigment melanin builds up in the iris. Less melanin produces green, grey, or light brown eyes. Eyes with very little melanin appear blue or grey. Figure 4. Report from The Times of India ("Study," 2007). Study--Eye Colour Matters From The Times of India New York: Success lies in the colour of your eyes, and those with blue ones are likely to achieve more in life than their peers as they tend to study more effectively and perform better in exams, says a study conducted by US scientists. The study did not mention anything about people with black irises. The test showed that brown eyed people had faster reaction time, but those with lighter eyes appeared to be better strategic thinkers. Brown eyed people succeeded in activities such as football and hockey, but lighter eyed participants proved to be more successful in activities that required skills in time structuring and planning such as golf, cross country running and studying for exams, the scientists said. Louisville university professor Joanna Rowe, who conducted the tests, said the results suggested an unexplored link between eye colour and academic achievement. "It is just observed, rather than explained," she said. "There's no scientific answer yet." Figure 5. Medline extract (Rowe & Evans, 2007). Ball colour, eye colour, and a reactive motor skill. Rowe PJ, Evans P Department of HPES/Crawford Gym, University of Louisville, KY 40292 Researchers investigating performance differences between light- and dark-eyed individuals have indicated that dark-eyed individuals perform better on reactive activities than light-eyed individuals. College students (61 men, 64 women) performed a forehand rally with different coloured raquetballs. Eye colour, sex, and total hits were recorded for each subject. Men scored significantly better with balls of each colour than did women. Dark-eyed men performed better than other subjects and performance was better with blue balls than yellow or green balls PMID:7808908 [PubMed - indexed for MEDLINE] Figure 6. A task for students after the Internet search. Draw a graph that could possibly represent the relationship between the following variables that would support the conclusions made by the researchers at the University of Louisville: a) Eye colour and reaction time. b) Eye colour and academic achievement. For each graph, explain in words why you chose the type of graph you used and the reasons for its shape, scale and units on each of the axes.
Particularly in light of the relatively small sample size reported in Figure 5, students should ask questions about other possible samples, including their own class. They can come up with their own activity to measure reaction time and see if a similar relationship exists for their sample. A common activity used in upper primary and middle school classrooms involves two students, where one holds a ruler above the outstretched out·stretch
tr.v. out·stretched, out·stretch·ing, out·stretch·es
To stretch out; extend.
Adjective forefinger forefinger /fore·fin·ger/ (-fing-ger) index finger; the second finger, counting the thumb as first.
See index finger. and thumb of another student. The ruler is dropped and the second student grabs it with the forefinger and thumb, then measuring the distance down the ruler as a gauge of reaction time. The shorter the distance measured, the quicker the reaction time. Another possibility is to use the Australian Bureau of Statistics' CensusAtSchool website, which has a reaction timer timer,
n radiographic timing device that functions as an automatic exposure timer and a switch to control the current to the high-tension transformer and filament transformer. The face of the timer is calibrated in seconds and fractions of seconds. based on responding to a colour change on the computer screen by clicking on a mouse. There are tasks for both right and left hands, and data can be recorded in class for each student. (1)
Data collected from 30 students in a grade 10 class are used here to explore questions related to the results claimed in the reports in the figures. The students used the CensusAtSchool site to collect their reaction time data.
Claim 1: Brown-eyed people had faster reaction times than others (Figures 2, 3, and 4)
Claim 2: Males had faster reaction times than females (Figure 5).
Claim 3: Dark-eyed males performed better than other subjects (Figure 5).
The graphs shown in the following figures were produced using the TinkerPlots software (Konold & Miller, 2005). The plots include hat plots, which are variations on box-and-whisker plots, showing the middle 50% of the data in the crown of the hat and the top and bottom 25% in the brims of the hat. The mean value for right hand reaction time is indicated on the horizontal axis for each subgroup sub·group
1. A distinct group within a group; a subdivision of a group.
2. A subordinate group.
3. Mathematics A group that is a subset of a group.
tr.v. of the sample.
Figure 7 shows the plot for right hand reaction time in relation to Claim 1, that brown-eyed people were quicker than light-eyed people (here "other" includes green, blue, grey, and hazel). It does appear from this grade 10 sample that evidence supports the claim. The class would need to discuss the number of students with brown eyes and whether this affects the confidence they have in their result.
The graph in Figure 8 supports Claim 2, that males have faster reaction times than females, certainly for this class. Not only do the average reaction times for the two subgroups support this but it can be seen that the crowns of the hats do not overlap o·ver·lap
1. A part or portion of a structure that extends or projects over another.
2. The suturing of one layer of tissue above or under another layer to provide additional strength, often used in dental surgery.
v. at all and only 3 of the 10 females are as fast as some of the males.
[FIGURE 7 OMITTED]
[FIGURE 8 OMITTED]
For this class of Grade 10 students, there are seven brown-eyed males. Figure 9 shows their reaction times compared with all other students in the class. Although the data sets overlap, again the mean values for the two groups and the non-overlapping crowns of the hat plots, provide support for Claim 3, that dark-eyed (brown-eyed) males have faster reaction times than the rest of the students in the class. Having seen the results in Figure 8, however, students should be suspicious of this outcome. If males have faster reaction times than females, then putting all of the females in the "other" group will be likely to make the brown-eyed males look even better. What about the brown-eyed males and the "other" males?
[FIGURE 9 OMITTED]
[FIGURE 10 OMITTED]
Figure 10 shows the comparison of brown-eyed and light-eyed males in the Grade 10 class. The spread of reaction times for the light-eyed males is greater. Again the mean for the brown-eyed males is quicker and the crowns of the hats only touch. It would appear from the evidence of this Grade 10 class that there might be something to the claim that dark-eyed males have faster reaction times than "other" males. Students then need to consider the sample size and how confident they can be when there are only seven brown-eyed males in the class.
Collecting a larger sample
The existence of the large data set collected through the ABS CensusAtSchool project allows random samples of up to 200 students to be collected. The data set contains eye colour as well as reaction times (right and left), making it possible to explore Claims 1, 2, and 3, as done for the grade 10 sample. One way to explore these claims is to collect two random samples, of 200 males and of 200 females. These can be selected from grade 11 and 12 students across Australia Australia (ôstrāl`yə), smallest continent, between the Indian and Pacific oceans. With the island state of Tasmania to the south, the continent makes up the Commonwealth of Australia, a federal parliamentary state (2005 est. pop. , as these students would be closest to the ages of the US students in the reports. The random samples report on a large number of variables but only reaction times, gender, and eye colour are of interest in this investigation. As well these large random samples are likely to have outliers or missing data for reaction time, or "other" as an eye colour, different from brown, blue, green, grey, or hazel. The presence of these values needs to be discussed and students made aware of the decision process in eliminating them. The suggestions for deleting large values are likely to be related to a student missing the colour change and waiting several seconds for it to occur or to dropping the mouse. The two samples can be combined in TinkerPlots and with plots created, the outliers and "other" colours "hidden." For the 400 students in the random sample used here, 28 cases were deleted Deleted
A security that is no longer included on a specified market. Sometimes referred to as "delisted".
Reasons for delisting include violating regulations, failing to meet financial specifications set out by the stock exchange and going bankrupt. , leaving 183 females and 189 males.
[FIGURE 11 OMITTED]
Figure 11 shows the comparison of brown-eyed students and "others" (blue, green, grey, and hazel). The distributions have similar spread and the crowns of the hats overlap with the "other" middle 50% range contained within the brown middle 50% range. In this case the mean for the light-eyed students' reaction time (0.328 s) is slightly less than that for the brown-eyed students (0.335 s). Hence there is no support for Claim 1 from this random sample.
Claim 2, that males have faster reaction times than females, however, is supported by this data set, as is seen in Figure 12. The females' distribution shows greater spread in the crown of the hat and a slower mean reaction time (0.352 s compared to 0.309 s) than the males' distribution. (2)
Turning to Claim 3, that dark-eyed males have faster reaction times than other students, the plots shown in Figures 13 and 14 demonstrate the fallacy fallacy, in logic, a term used to characterize an invalid argument. Strictly speaking, it refers only to the transition from a set of premises to a conclusion, and is distinguished from falsity, a value attributed to a single statement. reported in the report in Figure 5. When comparing the dark-eyed males with all other cases (including females) in Figure 13 it can be seen that the distribution for dark-eyed males has less spread and a centre 50% over the left part of the "other" cases' centre 50%. The mean reaction time is seen to be quicker (0.303 s compared to 0.336 s). (3) In Figure 14, however, the means are much closer together (0.303 s compared to 0.312 s) and the crown of the hat for dark-eyed males is inside of the crown for the other-colour-eyed males. (4) If for some reason it were decided to eliminate the five values greater than or equal to 0.5 and the four values less than 0.2, as other potential outliers, the difference would virtually disappear.
[FIGURE 12 OMITTED]
[FIGURE 13 OMITTED]
[FIGURE 14 OMITTED]
The results of repeating the questions that were asked of the grade 10 class of 30 students, with a random sample of 400 (372 with outliers removed) grade 11/12 students, were quite different. With the larger sample there was no support for Claim 2 that brown-eyed people have a faster average reaction time as measured by the ABS website timer or for a similar claim for brown-eyed males. The data did support brown-eyed males having a faster average reaction time than all other students (Claim 3) but this result was confounded by the result showing that the average reaction time for males was faster than for females (Claim 2).
Reporting the investigation
A final report written based on the data used in this article would be quite complex, given the differing evidence provided by the grade 10 class and the large random sample. The data, however, provide a stunning example of what is likely to happen in authentic settings when relatively small sample sizes are involved. Students may initially believe that the claims in the news reports are "rubbish." After collecting data from their own class, however, they may be converted to believing the claims. The need to collect a larger sample should become evident and in this case, the evidence supports scepticism about the original claim. Students may wish to collect further evidence from other classes or other large random samples. In their reports, they should also discuss the necessity to define carefully what is meant by reaction time, as it would appear from the report in Figure 5 that counts rather than time were used to define the variable of interest. The reports should finally point out the statistical illiteracy illiteracy, inability to meet a certain minimum criterion of reading and writing skill. Definition of Illiteracy
The exact nature of the criterion varies, so that illiteracy must be defined in each case before the term can be used in a meaningful of the Medline report, with students demonstrating their detective skills in finding this error.
As a cross-curriculum activity with Physical Education or Health Science subjects, it may be possible to attempt to replicate rep·li·cate
1. To duplicate, copy, reproduce, or repeat.
2. To reproduce or make an exact copy or copies of genetic material, a cell, or an organism.
A repetition of an experiment or a procedure. the experiment carried out in the US. The difficulty of course would be collecting a large random sample using the same variable.
Depending on the level of the class and the objectives of the curriculum, investigations based on this reported study can be quite short or extended even further than suggested here. All aspects of a statistical investigation--data collection, data representation, data reduction, and informal inference--are illustrated here, as well as the importance of considering the influence of variation and chance. Students could even try to contact the researchers for further information on their study. The important conclusion to this type of investigation is the development of critical statistical reasoning that questions unusual or suspicious claims discovered in the media or elsewhere in society. This article provides a model that can be used in other contexts discovered by students or their teachers. Once students have had success in this type of investigation they should become motivated mo·ti·vate
tr.v. mo·ti·vat·ed, mo·ti·vat·ing, mo·ti·vates
To provide with an incentive; move to action; impel.
mo to find more myths to investigate.
This article was written in association with Australian Research Council The Australian Research Council (ARC) is the Australian Government’s main agency for allocating research funding to academics and researchers in Australian universities. Linkage linkage
In mechanical engineering, a system of solid, usually metallic, links (bars) connected to two or more other links by pin joints (hinges), sliding joints, or ball-and-socket joints to form a closed chain or a series of closed chains. Grant No. LP0669106, which is also supported financially and in kind by the Australian Bureau of Statistics The Australian Bureau of Statistics (ABS) is the Australian government agency that collects and publishes statistical information about Australia and its people. Population and Housing
The agency undertakes the Australian Census of Population and Housing. and Key Curriculum Press, publisher of TinkerPlots software. The author gratefully thanks Paul Paul, 1901–64, king of the Hellenes (1947–64), brother and successor of George II. He married (1938) Princess Frederika of Brunswick. During Paul's reign Greece followed a pro-Western policy, and the Cyprus question was temporarily resolved. Tabart for bringing her attention to this media report, suggesting activities for students, and providing the authentic data from his class.
Chick, H. L. & Watson, J. M. (2001). Data representation and interpretation by primary school students working in groups. Mathematics Education Research Journal, 13, 91-111.
Clerkin, B. (2007, August 23). Why blue-eyed boys blue-eyed boy
informal a favourite (and girls) are so brilliant. Daily Mail. Retrieved 29 January January: see month. 2008 from http://www.dailymail.co.uk/pages/live/articles/technology/ technology.html?in_article_id=476244&in_page_id=1965&in_page_id=1965 &expand=true
Konold, C. & Miller, C. D. (2005). TinkerPlots: Dynamic data exploration [computer software]. Emeryville, CA: Key Curriculum Press.
Rowe, P. J. & Evans Ev·ans , Herbert McLean 1882-1971.
American anatomist who isolated four pituitary hormones and discovered vitamin E (1922). , P. (2007). Ball color, eye color, and a reactive reactive /re·ac·tive/ (re-ak´tiv) characterized by reaction; readily responsive to a stimulus.
1. Tending to be responsive or to react to a stimulus.
2. motor skill. PubMed PubMed Public/Publisher MEDLINE (NLM journal articles database) . Retrieved 29 January 2008 from http://www.ncbi.nlm.nih.gov/ pubmed/7808908
Study: Eye color matters. (2007, August 24). Times of India. Retrieved 29 January, 2008 from http://hoosierpundit.blogspot.com/2007/08/ study-eye-color-matters.html
Watson, J. M. (2006). Statistical Literacy at School: Growth and Goals. Mahwah, NJ: Lawrence Lawrence.
1 City (1990 pop. 26,763), Marion co., central Ind., a residential suburb of Indianapolis, on the West Fork of the White River. It has light manufacturing.
2 City (1990 pop. 65,608), seat of Douglas co., NE Kans. Erlbaum.
(1.) Data collected from the ABS website are of interest in comparing reaction times for left-handed left-handed
Using the left hand more skillfully or easily than the right. , right-handed right-handed
Using the right hand more skillfully or easily than the left. , and ambidextrous ambidextrous /am·bi·dex·trous/ (am?bi-dek´strus) able to use either hand with equal dexterity.
Able to use both hands with equal facility. people, for males and females, and for students in different grades from 4 to 12. The presence of eye colour in the data set also allows the extension activity suggested in this article.
(2.) A t-test t-test,
n an inferential statistic used to test for differences between two means (groups) only. This statistic is used for small samples (e.g.,
N < 30). Also called
t-ratio, stu-dent's t. carried out in Fathom fath·om
n. Abbr. fth. or fm.
A unit of length equal to 6 feet (1.83 meters), used principally in the measurement and specification of marine depths.
tr.v. indicated that there was a significant difference in the means of these two sets (t=5.183, p<0.0001).
(3.) A t-test carried out in Fathom indicated that there was a significant difference in the means of these two sets (t=3.744, p=0.00027).
(4.) A t-test carried out in Fathom indicated that there was not a significant difference in the means of these two sets (t=0.8772, p=0.38).
University of Tasmania (body, education) University of Tasmania -
<firstname.lastname@example.org See .edu.
(networking) edu - ("education") The top-level domain for educational establishments in the USA (and some other countries). E.g. "mit.edu". The UK equivalent is "ac.uk". .au>