Weird Statistics in the News
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Personality Affects Your Chances of Being Attacked by a Dog

Personality Affects Your Chances of Being Attacked by a Dog | Weird Statistics in the News | Scoop.it
A new study finds that emotionally stable people are less likely to be attacked by a dog. The question is why.
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Take a deep breath and think happy thoughts before approaching a dog.

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Weird Statistics in the News
Interesting or unusual and useful statistical data analysis articles.
Curated by Bill Bentley
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“Fixed mindsets” might be why we don’t understand statistics

“Fixed mindsets” might be why we don’t understand statistics | Weird Statistics in the News | Scoop.it
Study finds people prefer complicated methods because that's what they're used to.
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I agree with the article but as a statistician myself I can add that all stats software require inputs as percents or decimal fractions and output results that way.   It takes extra effort to translate those into 1 in X terminology  and it's not always nice clean numbers like in this article.  Would 23 out of 4716  be easier to understand than 0.004877?   We would have to round the answer to something simpler like 1 out of 200 and by doing so to simplify it, would change the anwer and possibly the meaning.  Their concept is right but they overly simplify the problem.

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30 Cheesy Math Jokes That'll Make "Sum" of Your Students LOL

30 Cheesy Math Jokes That'll Make "Sum" of Your Students LOL | Weird Statistics in the News | Scoop.it
Looking for a fun opener for your math class? We looked around and gathered 30 of the corniest, cheesiest, funniest math jokes to help you out.
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If you are a fan of numbers, you'll appreciate these 30 clever math jokes.   Not many are statistics jokes.  I guess the p was too low so the stats jokes had to go.

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12 Facts About Belly Buttons | Mental Floss

12 Facts About Belly Buttons | Mental Floss | Weird Statistics in the News | Scoop.it
Test your knowledge with amazing and interesting facts, trivia, quizzes, and brain teaser games on MentalFloss.com.
Bill Bentley's insight:

There are only a few statistics in this articls but the topic is unusual, so marginally qualifies as 'weird'.

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[NEWS] Moratuwa University develops ankle exoskeleton robot – Daily Mirror

[NEWS] Moratuwa University develops ankle exoskeleton robot – Daily Mirror | Weird Statistics in the News | Scoop.it
2018-08-08 00:00:43 Amashi Weerasingha, Kasun Harshana and Kesara Withanage Three students attached to the Bionics Laboratory of Department of Mechanical Engineering, University of Moratuwa have developed an ankle exoskeleton robot.
Bill Bentley's insight:

I'm posting this to apologize to the engineer in the picture.  I thought HE was the robot.  Upon reading further I realized it was an ugly metalic contraption worn on someone's lower legs.

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Looking for a job? Study reveals having a tattoo can get you one

Looking for a job? Study reveals having a tattoo can get you one | Weird Statistics in the News | Scoop.it
Looking for a job? Study reveals having a tattoo can get you one - Turns out, having a tattoo can give job candidates an advantage in competitive labor markets. According to a new study by the faculty at University of Miami Business School and the University of Western Australia, discriminating...
Bill Bentley's insight:

I'd like to see the data behind this claim but it's interesting anyway.  Read the part about electronic sensors being incorporated into tattoos.  A tattoo that measures your bio signals?  Wow.

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Ad space available on people's armpits /

Ad space available on people's armpits / | Weird Statistics in the News | Scoop.it
Ad space available on people's armpits...
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No weird statistics on this yet, just a weird idea.  I'm looking forward to reporting on the statistics later and offering both of my armpits for ads.   $90/hr/pit is pretty good income.  I suppose you have to walk around with your hands up as though you are being arrested. 

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Tutorial: The practical application of complicated statistical methods to fill up the scientific literature with confusing and irrelevant analyses

Tutorial: The practical application of complicated statistical methods to fill up the scientific literature with confusing and irrelevant analyses | Weird Statistics in the News | Scoop.it
James Coyne pointed me with distress or annoyance to this new paper, “Tutorial: The Practical Application of Longitudinal Structural Equation Mediation Models in Clinical Trials,” by K. A. Goldsmith, D.
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Mark Constantine on Twitter: "A classic good news/bad news situation… "

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Sometimes I wonder about my own profession.   I build prediction models too.  I'm inclined to believe the french fry one.

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March Chart Madness

March Chart Madness | Weird Statistics in the News | Scoop.it
Terrible charts seem to be in season. Rarely have I come across so many incredibly bad charts in such a short time: information graphics that don’t actually depict data, distorted representat…
Bill Bentley's insight:

This site has a weird collection of terrible data graphics.   Use it as examples of what not to do when displaying your data.

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Mini Brains Are Now Growing Their Own Veins

Mini Brains Are Now Growing Their Own Veins | Weird Statistics in the News | Scoop.it
The more like real brains they become, the more useful these organoids are for studying complex behaviors and neurological diseases.
Bill Bentley's insight:

It's almost scary that we can now grow simple brains and they are getting more complex all the time.   If we get a brain transplant, will all our memory and knowledge be lost and have to start over like a wiped computer memory?  In that case a person could be a 70 year old infant.  I think I know some of those.  Will we be able to download our brain information into a supercomputer and upload it back into our new brain?   If so, then we could upload the same information into multiple brains creating human thought clones.  Creepy.

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Using the best data possible, we set out to find the middle of nowhere - The

Using the best data possible, we set out to find the middle of nowhere - The | Weird Statistics in the News | Scoop.it
What America’s hardest-to-reach towns teach us about fighting malaria and the power of enormous data sets.
Bill Bentley's insight:

Has anyone ever told you they live in 'the middle of nowhere'?  Where is that exactly?   This great article outlines a statistical analysis of the world to answer that very question.  I'm a big city guy myself so have never been there.

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Why Don't We Always Make Smart Decisions? Blame This Brain Chemical, Science Says

Why Don't We Always Make Smart Decisions? Blame This Brain Chemical, Science Says | Weird Statistics in the News | Scoop.it
Your body makes you feel good when you think you're right. Even when you're not.
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Short and interesting read on how biology can trump data when it comes to making decisions.  I'm sure this is relevant to our current political climate, I just don't have the data to prove it.

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AI-powered CAA roadside assistance will be dispatched before you break down | IT World Canada News

AI-powered CAA roadside assistance will be dispatched before you break down | IT World Canada News | Weird Statistics in the News | Scoop.it
By using new predictive analytics technology its developed in-house, the Canadian Automobile Association (CAA) says it will be able to send out a truck to a...
Bill Bentley's insight:

This sounds like an inappropriate use of AI.   Wouldn't it be better if their breakdown predictor warned them to get their vehicle repaired and not go on the trip rather than predict where they will break down and send an expensive tow truck?

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46 Mouthwatering Facts About Pizza | Mental Floss

46 Mouthwatering Facts About Pizza | Mental Floss | Weird Statistics in the News | Scoop.it
Test your knowledge with amazing and interesting facts, trivia, quizzes, and brain teaser games on MentalFloss.com.
Bill Bentley's insight:

This fun compilation of pizza statistics is sure to have you running out and ordering one for dinner tonight!

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Search of Fuzzy Periods in the Works of Poetry of Different Authors

Search of Fuzzy Periods in the Works of Poetry of Different Authors | Weird Statistics in the News | Scoop.it
Advances in Fuzzy Systems is a peer-reviewed, Open Access journal which aims to provide a forum for original research articles in the theory and applications of fuzzy subsets and systems. The goal of the journal is to help promote the advances in the development and practice of fuzzy system...
Bill Bentley's insight:

Finally some clarity on this.  I read and write poetry but 'fuzzy periods' have bothered me and others for years.  If I every use my stats knowledge to study something like this please slap me.

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On the complementarity of classical test theory and item response models: item difficulty estimates and computerized adaptive testing

On the complementarity of classical test theory and item response models: item difficulty estimates and computerized adaptive testing | Weird Statistics in the News | Scoop.it
1 INTRODUCTION The increasing usability of computers and Web-based assessments requires innovative approaches to the development, delivery, and scoring of tests. Statistical methods play a central role in such frameworks. The item response model (IRM) (LORD; NOVICK, 1968) has been the most common statistical method used. In computer-based adaptive testing (CAT), IRM allows adaptive item selection from an item bank, according to examinee proficiency during test administration. The efficiency of CAT is realized through the targeting of item difficulty to the examinee proficiency (WISE; KINGSBURY, 2000). It implies an item bank or multiple item banks properly developed. A good item bank should cover all aspects of the construct to be measured (content validity) and contain a sufficient number of items to ensure measurement accuracy in the domain, i.e., for all scale values. Items should fulfill requirements set in the American Educational Research Association (AERA), the American Psychological Association (APA), and the National Council on Measurement in Education (NCME) (1999). Stocking (1994) found that doubling the number of item banks reduced test overlap to a much greater extent than doubling the number of items in each bank (apud NYDICK; WEISS, 2009). The development of an item bank for CAT is a complex and multidisciplinary process that follows seven major steps (e.g., BJORNER et al., 2007) represented in Diagram 1, thus, requiring experts from the subject–scientific areas of Construct Framework (steps 1, 2, 5, and 7), Statistics (steps 3, 4, 5, 6, and 7), and Computer Science and Informatics (steps 3, 6, and 7). Once an item bank is available for CAT use, its management requires decisions on several issues such as item bank size and control, security protocols (including item exposure control), statistical modeling, item removal and revision, item addition, maintenance of scale consistency, and use of multiple banks (WISE; KINGSBURY, 2000). Thereafter, CAT administration is basically the repetition of a two-phase process. As Wise and Kingsbury (2000) explain, first, an item with difficulty matched to the examinee’s current proficiency estimate is administered. Second, the examinee’s response to the item is scored, and the proficiency estimate is updated. This sequence is repeated until some stopping criterion is met, usually a predetermined maximum number of items or measurement precision. Thus, despite obvious advantages of adaptive testing, there are still some limitations, such as the high cost related to item bank development. However, the cost could be reduced by decreasing expenses on item writing, pretesting, and calibrating new items (VELDKAMP; MATTEUCCI, 2013), involving steps 2, 3, and 4 of Figure 1. Figure 1  Since Classical Test Theory (CTT) methods are less demanding of sample size, the complementarity between CTT and IRMs jointly with the existence of multiple item banks, offer exceptional research opportunities for reducing such costs. As a previous step, this study examines the empirical relationship between indexes and parameters resulting from both approaches in order to justify and support the use of CTT in item pretesting and pre-calibration, thus reducing the cost of item bank development. Further work remains for demonstration of how any arbitrary scale derived from the pre-calibration step can be transformed into the scale adopted by the assessment system. Throughout the paper, we will address two research questions: (1) What is the level of association between CTT indexes and IRM parameter estimates? (2) Can CTT provide initial item difficulty estimates for posterior IRM use in CAT? The CTT model and the generalized partial credit model (GPCM) are applied to data collected from the Portuguese student population enrolled in the 4th and 6th grades and to those who were administered with mathematics and mother-language tests. The number of students involved is approximately 108,000 in each grade. Estimates of item discrimination and difficulty are obtained and compared. Percentile confidence intervals based on 1000 bootstrap samples are presented for correlation between item difficulty estimates. The study is organized as follows: the next section describes the data and statistical methods used. The results are presented in section three, and conclusions are considered in the last section. 2 METHODOLOGY This section comprises three parts. The first part presents details and characteristics of the data. The second addresses the statistical specification of models in use and explains how to quantify the level of association between estimates obtained from the CTT and the IRM. The third presents a brief description of various steps in the CAT framework. 2.1 Data In Portugal, Primary School Assessment Tests (Provas de Aferição do Ensino Básico) are the responsibility of GAVE (Gabinete de Avaliação Educacional), the office of educational assessment, which aims to evaluate how objectives established for each education cycle are achieved. These instruments are yearly administered to all students enrolled in the fourth and sixth years of schooling, in mathematics, and in the mother-tongue language (Portuguese), according to provisions of law no. 2351/2007, of February 14, II Series. GAVE tests are always administered to the population nationwide and are based on specific competences of the mathematics and Portuguese subjects presented in the document National Curriculum of Primary School: Key competences and the current syllabus. The mathematics test assesses understanding of concepts and procedures, reasoning and communication abilities, and competence for using mathematics in analysis and problem solving. In the academic year 2006–2007, the mathematics test was administered to 108,441 students attending the 4th grade and also to 108,296 students attending the 6th grade. These tests were composed of two identical parts, including 27 items and containing multiple choice, short answer, completion, and open-ended questions, covering the following content: numbers and calculation; geometry and measurement; statistics and probabilities; and algebra and functions. From now onward, these tests are called Math4 and Math6 for the 4th and 6th grades, respectively. Portuguese tests involved 108,447 students in the 4th grade and 108,548 students in the 6th grade. Three competences were assessed: reading comprehension, explicit knowledge of language, and written expression. These tests were composed of two parts. The first part mainly contained short answer items, completion, right or wrong association, and multiple choice questions. The second included extensive composition items in which a text of 20–25 lines is produced. Portuguese tests were composed of 27 and 33 items for the 4th and 6th grades, respectively. From now onward, Portuguese tests of the 4th and 6th grades are called Port4 and Port6, respectively. Before statistical modeling, partial scoring of open-ended answers and extensive composition was performed by experts. The tests’ reliability, as demonstrated by the coefficient of internal consistency, i.e., the coefficient of Kuder–Richardson, is p ≥ 0.85. 2.2 Statistical methods Fundamentals of statistical methods for educational measurement are presented in Statistical Theories of Mental Test Scores by Lord and Novick (1968). According to them, the definition of measurement is “a procedure for the assignment of numbers (scores, measurements) to specified properties of experimental units in such a way as to characterize and preserve specified relationships in the behavioral domain” (p. 17). Two main statistical approaches are used in educational measurement: Classical Test Theory (CTT) and Item Response Models (IRM). Some examples of introductory readings and reviews may be found in Hambleton, Swaminathan, and Rogers (1991), Hambleton (2004) and Klein (2013). The rest of this section presents the model and assumptions underlying classical test theory, explanation and functional specification of the generalized partial credit model, and a brief review of the complementarity of these statistical methods. 2.2.1 Classical test theory It is assumed that variable X represents competencies/skills gained by the student during the learning process. The observable variable X0 is generally obtained by test administration. If tests were instruments with absolute precision, the observed value X0 , regardless of the test used, would be equal to true value X. In a hypothetical situation where the student is tested t times, equation (1) represents the relationship between the true and the observed value, where ε represents the measurement error. Measurement error is assumed to be non-systematic, homoscedastic, and non-correlated with the true value X. Characteristics of items are quantified through the discrimination index (ci) and the difficulty index (pi). The discrimination index measures capacity of the item to distinguish the high performance group of students from the low performance group of students, and its values vary from −1 to 1. The difficulty index (pi) is provided by the proportion of correct answers to the item i (e.g., Guilford; Fruchter, 1978). Therefore, high values indicate easy questions. 2.2.2 Item response models Item response models (IRM) rest on two basic postulates (HAMBLETON; SWAMINATHAN; ROGERS, 1991; HAMBLETON, 2004). According to the first postulate, the examinees’ performance on an item can be explained by their ability; according to the second, the relationship between the probability of a correct answer to the item and the examinee’s ability is described by a function called the item characteristic curve. In this class of models, item response may be dichotomous or polytomous. Additionally, the various IRMs classification depends on the number of latent traits the item represents, giving rise to unidimensional and multidimensional models. The Generalized Partial Credit Model (GPCM) (MURAKI, 1993, 1997; MURAKI; BOCK, 2002) is a unidimensional model for analyzing responses scored in two or more ordered categories. The aim is to extract from an item more information about the examinee’s level than simply whether the examinee correctly answers the item. Items are ranked in which examinees receive partial credit for successfully completing the various levels of performance needed to complete an item. This model relaxes the assumption of items’ uniform discriminating power and includes parameters to represent item difficulty and discrimination. The model is applied to several types of items, such as multiple choice, short answer, completion, and open response items (with the previous items that were gradually scored). Thus, the GPCM suitable for such data is specified by equation (2), where i is the item number (i = 1,.,I; I is the total number of items in the test); Pik (θ) is the probability that an examinee with latent factor θ selecting the kth category from mi possible categories for the polytomous item i; ai is the discrimination parameter for item i, using a logistic metric. In addition, βij = bi - dj, where bi is the difficulty/location parameter of item I, and dj is the parameter of the intercept category, with d1 = 0. According to equation (2), the probability of the student to answer (or to be ranked) in the k category is a conditional probability on the answer to the k-1 category. That is to say, the answer to category k has underlying response criteria satisfaction that is associated with the previous category. Estimates are obtained by maximum likelihood procedure, using the EM algorithm. This model, estimation procedures, and maths data were utilized by Ferrão, Costa, and Oliveira (2015) for linking scales and by Ferrão and Prata (2014) for a simulation CAT study. 2.2.3 Complementarity In the paper “The taxonomy of item response models,” Thissen and Steinberg (1988) propose three distinct classes of models with which models are distinguished by their assumptions and constraints on their parameters. Additionally, Goldstein and Wood (1989) present arguments in favor of the unity of item response models by sitting them within an explicit linear modelling framework. The logistic models […] can be seen merely to be one class out of many possible classes of models. […] In practice, the simple identity models used over the effective response range, typically give near equivalent results (p. 163). The paper published by Hambleton and Jones (1993) describes and compares (similarities and differences of) the methodological approaches mentioned above. Two of these approaches are relevant for this paper’s purpose. They concern the relationship between the IRM item difficulty parameter, the CTT index of difficulty, and the relationship between the IRM discrimination parameter and the CTT bi-serial correlation. Lord (1980) describes a monotonic relationship between the CTT index of item difficulty (pi) and the IRM item difficulty parameter (bi) so that as pi increases, bi decreases when all items discriminate equally. If items have unequal discrimination values, then the relationship between them depends on the item bi-serial correlation. Lord also demonstrates that, under certain conditions, the item bi-serial correlation ri and the IRM item discrimination parameter approximately monotonically increase functions of one another, i.e., where ai is the item i discrimination parameter estimate, and ri is the item i bi-serial correlation. 2.3 Computer-based adaptive testing As aforementioned, in CAT, item response models are applied to establish a relationship between observed responses and ability of the examinee, enabling the item selection adaptively, from an item bank, according to examinee ability during test administration. Thus, the test is tailored to each examinee, and it begins by selecting an initial item. If the examinee answers incorrectly, then an easier item is selected for administration; however, if not, a complex one is administered. Each item is scored, and an estimate of the examinees’ ability is obtained. This process of selection and evaluation is iteratively conducted until a termination criterion is met. Thus, despite being a real-time computing platform, the process implies the existence of a calibrated item bank. Several areas of knowledge are involved in the use of CAT. Figure 2 presents the knowledge areas and their relationships that support the platform. Figure 2  The CAT platform concerns operations from modular structures of Statistical Methods (S), Content (C), and Informatics (I), which provide elements to be integrated throughout the Adaptive Test Developer (ATD). The modular structure S comprises statistical methods for item calibration, scoring, scale fitting, and linking, examinees’ ability modeling, test measurement error, and reliability; structure I contains a computer or Web application with interfaces to examinees via desktop or mobile devices. The server connects the database that contains the item bank (module C) and the statistical methods (module S) using the ATD to adapt tests to examinees; structure C includes the item bank (in general, each item record is defined by question, by type of question and field specification, correct answer, its statistical properties-discrimination, difficulty, information, level of exposure to date, and whether it is an anchor item), and the item bank manager, which is software for operations with items. 3 RESULTS CTT and GPCM were applied to Math4, Port4, Math6, and Port6 data. Tables 1 to 4 contain discrimination and difficulty indexes, bi-serial correlations, and estimates of GCPM discrimination and difficulty parameters. Since intersection parameters are not used for any research questions addressed in this study, their estimates are not presented. The chi-square hypotheses test for goodness of fit suggests this IRM as an adequate model at the 5% level of significance. Table 1  Math4 CTT IRM Item Discrimination Index (c) Difficulty Index (p) Bi-serial Correlation (r) Discrimination Estimate (a) Difficulty Estimate (b) 1 0.650 0.647 0.532 0.785 -0.611 2 0.610 0.630 0.507 0.714 -0.569 3 0.569 0.303 0.458 0.340 0.215 4 0.126 0.913 0.172 0.278 -5.159 5 0.670 0.667 0.594 0.604 -0.670 6 0.414 0.837 0.505 0.981 -1.412 7 0.330 0.817 0.381 0.291 -1.890 8 0.742 0.366 0.551 0.393 0.241 9 0.242 0.874 0.318 0.219 -2.835 10 0.610 0.542 0.461 0.302 -0.210 11 0.412 0.787 0.43 0.633 -1.478 12 0.215 0.917 0.364 0.821 -2.220 13 0.618 0.703 0.545 0.860 -0.817 14 0.107 0.947 0.179 0.283 -4.001 15 0.373 0.800 0.37 0.535 -1.767 16 0.558 0.743 0.544 0.492 -0.951 17 0.747 0.582 0.588 0.421 -0.467 18 0.500 0.757 0.472 0.530 -1.984 19 0.448 0.838 0.506 1.033 -1.385 20 0.674 0.475 0.547 0.502 -0.544 21 0.585 0.670 0.489 0.364 -0.786 22 0.556 0.472 0.409 0.482 0.153 23 0.625 0.674 0.512 0.744 -0.751 24 0.359 0.833 0.41 0.355 -1.847 25 0.340 0.828 0.363 0.588 -1.858 26 0.627 0.428 0.497 0.442 -0.274 27 0.639 0.546 0.475 0.615 -0.219 Font: Authors (2014). Table 2  Port4 CTT IRM Item Discrimination Index (c) Difficulty Index (p) Biserial Correlation (r) Discrimination Estimate (a) Difficulty Estimate (b) 1 0.380 0.744 0.376 0.270 -2.415 2 0.228 0.870 0.305 0.329 -3.569 3 0.490 0.246 0.461 0.324 0.116 4 0.312 0.771 0.334 0.297 -2.507 5 0.335 0.806 0.380 0.343 -3.188 6 0.196 0.162 0.229 0.286 0.640 7 0.438 0.668 0.412 0.299 -1.435 8 0.272 0.897 0.417 0.450 -3.130 9 0.493 0.461 0.424 0.375 -2.328 10 0.565 0.549 0.534 0.239 -1.530 11 0.388 0.266 0.352 0.363 -1.106 12 0.243 0.879 0.393 0.579 -2.343 13 0.486 0.723 0.519 0.535 -1.209 14 0.398 0.350 0.331 0.318 -0.985 15 0.457 0.701 0.461 0.475 -2.603 16 0.360 0.829 0.476 0.313 -2.141 17 0.321 0.881 0.534 0.764 -1.952 18 0.364 0.333 0.357 0.268 -0.739 19 0.419 0.675 0.408 0.303 -1.726 20 0.102 0.955 0.283 0.474 -3.221 21 0.673 0.307 0.650 0.895 -0.427 22 0.433 0.157 0.480 1.286 -0.219 23 0.447 0.169 0.494 2.032 -0.421 24 0.476 0.187 0.500 1.955 -0.549 25 0.438 0.163 0.480 1.554 -0.768 26 0.524 0.228 0.507 1.091 -0.517 27 0.557 0.283 0.480 0.598 -1.055 Font: Authors (2014). Table 3  Math6 CTT IRM Item Discrimination Index (c) Difficulty Index (p) Biserial Correlation (r) Discrimination Estimate (a) Difficulty Estimate (b) 1 0.348 0.841 0.381 0.402 -2.034 2 0.647 0.527 0.579 0.531 -0.476 3 0.280 0.864 0.342 0.544 -2.296 4 0.546 0.683 0.534 0.625 -0.888 5 0.352 0.805 0.379 0.508 -1.872 6 0.738 0.427 0.721 0.347 0.062 7 0.348 0.841 0.412 0.431 -1.664 8 0.381 0.703 0.353 0.197 -1.541 9 0.728 0.350 0.762 0.431 0.221 10 0.122 0.181 0.169 0.219 4.170 11 0.569 0.437 0.496 0.300 -1.102 12 0.126 0.037 0.319 0.536 2.200 13 0.559 0.362 0.519 0.734 0.573 14 0.632 0.406 0.607 0.307 0.206 15 0.699 0.262 0.818 0.612 0.564 16 0.728 0.360 0.788 0.882 -0.138 17 0.544 0.247 0.596 0.364 0.447 18 0.527 0.765 0.552 0.485 -1.248 19 0.530 0.348 0.531 0.749 0.629 20 0.175 0.049 0.402 0.462 2.019 21 0.476 0.260 0.486 0.696 1.110 22 0.593 0.298 0.591 0.440 0.017 23 0.461 0.208 0.501 0.336 0.599 24 0.491 0.490 0.439 0.431 0.056 25 0.627 0.402 0.599 0.370 0.134 26 0.472 0.585 0.406 0.228 -0.654 27 0.530 0.449 0.505 0.290 0.093 Font: Authors (2014). Table 4  Port6 CTT IRM Item Discrimination Index (c) Difficulty Index (p) Biserial Correlation (r) Discrimination Estimate (a) Difficulty Estimate (b) 1 0.484 0.607 0.416 0.404 -0.699 2 0.512 0.618 0.471 0.354 -2.931 3 0.258 0.320 0.231 0.175 2.594 4 0.028 0.991 0.141 0.470 -6.256 5 0.052 0.978 0.166 0.414 -5.447 6 0.249 0.442 0.202 0.207 -3.025 7 0.223 0.892 0.342 0.485 -2.872 8 0.417 0.743 0.407 0.269 -2.272 9 0.161 0.921 0.269 0.487 -3.279 10 0.452 0.439 0.379 0.211 -0.715 11 0.479 0.686 0.439 0.376 -1.328 12 0.451 0.529 0.386 0.159 -1.844 13 0.299 0.668 0.263 0.259 -1.659 14 0.207 0.192 0.207 0.109 3.398 15 0.289 0.825 0.330 0.415 -2.405 16 0.513 0.558 0.470 0.506 -0.312 17 0.118 0.059 0.212 0.423 2.028 18 0.142 0.040 0.348 0.407 1.471 19 0.283 0.111 0.402 0.416 -0.560 20 0.217 0.092 0.327 0.617 0.977 21 0.391 0.207 0.463 0.343 0.988 22 0.475 0.506 0.422 0.419 -2.155 23 0.389 0.667 0.371 0.428 -2.911 24 0.405 0.279 0.380 0.460 -0.605 25 0.508 0.579 0.464 0.410 -1.261 26 0.052 0.978 0.200 0.428 -3.202 27 0.603 0.469 0.517 0.559 -1.223 28 0.509 0.228 0.524 0.813 -0.768 29 0.420 0.175 0.496 1.159 -0.427 30 0.415 0.168 0.493 1.401 -0.610 31 0.391 0.141 0.497 1.295 -0.761 32 0.354 0.128 0.447 1.160 -0.339 33 0.585 0.279 0.567 0.514 -0.603 Font: Authors (2014). Regarding Math4 test, joint analysis of item properties based on CTT and IRM, presented in Table 1, indicates that most items discriminate; items 4, 9, and 14 slightly discriminate; and item 19 is very discriminatory in both approaches. Concerning the difficulty parameter, we verify that approximately 44% of items are easy, whereas items 4 and 14 are very easy. In general, results demonstrate that the tests are mainly composed of discriminative and very discriminative items and, additionally, items of all difficulty levels. A joint analysis of Port4 reveals that, in general, the test items do discriminate, with the exception of item 6, which slightly discriminates, and item 26, which is very discriminative and has a medium difficulty level. Additionally, items 2, 5, 8, 12, 16, 17, and 20 are very easy. Concerning Math6 items, analysis based on CTT and IRM shows that the most discriminative items are 13, 15, 16, 19, and 21; the least discriminative items are 10 and 20. The difficulty index and parameter indicate that the easiest items are items 1, 3, 5, 7, and 18; the most difficult items are 10, 12, and 20. In particular, item 12 is slightly discriminative according to the CTT approach and discriminative according to the GPCM approach. For Port6 items, analysis based on the two approaches reveals that items 3, 4, 5, 7, 9, 13, 14, 15, 17, 18, 19, and 26 discriminate slightly and that there is one set of six very easy items (4, 5, 7, 9, 15, and 26) and a set of three very difficult items (14, 17, and 18). The relationship between the bi-serial correlation (r) and the discrimination parameter estimate (a), given by formula (3), indicates a moderate correlation varying from 0.4 to 0.5. Concerning difficulty, the correlation between p and b is very strong since it ranges from −0.8 to −0.9, i.e., the correlation is −0.83 in Mathematics 4th grade, −0.88 in Portuguese 4th grade, −0.88 in Mathematics 6th grade, and −0.80 in Portuguese 6th grade. Percentile confidence intervals of 95% based on 1000 bootstrap samples are presented in Table 5. The intervals confirm that in the population, the correlation is strong since its absolute value is always greater than 0.71. In this sense, results support this study’s purpose of providing empirical evidence on the complementarity between the two statistical approaches regarding the estimate of item difficulty. Table 5  Subject/Grade Correlation 95% Confidence Interval Lower Upper Mathematics / 4th grade -0.826 -0.927 -0.766 Portuguese / 4th grade -0.883 -0.938 -0.809 Mathematics / 6th grade -0.879 -0.977 -0.799 Portuguese / 6th grade -0.805 -0.885 -0.712 Font: Authors (2014). 4 CONCLUSION The results obtained in this study show a very strong correlation between the CTT index of difficulty and the IRM item difficulty parameter estimate. The correlation is −0.83 in Mathematics 4th grade, −0.88 in Portuguese 4th grade, −0.88 in Mathematics 6th grade, and −0.80 in Portuguese 6th grade. The results also suggest that the level of association does not depend on subject or on grade. A moderate relationship between the IRM estimate of discrimination and the approximation given by the bi-serial function was verified. In addition, it was shown that even when items do not discriminate equally, a monotonic relationship exists between the CTT index of item difficulty and the IRM item difficulty parameter. Therefore, CTT may be utilized as initial estimates for item pretesting and pre-calibration in item bank development, particularly supporting implementation of Web-based adaptive tests. Since the sample size required for item pretesting and calibration is a crucial aspect for development of item banks, these are promising results for the future of computer or Web-based testing. Further work is needed to determine whether changes in pretesting and in algorithms related to adaptive test design and administration affect score precision and reliability.
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I don't expect you to read this statistics article because apparently they ran out of money before they could hire an editor.

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Claim: Global warming to cause more suicides

Claim: Global warming to cause more suicides | Weird Statistics in the News | Scoop.it
From the “P-hacking gets you any claim” and the “that’s why people move to Florida” departments.By Mike Bastasch A July study claims that thousands of more people wil…...
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This article explains statistics that compare global warming and suicides.   It claims positive correlation but says the correlation is NOT significant.  Still it blasts their 'conclusion' into the headlines.  Shame  shame shame!

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Oceanz and Cooperative DOOR Partner to Stop Food Waste with 3D Printed Vegetables

Oceanz and Cooperative DOOR Partner to Stop Food Waste with 3D Printed Vegetables | Weird Statistics in the News | Scoop.it
I recently saw a viral tweet circulating that read, My waiter asked, 'Now, do we want straws OR do we want to save the turtles?' and honestly we all deserve that environmental guilt trip. I don't know if this conversation actually took place or not, but the writer has a point.
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If 3D food printers are ever invented and affordable, I'll buy one.  I'd like to know what is in the cartridges though?  Quinoa?   I certainly won't print octopus.   More likely a chocolated covered Dove bar.  mmmm.

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Statisticians are the most humane mathematicians

Check out this article on LinkedIn....  

How math can become a moral hazard: Unlike other subjects, math offers the comfort of a single correct answer. It’s precisely that quality that concerns University of Exeter math education professor Paul Ernest, who warns that such cold logic may encourage students to discount the ethical dimensions of real-life problems they face. To make math more humane, Ernest suggests that schools teach ethics and philosophy side by side with math so students learn to see that, in the professional world, numbers problems are often human problems too. • Here’s what people are saying. 

Bill Bentley's insight:

I found this LinkedIn article interesting.   It doesn't apply to me or my fellow statisticians or data scientists.   Our answers are almost never the only one.  We present a range of possible answers.  They are all presented with conditions and assumptions which our audiences seldom understand.   I'm sure that makes us the most humane mathematicians!

 

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xkcd: Python Environment

xkcd: Python Environment | Weird Statistics in the News | Scoop.it
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When I need to install a new version of Python I just wipe the hard drive and install a new OS and everything clean.  :)

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Female goat farmers surprised by statistics showing they generally earn more than men - ABC News (Australian Broadcasting Corporation)

Female goat farmers surprised by statistics showing they generally earn more than men - ABC News (Australian Broadcasting Corporation) | Weird Statistics in the News | Scoop.it
Goat farmers are among a list of 80 occupations where women on average earn more than men, according to the latest tax office statistics. But that comes as a surprise to women working in the industry.
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Goats are known to be affectionate despite the common perception that they are always butting heads.  I see many more goats in our future!

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Some Unexpected Statistics To Keep You Smart (25 pics)

Some Unexpected Statistics To Keep You Smart (25 pics) | Weird Statistics in the News | Scoop.it
Some Unexpected Statistics To Keep You Smart (25 pics)
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Some real and often amazing stats about our world.  Regarding animal farts, scientists have equipped cows with fart catchers to determine volume and composition of them while still allowing them to do their business.   Some engineer was assigned that project.   Engineering isn't always glamorous.  I've done projects like that!

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Companies Are Betting on Lab-Grown Meat, but None Know How to Get You to Eat It

Companies Are Betting on Lab-Grown Meat, but None Know How to Get You to Eat It | Weird Statistics in the News | Scoop.it
A new company, IndieBio, wants to feed lab-grown meat to your pets before getting humans to eat the stuff.
Bill Bentley's insight:

If they want us to like this stuff they need to make it smell like bacon. I do not start salivating when I see my dog eating from his bowl, no matter what is in it.

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