Masaryk University Brno, Department of Anthropology, Faculty of Science Kotlářská 2, Brno, Czech Republic

Size: px
Start display at page:

Download "Masaryk University Brno, Department of Anthropology, Faculty of Science Kotlářská 2, 611 37 Brno, Czech Republic"

Transcription

1 Variability and Evolution, 2003, Vol. 11: 5 30 ANALYSIS MIROSLAV KRÁLÍK, VLADIMÍR NOVOTNÝ Masaryk University Brno, Department of Anthropology, Faculty of Science Kotlářská 2, Brno, Czech Republic EPIDERMAL RIDGE BREADTH: AN INDICATOR OF AGE AND SEX IN PALEODERMATOGLYPHICS KRÁLÍK M., NOVOTNÝ V Epidermal ridge breadth: an indicator of age and sex in paleodermatoglyphics. Variability and Evolution, Vol. 11: 5 30, Tabs. 5, Figs. 9. Adam Mickiewicz University, Faculty of Biology, Institute of Anthropology, Poznań. Abstract: Epidermal ridge breadth of human fingerprints was investigated on ceramic artifacts from contemporary ceramic workshops. Our investigation has shown that mean epidermal ridge breadth (MRB) as observed on ceramics can be used as an indicator of age (from birth to maturity) and sex of the artifact maker in adulthood. In this study, we suggest a new method of scanning, measuring and data processing. The best age estimation method (using equation proposed by Kamp et al. from Grinnell College, USA, and modified after shrinkage by 7.5%) yielded results with mean error of estimates 0.18 years (SD = 2.36 years), median absolute error of estimates was 1.71 years and only in 3.6% of cases the absolute errors were higher than 5 years. Therefore, in a particular ethnic group epidermal ridge breadth of fingerprints on ceramics is suitable for comparing of individuals ages. The number of fingerprints and ridges per individual had no influence on estimation errors. In adults, sexual dimorphism was clearly present even though artifacts were made from different types of ceramic clays. Ridge breadth is 9% greater in males than in females. On the whole, MRB under 0.39 mm signifies a sub-adult individual under 15 years of age and MRB values over 0.52 mm come solely from adult males. However, age changes of ridge breadth in teenagers overlap with adult sexual dimorphism and therefore, in case of MRB values between 0.39 and 0.52 mm, variability in both age and sex should be taken into account. If this method is further developed, especially the qualitative aspects of fingerprints and properties of ceramic clay, it has great potential for illuminating the social background of ceramics-making in ancient cultures. Key words: fingerprints, ceramics, epidermal ridge breadth, age estimation, sexual dimorphism, paleodermatoglyphics

2 6 M. Králík, V. Novotný Introduction: Paleodermatoglyphics Archeologists frequently find artifacts imprinted with human fingerprints. Ancient fingerprints have been found on ceramics (e.g. Šikulová 1956; Pavelčík 1958; Klíma 1963; Šefčáková 1998; Einwögerer 2000), parchment (Bartsocas 1982), organic substance (Mania, Toepfer 1973; Koller et al. 2001) and other types of materials. Despite the diversity of archeological materials, it is ceramic clay, which has the optimal properties to be a transfer medium for fingerprints. Clay is sufficiently plastic for imprinting, and finger molding is a direct part of many manufacturing procedures. Fingerprints are mostly unintentional results of shaping, molding and touching wet clay. Once dried and fired, the clay hardens and becomes chemically stable which allows the prints to be preserved indefinitely; fingerprints on ceramics can even be preserved in shipwrecks buried in seawater (Corey 2002). At the same time, ceramic material is fragile, so the objects often break and need to be renewed. From the Neolithic to recent times, ceramics, especially various pots, form a significant part of the archeological record. Epidermal ridges and their arrangement (dermatoglyphic patterns) exhibit a number of properties that reflect the biology of an individual. Dermatoglyphic features statistically differ between the sexes, ethnic groups and age categories. Dermatoglyphs and their components are both environmentally and genetically determined, although the arrangement of ridges remains constant throughout life. Theoretically, it is possible to use human fingerprints on archeological finds similarly to skeletal remains: for estimation of interconnected biological properties of the people who left the prints. However, opposed to the obvious dermatoglyphic cards (ink-method), fingerprints on ceramics are fragmentary; they reflect heterogeneous regions of hand (friction skin, papillary terrain) and are likely to reflect more than one individual on one artifact. Studying such prints is more limited by the fragmentation and incompleteness of natural biological units (hand, thenar, finger-ball), than skeletal remains in skeletal anthropology. In reality, it is not possible to recognize particular area of the hand from the small print of epidermal ridges, so the methods of the standard dermatoglyphics are often inapplicable. Although dermatoglyphics has been experiencing a boom for decades (bibliographies e.g. Mavalwala 1977; Figueiras 1993) and dactyloscopy (police fingerprinting) is still the most widely used method of police identification of individuals, the study of fingerprints on archeological artifacts has not developed into a coherent approach with goals and methods. Ancient prints still continue to be dismissed as trivial curiosities even though the modern analysis of fingerprints first began after the discovery of fingerprints on Japanese prehistoric ceramics at the end of nineteenth century (Faulds 1880). Despite this situation, several innovative works have appeared during the second half of the twentieth century, frequently mutually unknown to the authors. Cummins (1941) divided prints on ceramics into intentional prints, which signify a meaning or

3 Epidermal ridge breadth: an indicator of age and sex in paleodermatoglyphics 7 signature, and unintentional prints, which are accidental results of molding. Others tried to identify fingerprints precisely and proceeded in dermatoglyphic analysis as far as possible. Their approaches focused on minutiae and the remaining dermatoglyphic patterns, while aiming to compare the character of ancient fingerprints with fingerprints of recent populations (Valšík 1951; Vlček 1951, 1952; Cseplák 1982; Szilvássy 1983). Sládek (1994) also reconstructed the shaping sequence of small figurines based on the position of fingerprints on their bodies. Åström and Eriksson (1980) used frequencies of dermatoglyphic patterns on ancient ceramics as an indicator of the ceramists ethnicity. Finally, some works focused on epidermal ridge breadth and its biological connections with sex and age (Basilidade, Rişcuţia 1974; Lička, Musil 1975; Primas 1975; Cseplák 1982; Kamp et al. 1999; Králík 2000; Králík, Novotný, Oliva 2002). During the International Conference on Dermatoglyphics, Athens, Greece, September 20 30, 1981, Bartsocas suggested the term paleodermatoglyphics to be used for the study of dermatoglyphics through antiquity in archeological and anthropological material (mummies), as well as in the ancient texts (Bartsocas 1982). For the Czech version of the paleodermatoglyphic history see Králík and Novotný (2003a, b). The English version is being prepared for printing. In contrast to other materials, the originator of a fingerprint on a ceramic item was necessarily in direct contact with the artifact at the time of its origin; he/she directly participated in its creation. A fingerprint on a potsherd is an example of direct association between culture and biology of an imprinted person. That is why we have been focusing mainly on fingerprints on ceramics. We have studied dermatoglyphic features that could be preserved in obvious fragmentary fingerprints on ceramics. Among them, ridge breadth has been chosen as a convenient variable observable on the majority of fingerprints. The present paper should be taken as a contribution to improvement of paleodermatoglyphic methods based on epidermal ridge breadth. Epidermal ridge breadth: definition and determination After Memorandum on Dermatoglyphic Nomenclature (Penrose 1968, p. 1): the true breadth of a ridge is defined as the distance between the center of one epidermal furrow and the center of the next furrow along a line at right angles to the direction of the furrows. The definition refers to classical black-ink fingerprints on white paper. Black lines of a fingerprint are called epidermal ridges like the original structures of the skin. With Penrose and others, we have to distinguish ridge breadth and printed ridge (line) width since the black line is a mere negative of the ridge top (Fig. 1). Unfortunately some authors used both terms breadth and width in the sense of Penrose s breadth. Since it is not possible to measure true ridge breadth from ink fingerprints (Penrose 1968), indirect methods (first used by Schlaginhaufen 1905) are used for determination of ridge breadth: the number of ridges crossing a defined line transversely is counted and the ridge breadth is a result of dividing the two figures. The line can be

4 8 M. Králík, V. Novotný Fig. 1. Epidermal ridge breadth of the epidermis (upper row), in ink fingerprint (middle row) and in plastic fingerprint on ceramics (bottom row). The left images are cross-sections and the right images are looking from above of a defined length and is placed upright on the stream of ridges, or in a defined position located between standard dermatoglyphic landmarks. Some authors used the line of a defined length and placed it transversely to the ridges on all dermatoglyphic regions (Cummins et al. 1941; Ohler, Cummins 1942), or in a single region. A bulk of works on dermatoglyphics determined ridge breadth as an additional variable to the well established a b ridge count (in the second interdigital area of the hand) (after Penrose, Loesch 1967). Only the measure of distance between a and b triradius had to be completed. Ridge breadth is obtained by calculating (DL+DR)/(CL+CR+2), where D is distance and C is the ridge count. Two ridges are added because triradial points are omitted in the ridge count. But the line joining a and b triradius may not be perpendicular to dermal ridges, especially when it is close to the triradius. Therefore the technique (a b ridge breadth) does not fully conform to Penrose s definition; in a sense it measures the ridge density but not the ridge breadth in a defined region. Another technique makes use of an equilateral triangle, whose apex lies in the center of a dermatoglyphic pattern and the two sides of 10-mm lengths are perpendicular to the stream of ridges of a distal parallel system (Loesch, Martin 1984a, b). Finally, Acree (1999) counted all ridges in a defined area of 25 mm 2 and Moore (1989) measured ridge to ridge distance from the center of one ridge to the center of the neighboring ridge.

5 Epidermal ridge breadth: an indicator of age and sex in paleodermatoglyphics 9 Some authors expressed their results in mean ridge breadth (in mm or μm) and others (predominantly in archeology and police fingerprinting) express their results in density of ridges (for instance 21 ridges per 1 cm). Epidermal ridge breadth: variability Since various authors employed different methods of measurement, the results are not completely comparable between the different studies. However, it is apparent from the results that many tendencies appear universally even when using the different methods, e.g. sexual dimorphism (Tab. 1). The first author who presented extensive reports on adult human epidermal ridge breadth on whole palm and fingers was Cummins and his co-workers (Cummins et al. 1941; Ohler, Cummins 1942). From their results it is evident that the epidermal ridge breadth varies considerably between different dermatoglyphic regions and also between the sexes. Ridges on the palm were coarser than on the fingertips. Digit I had a higher ridge breadth than all the other digits, the order of the decreasing ridge breadth was: I > II > III > V > IV and in the palm: thenar first inter-digital region > hypothenar > inter-digital II > inter-digital IV > inter-digital III. The ridges on the right hand are coarser. Hecht was the first author who reported on ridge breadth growth (Hecht 1924, cit. by Cummins et al. 1941). The average ridge breadth of single ridges in fingertip patterns was as follows: 0.15 mm (three premature infants); 0.18 mm (7 newborn infants); mm (10-year olds); mm (adult women); 0.50 mm (adult men); the numbers of participating subjects were not given in the latter three categories. Loesch and co-workers made the first equation of epidermal ridge breadth growth in the second interdigital area (a b ridge breadth) on a sample of Polish children from 0 to 12 years of age (Loesch, Godlewska 1971; Loesch, Czyżewska 1972). David (1981) studied a b ridge breadth and stated that at the age of more than 16 years the increase in ridge breadth was small. The difference between years olds and adults over 20 years old was not significant in either sex. In general, males have coarser ridges than females and the difference is approximately 10%. Ohler and Cummins (1942) were the first authors who exhaustively investigated sexual dimorphism in the epidermal ridge breadth. Sexual differences in a b ridge breadth are significant from the category of years of age (Loesch, Czyżewska 1972). The a b ridge breadth increases with the number of sex chromosomes (Penrose, Loesch 1967). The Y-chromosome affects the ridge breadth more than the X-chromosome. The a b ridge breadth in people with testicular feminization syndrome lies between the sexes although it tends to be closer to the values for females (compared to the males) (Polani, Polani 1979). Jantz, Parham (1978) studied the ethnic differences in the a b ridge breadth among Yoruba students (Nigeria), English (data from Penrose, Loesch 1967) and Jews (data

6 10 M. Králík, V. Novotný Table 1 Variability of epidermal ridge breadth with emphasis on sexual dimorphism. All results are converted to micrometers. Differences between the sexes in each sample are presented also as percentages with reference to males Authors Comment Sample n Mean (SD) [µm] Diff. [%] Males Females Hecht 1924 Fingers 500 Hecht 1924 Fingers Cummins et al All regions combined 4/5 Euro Americans, 1/5 Jews (29) Ohler, Cummins 1942 All regions combined 90% Euro Americans, 10% Jews (27) Cummins et al Ball of II-nd finger 4/5 Euro Americans, 1/5 Jews (42) Ohler, Cummins 1942 Ball of II-nd finger 90% Euro Americans, 10% Jews (34) Loesch, Martin 1984b Triangle, finger IV Australians of European origin (38) Loesch, Martin 1984b Triangle, finger IV Polish, adults (37) 9 2 Loesch, Martin 1984b Triangle, finger IV Polish, adults (38) Loesch, Martin 1984b Triangle, finger III Australians of European origin (47) Loesch, Martin 1984b Triangle, finger III Polish, adults (43) 32 7 Loesch, Martin 1984b Triangle, finger III Polish, adults (36) Cummins et al II-nd interdigital area 4/5 Euro Americans, 1/5 Jews (50) Ohler, Cummins 1942 II-nd interdigital area 90% Euro Americans, 10% Jews (39) Penrose, Loesch 1967 A b ridge breadth English, over 20 years (41) 51 9 Penrose, Loesch 1967 A b ridge breadth English, over 20 years (39) Losch, Czyżewska 1972 A b ridge breadth Polish, from 12 to 13 years (41) 21 4 Losch, Czyżewska 1972 A b ridge breadth Polish, from 12 to 13 years (30) Losch, Czyżewska 1972 A b ridge breadth Polish, from 13 to 14 years (56) Losch, Czyżewska 1972 A b ridge breadth Polish, from 13 to 14 years (50) Katznelson, Ashbel 1973 A b ridge breadth Jews (45) 51 9 Katznelson, Ashbel 1973 A b ridge breadth Jews (74) Jantz, Parham 1978 A b ridge breadth Yoruba (55) 49 8 Jantz, Parham 1978 A b ridge breadth Yoruba (41) Polani, Polani 1979 A b ridge breadth (43) 38 7 Polani, Polani 1979 A b ridge breadth (44) David 1981 A b ridge breadth 20 years and more (48) 49 9 David 1981 A b ridge breadth 20 years and more (43) David 1981 A b ridge breadth From 16 to 19 years (49) 47 9 David 1981 A b ridge breadth From 16 to 19 years (38) Stücker et al Original method, fingers Dactyloscopic database (89) 44 9 Stücker et al Original method, fingers Dactyloscopic database (49) Moore 1989 Original method, fingers Dactyloscopic database Moore 1989 Original method, fingers Dactyloscopic database Primas 1975 Fingerprints on ceramics (41) Primas 1975 Fingerprints on ceramics (34) present data Fingerprints on ceramics Czech, adults (36) 44 9 present data Fingerprints on ceramics Czech, adults (31) from Katznelson, Ashbel 1973). Ethnic differences were substantial in both sexes. Loesch and Martin (1984b) also discovered that the ridge breadth on fingers III and IV in Polish and Australian males of European origin were different, i.e µm and µm (for finger III), µm and µm (for finger IV), respectively. The ridge breadth covaries with other dermatoglyphic features. In fingers the ridges are coarser in the ulnar loops than in whorls (Cummins et al. 1941). There is

7 Epidermal ridge breadth: an indicator of age and sex in paleodermatoglyphics 11 a negative correlation between the breadth of ridges and the number of minutiae of the end type on fingers IV and III indicating that narrow ridges are more likely to be interrupted by ends (Loesch, Martin 1984b). However, a b ridge breadth and ridge count of the first finger are entirely independent traits (Loesch, Lafranchi 1990). The epidermal ridges, between which interstitial ridges are present, are significantly further apart from each other than those without interstitial ridges (Stücker et al. 2001). The epidermal ridge breadth also correlates with some anthropometrical parameters. Ridge breadth correlates with hand length, hand breadth and breadth of the distal phalanx (Cummins et al. 1941). However, the authors discovered that the coefficient of variation of the epidermal ridge breadth was much higher than the coefficient of variation of hand length. Therefore, ridge breadth is subject to a wider variation than hand size so there must be another factor than size of hand, that influences ridge breadth. Loesch and Lafranchi (1990) showed that the a b ridge breadth is closely related to wrist width. In adults the coefficient of correlation between ridge density and body height was 0.16 (Cummins et al. 1941) and because it is consistent in all dermatoglyphic regions when considered separately, the authors regard the relation as true. The a b ridge breadth correlates positively with chest circumference but only slightly positively with the body mass index (BMI) and negatively with the length of the lower limbs % of the variability in body measurements is accounted for by the variability in breadth of individual s ridges (Loesch, Lafranchi 1990). On the whole, the variability of the epidermal ridge breadth in humans is substantial. The greatest changes in the ridge breadth occur between birth and maturity. Sexual dimorphism in epidermal ridge breadth was also verified by many samples. Nevertheless it must be noted that differences between single ridges in a limited area of the epidermis may be higher than the variability between individuals and groups described by mean values, regardless of the mean breadth determination method. Ridge breadth values from prints on ceramics are closest to the values for finger balls of distal phalanges, and this is the case for both the mean values and the variability patterns (Tab. 1). Ridge breadth of fingerprints on ceramics The appearance of an epidermal ridge imprinted on ceramics is caused by the contrast between light and shadows on a three-dimensional negative. The distance between the edges of one shadow and the same point on the edge of the next shadow vertical to the edges, corresponds to ridge breadth (as defined by Penrose). Therefore the ridge breadth can be measured directly (Fig. 1). Clay, however, is not completely homogenous the dimensions of the mineral grains are often comparable to the ridge dimensions. So, the mineral grains can distort details of the ridges and its borders. Therefore it is better to measure a bundle of ridges. On the other hand, a fingerprint on

8 12 M. Králík, V. Novotný a ceramic piece is three-dimensional, frequently more or less concave. Hence the linear measure is more a tangent of the curve, rather than the true length of the curve. Moreover, recording haphazard fingerprints on ceramics is not standardized. Since the epidermal ridge breadth varies considerably between various dermatoglyphic regions of one individual, and even between sections of a particular dermatoglyphic region, an uncontrolled set of tiny fingerprints is a rather questionable representation. Besides, the epidermis is elastic so during imprinting it is temporarily deformed due to the forces and their directions. The prints reflect the deformation event. This is caused by factors such as softness of the epidermis and clay hardness. Fingerprints just formed on the wet clay can be deformed by subsequent molding. Substantial changes of the ridge breadth might occur as a result of the deformation. The ridge breadth can increase or decrease especially in artifacts made by free hand or when there is excessive amount of water in the clay. Therefore it is important to exclude at least visibly deformed fingerprints from metrics. Unfortunately, it is not so easy to distinguish deformed and non-deformed fingerprints. Finally, the clay body changes during drying and burning the absolute size of the artifact as well as the impressions on its surface change. Linear shrinkage of ceramics varies between 0 and 20% (on average 7 10%) (Lach 1989), which is similar to, for example, sexual dimorphism (see Tab. 1). However, at the present time a precise estimation of the shrinkage of the finished ceramic matter is not possible. To sum up, the biological variability of the ridge breadth as imprinted on ceramics is confounded by many factors: shrinkage, pressure deformation, unknown application of fingers and palms in molding. It is not certain if any reasonable metric estimation is possible and if unknown factors do not destroy the useful biological trends. Ridge breadth in retrospective estimations In spite of these well-founded doubts, several works used epidermal ridge breadth in paleodermatoglyphics. Primas (1975) evaluated fingerprints on pottery from Heuneburg (Germany) and she attempted to estimate sex of the creators based on the epidermal ridge breadth. The material was from Iron Age, when, in many parts of Europe, we can detect a transition from handmade domestic pottery, to pottery as a specialized craft where the items were manufactured on the pottery wheel. In one collection of fingerprints on pots with a stepped edge, Primas discovered that these fingerprints had an average of 19.1 ridges per 1 cm. Based on reference values (according to the works of Cummins et al and Ohler, Cummins 1942), and her own experimental measurements of recent populations (females: 23.2 ridges per 1 cm, males: 20.8 ridges per 1 cm), she attributed these prints to males. She concluded that the Golasecca culture (9 th century B.C. to the 4 th century B.C.) can be noted for the manufacture of advanced pottery by male craftsmen with all the social consequences and influences it had on the neighboring cultures.

9 Epidermal ridge breadth: an indicator of age and sex in paleodermatoglyphics 13 We can also mention the work of Basilidade and Rişcuţia (1974) who studied ridge breadth of fingerprints on Romanian Neolithic ceramics. They attributed these prints to males based on the mean ridge breadth of 0.55 mm. Lička and Musil (1975) provided interesting information about the application of fingerprints, especially the ridge breadth in archeology and criminalistics. Acree (1999) introduced a method of sex assessment from fingerprints to criminalistics, also based on epidermal ridge breadth. Cseplák (1982) published a report on finger and nail prints on fragments of Neolithic pots years old from Hungary. The epidermal ridge breadth varied between 270 and 600 μm. Kamp et al. (1999) published seminal research of exemplary quality that represents a new direction for future research in paleodermatoglyphics. This work involves a critical theoretical approach based on extensive dermatoglyphic literature, suggested method, experimental testing of methodology and the development of a model, application of the model to specific data and the interpretation of results, taking into account all the relevant information. The authors obtained fingerprints by experiment and measured the ridge breadth directly on the ceramics with digital calipers. They developed a linear regression model of the growth of the epidermal ridge breadth during postnatal growth and maturation (from 5.4 to approx. 21 years of age). The model was then applied to two artifact assemblages of Amerindian utilitarian and funerary ceramics from northern Arizona. On the basis of the discovered differences the authors demonstrated that one pottery type the zoomorphic figurines were manufactured by children, and the second type craftsman-quality pots were manufactured by adults. They also developed a model for the relationship between ridge breadth and body height during postnatal growth. This is the best work in paleodermatoglyphics so far and it represents great progress in this field. In his Master s thesis, Králík (2000) reviewed the current state of paleodermatoglyphics and experimentally attempted to find the best method for estimating age from birth to adulthood based on the epidermal ridge breadth. The ridge breadth was computer-measured from photographs. On a small sample of 140 prints on ceramic artifacts from 13 individuals, the author tried to deal with the main unknown factors affecting ridge breadth data and estimation. In 6 steps he generated several theoretical variants of shrinkage, selection of fingerprints, measurement method, mean value counting and regression equations. By combination of all variants, 432 different protocols for age estimations were obtained. Differences between the age estimates and the true ages from each protocol were subjected to statistical analysis. The equation that originated from fingerprints on ceramics (Kamp et al. 1999) provided the best estimations. The best estimations were achieved when the ridge breadth was multiplied by a coefficient of (according to common shrinkage of ceramic clay 7.5%). The mean absolute difference between true age and estimates was 2.03 years and only in 3.3% estimations it was more than 5 years (Abstract Králík 2003). Králík, Novotný and Oliva (2002) rediscovered a forgotten fingerprint on the Venus figurine from Dolní Věstonice (Gravettian, 25,000 B.P.) found in Moravia,

10 14 M. Králík, V. Novotný Czechoslovakia, in According to the ridge breadth (0.37 mm), the fingerprint maker may have been a sub-adult individual or an adult female but probably not an adult male. However, this one and only fingerprint available is very small in size and therefore within the limit of observability. It might represent a point at the extreme end of the range of variability. It is also possible that the wet clay was deformed with the fingerprint. Moreover, the maker of the fingerprint may not be the creator of the artifact. Research is currently continuing on fingerprints on Central European Gravettian ceramics from sites at Dolní Věstonice, Pavlov (Czech Republic) and Krems (Austria). The results are expected to contribute to clarifying the origin and function of these ceramics, the oldest ceramics in the world. In this article we would like to test several equations for the estimations of age from the ridge breadth on a larger sample of ceramics than was used by Králík (2000), and attempt to evaluate the effect of age changes and sexual dimorphism on ridge breadth. The natural character of fingerprints, unaffected by our presence, and the large variability of ceramic factors, are emphasized at the expense of totally controlled conditions and the statistical design of the sample. Material The material consists of recent artifacts (Fig. 2) made by three different groups (setting) of individuals of known age and sex. One group represents works of 56 children from the Tišnov Primary School of Art (Moravia, Czech Republic). All artifacts were created before our first contact with the school. The authors applied several techniques during the creation process: shaping by free hand, lathing on potter s wheel, cutting out of kneaded plates, building from kneaded plates. Thus, with respect to hand and finger mechanics, the fingerprints were the results of various printing conditions. Artifacts were created from several types of clay. In the majority of artifacts, the type of clay and its shrinkage was ascertained. Since artifacts were made during normal teaching lessons with the children together in one classroom (workshop), an artifact made by a particular child may also bear the fingerprints of his/her classmates. The second group consists of works of 20 adult professional ceramists, 6 males and 14 females, from 20 to 61 years of age. The artifacts were obtained at retail outlets and were made (formed, dried and burnt) under real-life conditions of present day ceramics production/creation. Thus, the artifacts were manufactured before our first contact with the author or a particular ceramic studio so aspects of shrinkage could not be ascertained. Various clays were used. The fingerprints from this group were used to test sexual dimorphism. By our special request, non-professionals unskilled in ceramic making produced the third group of artifacts (small figurines and pots) from ceramic clay (provided by us), while we were present. Adults from this group (17 males and 13 females from 19 to 77 years of age) were added to the adult professionals to test sexual dimorphism. In

11 Epidermal ridge breadth: an indicator of age and sex in paleodermatoglyphics 15 Fig. 2. Examples of ceramic artifacts used for fingerprint analysis (children from Tišnov Primary School of Art row 1 and 2; professional ceramists row 3 and 4) this group, the sub-adults (15 persons) were added to illustrate the overall variability of ridge breadth in relation to age and sex. All artifacts were evaluated after ceramic shrinkage and burning. The fingerprints of the three groups were automatic and unintentional results of the molding. All authors were of Czech origin and lived in western Moravia, near the town Tišnov. Age of each subject at the time of molding was retrospectively ascertained in months and recounted to years (i.e years). In some adult professionals the age was rounded off to whole years. Artifacts surfaces were complex. Fingerprints were fragmentary; frequently no dermatoglyphic pattern was distinguishable. Preservation of ridges substantially varied from one part of the fingerprint to another. Sometimes, two parts of one fingerprint

12 16 M. Králík, V. Novotný seemed to indicate two separate fingerprints. In other cases, several (two or more) fingerprints were superimposed on each other. (We called this situation cross fingerprints.) In order to deal with this complex situation it was essential to define the fingerprint as a unit of analysis. Our definition of a fingerprint is the part of ceramic surface with friction skin negative that was naturally separated from the others of its kind, or one that was artificially separated for the purpose of photography. In spite of the above-mentioned complexities, the majority of the single fingerprints represented one single imprinting event. The size of the fingerprints varied, from approximately several square millimeters to several square centimeters. Method Only well-preserved fingerprints were recorded. Blurred, deformed and unclear fingerprints were discarded. A total of 568 fingerprints were included in the study. For scanning the fingerprints (Fig. 3) we used macro-photography camera Nikon Coolpix 4500, 4 Mpix. Artifacts were fixed by dipping in coarse sand or mustard seeds in an appropriate container and photographed. Light was provided by a halogen lamp. Calibration of the images was provided with a square of calibrated paper (3 3 mm) placed near each fingerprint parallel to its surface plane. To minimize lens distortion near the margins of the field of vision, fingerprints and calibration were situated in the center of the image. The axis of the camera was perpendicular to the fingerprint surface. Photos were then processed on a personal computer via image analysis software UTHSCSA ImageTool for Windows Version We measured the width of a bundle of ridges on the longest possible section perpendicular to the stream of ridges and counted the number of involved ridges. The mean value of ridge breadth from each measurement was a result of dividing the Fig. 3. Schematic representation of the recording of fingerprints

13 Epidermal ridge breadth: an indicator of age and sex in paleodermatoglyphics 17 Fig. 4. Depiction of epidermal ridge breadth and its measurement on a ceramic piece two figures. The mean ridge breadth was calculated from several measurements on each fingerprint (Fig. 4). The mean value for each artifact the mean epidermal ridge breadth of an individual (MRB) was calculated from the values of all fingerprints on a particular artifact. In the case of more artifacts being made by one individual, the individual value was obtained from all fingerprints of the particular individual. During these measurements the author s identity was unknown. For estimations of the age from MRB we used the following equations (Fig. 5): LC equation after Loesch and Czyżewska (1972): y = x (y MRB in μm, x age in years). LCmod equation after Loesch and Czyżewska (1972) modified by recounting according to the mean ridge breadth ratio between hand and fingers in males (according data from Ohler, Cummins 1942) combined with shrinkage (7.5%), the ridge breadth in equation was multiplied by x = (y ) / (y MRB in μm, x age in years). KA equation after Kamp et al. (1999): y = 614 x 112 (y age in months, x MRB in mm). KAmod equation after Kamp et al. (1999) modified according to shrinkage rate of 7.5% (this estimation provided the best results on a pilot sample, Králík (2000)), the ridge breadth was multiplied by y = x 112 (y age in months, x MRB in mm). PM1 simple linear regression equation obtained directly from our present data; MRB was the independent variable. PM2 simple linear regression equation obtained directly from our present data; MRB was the dependent variable. One assumption of the least squares model is that the independent variable is measured without error. This is more likely to be the case for age than epidermal ridge breadth. The second reason for introducing PM2 was

14 18 M. Králík, V. Novotný Fig. 5. The relationship between age and mean epidermal ridge breadth including the linear regression models used for estimation comparison with equation LC, where the age was also the independent variable. KAts equation after Kamp et al. (1999) modified according to true shrinkage of each ceramic matter, which were empirically ascertained y = 614 ts x 112 (y age in months, x MRB in mm, ts true shrinkage). True shrinkage varied between 7% and 12%, so ts is different in each case. For each equation we calculated the differences between the true and estimated age errors of estimates, which were subjected to statistical analysis. Since sex assessment from fingerprints is not possible at present in the study of age differences, we include boys and girls in the same group. Absolute errors (positive values of errors) of PM1 were used to study the relation between the number of measured units (fingerprints, ridges) per individual, and the accuracy of estimation. In adults, we compared the differences in MRB between sexes and between professionals and non-professionals. Statistical operations were performed in the STATISTICA version 6, StatSoft, Inc. (2001) and Rundom Projects Version 1.1 (Jadwiszczak 2003). Results Age estimations In a sample of 56 individuals aged between 5.92 and years there was an underrepresentation in younger categories and also a disproportion in sexes (13 boys and 43 girls). Since this sample includes all children attending the ceramic workshop it was a natural sample of young ceramic makers and the disproportion of sexes is likely to reflect gender preferences for ceramic making.

15 Epidermal ridge breadth: an indicator of age and sex in paleodermatoglyphics 19 Although our data did not fulfill all the assumptions for the parametric least squares model (unequal number of subjects in individual age categories), we built linear regression equations (sexes combined): PM1: y = x (y age in years, x MRB in mm). (r = 0.681; r 2 = 0.464; F(1;54) = ; p = 0.0; Std. Err. of Estimate = 2.381) PM2: y = x (y MRB in mm, x age in years) (Std. Err. of Estimate = 0.031) Descriptive statistics of errors for all equations are given in Tab. 2 and Fig. 5. Given the nature of the models there is no difference in means between PM1 and PM2 (Tab. 3, Fig. 6). However, the variability of estimates is significantly greater in PM2. Although the difference between KA and PM1 is significant, variances of errors for KA and PM1 are identical because slopes of the models are almost identical (correlation coefficient between errors of KA and PM1 is ). Differences in mean errors of LC and PM1 are substantial but differences between variances of LC and PM1 errors are not significant. The mean for LCmod is close to zero and differs insignificantly from PM1 but its variability is higher than results from all other equations, except PM2. Errors from KAmod differ only by 0,18 years from zero and although this value is significantly different from PM1, variability around mean is indistinguishable from PM1. Results of KAts are insignificantly higher than PM1 and the variance of KAts significantly differs only from LCmod and PM2. Model PM1 yielded the best results. Since it was based directly on the data, we consider KAmod the best equation for the estimation of age. Mean absolute error of estimates of KAmod was 1.87 years (SD = 1.43), median absolute error was 1.71 years. In 60% of cases absolute error was lower than 2 years, in 91% of cases lower than 4 years, and only in 3.6% of cases the absolute error was higher than 5 years. Valid n = 56 Descriptive statistics of errors of estimates (in years). Negative errors are underestimations Mean Conf. 95% Conf. +95% Median Var. SD St. Error Perc. 5 Perc. 95 Min. Table 2 Max. LC LCmod KA KAmod PM PM KAts

16 20 M. Králík, V. Novotný Fig. 6. Errors of estimates from different equations Table 3 Comparison of means and variability of estimation errors obtained from applied equations (significant differences highlighted) n = 56 LC LCmod KA KAmod PM1 PM2 KAts S = S = S = S = S = S = LC p = 0 p = 0 p = 0 p = 0 p = 0 p = 0 LCmod L = 1.71 p = 0.19 KA L = 1.29 p = 0.26 KAmod L = 1.34 p = 0.25 PM1 PM2 KAts L = 1.31 p = 0.26 L = 2.67 p = 0.11 L = 0.93 p = 0.34 L = 5.57 p = 0.02 L = 5.64 p = 0.02 L = 5.59 p = 0.02 L = 0.13 p = 0.72 L = 4.76 p = 0.03 S = p = 0 L = p = 0.97 L = p = 0.99 L = 6.94 p = 0.01 L = 0.02 p = 0.88 S = p = 0.01 S = p = 0 L = 5.56 p = 0.98 L = 7.02 p = 0.01 L = 0.03 p = 0.85 S = p = 0.07 S = p = 0 S = 9.81 p = 0 L = 6.97 p = 0.01 L = 0.03 p = 0.87 S = p = 0 S = p = 0 S = 9.81 p = 0.59 S = 0 p = 1 L = 6.08 p = 0.01 S = 26.2 p = S = p = 0 S = p = 0 S = 4.85 p = 0.14 S = 4.85 p = 0.77 Upper matrix: Fisher s paired comparison randomization test (two-sided test), randomizations, S (sum of pair differences) and p. Lower matrix: Levene s test for constant variance, randomization version, randomizations, L (Levene s F) and p

17 Epidermal ridge breadth: an indicator of age and sex in paleodermatoglyphics 21 Mean error (PM1) for males is 1.11 years (SD = years), for females years (SD = 2.466). The method overestimated the age of males and underestimated the age of females. The difference is of marginal significance (t-test: p = 0.052; two-sample randomization test: p = 0.052), it may be due to the absence of boys in the oldest age category where sexual dimorphism is well expressed. The number of ridges of each individual varied from 27 to 287, the number of fingerprints from 2 to 8. Outliers (363 and 447 ridges on 11 and 16 fingerprints respectively) were excluded from this analysis. We divided the cases into two groups according to the success of the estimations (absolute errors) of PM1. In estimates with absolute error lower than 1.57 years, each individual has an average of 4.62 fingerprints and an average of ridges. In estimates with absolute error higher than 1.57 years, each individual has an average of 4.33 fingerprints and an average of ridges. There is some tendency for better estimates when more ridges and fingerprints were measured but it is not statistically significant for the number of ridges (t-test: p = 0.14; two-sample randomization test: p = 0.14) nor the number of fingerprints (t-test: p = 0.47; two-sample randomization test: p = 0.52). Sexual dimorphism Differences in mean ridge breadth (MRB) between sexes in adults (Fig. 7) were tested using two-sample randomization tests for mean differences. For both groups, the professionals (17 males and 13 females) and the non-professionals (23 males and Fig. 7. Differences in mean ridge breadth (MRB) between sexes

18 22 M. Králík, V. Novotný Table 4 Sexual dimorphism in MRB and differences between professionals and non-professionals Mean [mm] n SD Males professionals non-professionals Females professionals non-professionals All Comparison of means and variability of MRB in adults (significant differences highlighted) (1) (2) (3) (4) Males professionals (1) p = 0.29 p = 0.02 p = 0.31 non-professionals (2) p = 0.12 p = 0.00 p = 0.00 Females professionals (3) p = 0.07 p = 0.80 p = 0.08 non-professionals (4) p = 0.23 p = 0.74 p = 0.57 Table 5 Upper matrix: p of two-sample randomization test, randomizations. Lower matrix: p of Levene s test for constant variance, randomization version, randomizations 27 females) significant differences between the sexes were found (Tab. 4, 5). When the differences between the professionals and the non-professionals are considered separately for each sex, they were not significant, so the combined mean value for each sex was calculated as follows: males mm (SD = 0.036), females mm (SD = 0.031). The mean values were compared to the mean values (see Tab. 1) obtained by Primas (1975). The differences were not significant for males (two-sided t-test: p = 0.096; Fisher s one-sample two-sided randomization test: p = 0.1) and significant for females (two-sided t-test: p = 0.005; Fisher s one-sample two-sided randomization test: p = 0.006). Combining age and sex We can evaluate the overall variability of mean ridge breadth (MRB) (Fig. 8) according to sex and age, irrespective of the professional skills of authors and ceramic clays being used. Sub-adults and adults from previous comparisons were combined and 15 children (non-professionals) were added. (Imprints of two extremely young children were obtained by putting small pieces of clay into their hands as a toy.) All our subjects with MRB values below 0.39 mm were sub-adults under 15 years of age, all those with MRB values over 0.52 mm were adult males. MRB values between these two figures represent people of both sexes from an age of 8.83 years

19 Epidermal ridge breadth: an indicator of age and sex in paleodermatoglyphics 23 Fig. 8. The relationship between age and mean epidermal ridge breadth, all groups combined (a boy) to an old age. Therefore all estimations of age from MRB over 0.39 mm lie in the zone of overlap with adults. The difference between female subjects 15 to 20 years old (n = 12, mean = mm, SD = 0.023) and adults (n = 27, mean = mm, SD = 0.031) was significant ( permutations, two-sample randomization test: p = 0.039; two sample bootstrap t-test: p = 0.039). In males, the difference was not tested due to the small number of boys. Discussion and conclusion Our results are in agreement with most other studies, in that the measurement of the epidermal ridge breadth of fingerprints on ceramics might be used as an indicator of the ceramists age and sex. These biological trends are present not only on controlled laboratory samples in experimental conditions but also in retrospectively ascertained conditions of contemporary ceramic production. We have to note some disproportion in sexes among present ceramists in favor of females, both in children and in adults. The question is if this situation is specific only for our recent conditions or if it is a general trend in ceramic manufacturing.

20 24 M. Králík, V. Novotný Concerning the age estimation, using the regression model by Kamp et al. (1999) resulted in errors of the same variability as the model based directly on the present data (PM1). After correcting for shrinkage of clay (7.5%) Kamp s model (KAmod) yielded results with mean value of errors near zero even though our sample came from a different population and we used a different measurement technique. However, we have to comment on a very surprising correlation (r = ) between errors of the present model and the model by Kamp et al. (1999). Theoretically, if the sexes in our sample were in proportion, the regression line for our model (PM1) would shift slightly. The correlation coefficient would then be lower. Some differences between the two samples are also apparent from the results based on true shrinkage (KAts results). Let us assume an equal proportion of females and males in the study of Kamp at al. (1999). The shrinkage rate assumed in the KAts model is based on empirical values therefore it should be optimal. Thus, when the KAts model is applied to our sample (overrepresented by females), it is more likely to underestimate age than to overestimate it because of sexual dimorphism; lower values in females should lower the estimations. Despite these expectations, the KAts model slightly overestimated the age. This could indicate some systematic shift either due to differences between the techniques and/or differences between the populations. So the above-mentioned unusually high correlation coefficient is a result of an accidental interplay of several factors; nevertheless, the similarity of the two models (KAmod and PM1) is a good indicator of the applicability of this biological trend to age estimation. Since the actual shrinkage rates of prehistoric ceramic artifacts are unknown we consider the equation by Kamp et al. (1999), when corrected for shrinkage by 7.5% (Králík 2000), the best tool for estimates of age in paleodermatoglyphics today. In future, it would be very beneficial if methods allowing accurate detection of the shrinkage rate of a particular piece of ancient ceramics, could be developed. Equation by Loesch and Czyżewska (1972) severely underestimated the actual age. After modifying this equation (from palm to fingers and from paper to ceramics), the estimations substantially improved the mean error so the compensation was almost optimal. The slope of the regression line changed after correcting of the equation (i.e. multiplying the ridge breadth); this increased the variability of errors. At first sight it may seem that adding (rather than multiplying) a constant is a better modification. Since the size of imprints on ceramics changes proportionally (i.e. we cannot correct for it by adding a constant) the increase of variability after our correction may indicate actual differences between our sample and the Polish sample (this also applies to the differences between KA and KAmod). From the available data it is not possible to determine whether the low predictive power of LCmod is because it was originally not developed for this purpose (i.e. fingerprints on ceramics), or because it uses the MRB as the dependent variable. However, the similarity of the LCmod regression line with the line of our second model (PM2) may also indicate that using ridge breadth as dependent variable in regression is entirely inappropriate for age estimates.

21 Epidermal ridge breadth: an indicator of age and sex in paleodermatoglyphics 25 Changes in MRB connected with age during growing up consistently peter out around the age when sexual differences are established. Tendencies for higher values in boys are apparent from the age of ten. Based on the summary graph, women reach adult values before men. However, the low number of men in our age sample may cause this pattern. On average, ridge breadth is 9% thinner in women compared to men, however the overlap is marked. The threshold between children and maturity seems to be the value of 0.4 mm. Above this value, MRB on its own is not an adequate indicator of age. For example, a print with MRB value of 0.43 mm can belong to an immature individual or an adult, but is more likely to be a female than a male. The graph (Fig. 8) also shows that a 12 year-old female can have an MRB value above 0.46 mm, even though we only know of one such case. Although it is not out of question that some of these borderline cases can indicate the presence of more than one subject, in our opinion, age estimates from MRB values higher than 0.4 mm will always be uncertain, because age and sexual dimorphism can be acting together. This is not only the case in estimates in individual artifacts but also in a more general sense when comparing groups of prints or artifacts. It would be helpful if the sex of the author of the prints could be determined. Although the difference between professional ceramists and non-professionals was not statistically significant, it is consistent in both men and women. This could indicate that this is a real trend, regardless of whether it is caused by differences in clay molding or actual biological differences. The oldest female subject in our sample, who spent her life laboring on the land, had coarser ridges than the majority of the male subjects. So the question is, to what extent can high loading on the hands over a long-term period change the epidermal ridges. Can it be postulated that hard labor was more common in past agricultural societies than today? Our procedure assumes a simple relationship: 1 artifact = 1 individual, in other words, in a particular artifact we expect to find prints of a single producer/creator. Since several people usually work in a ceramic workshop together, this assumption is somewhat uncertain. However, the biological trends in question were still apparent even though we could not be quite certain whether all the prints on artifacts belong to their respective authors. This could indicate that despite the presence of more than one person in the workshop, the actual molding and shaping of soft printable clay is a one (wo)man show. However, in ancient cultures this may not always be the case, e.g. if the ceramic object is produced during a ritual. Kamp et al. (1999) pointed out that it is likely that certain fingers and finger portions are preferentially represented, in other words the homogeneity of MRB is likely to be caused by similar use of fingers and palms in molding, which may be related to a particular molding process. It is interesting then, that age changes and sexual dimorphism in adults are still perceptible, even though the ceramists used a variety of ceramic clays and molding procedures. If we compare the variability in MRB in adults in our sample with previous research, it does not appear, that the variability increases with greater variety of ceramic clays used.

AP Physics 1 and 2 Lab Investigations

AP Physics 1 and 2 Lab Investigations AP Physics 1 and 2 Lab Investigations Student Guide to Data Analysis New York, NY. College Board, Advanced Placement, Advanced Placement Program, AP, AP Central, and the acorn logo are registered trademarks

More information

Chapter 6: The Information Function 129. CHAPTER 7 Test Calibration

Chapter 6: The Information Function 129. CHAPTER 7 Test Calibration Chapter 6: The Information Function 129 CHAPTER 7 Test Calibration 130 Chapter 7: Test Calibration CHAPTER 7 Test Calibration For didactic purposes, all of the preceding chapters have assumed that the

More information

METHODS OF GEOREFERENCING OLD MAPS ON THE EXAMPLE OF CZECH EARLY MAPS

METHODS OF GEOREFERENCING OLD MAPS ON THE EXAMPLE OF CZECH EARLY MAPS CO-314 METHODS OF GEOREFERENCING OLD MAPS ON THE EXAMPLE OF CZECH EARLY MAPS CAJTHAML J. Czech Technical University in Prague, PRAGUE 6, CZECH REPUBLIC BACKGROUND AND OBJECTIVES Old maps are unique source

More information

Algebra 1 2008. Academic Content Standards Grade Eight and Grade Nine Ohio. Grade Eight. Number, Number Sense and Operations Standard

Algebra 1 2008. Academic Content Standards Grade Eight and Grade Nine Ohio. Grade Eight. Number, Number Sense and Operations Standard Academic Content Standards Grade Eight and Grade Nine Ohio Algebra 1 2008 Grade Eight STANDARDS Number, Number Sense and Operations Standard Number and Number Systems 1. Use scientific notation to express

More information

2. Simple Linear Regression

2. Simple Linear Regression Research methods - II 3 2. Simple Linear Regression Simple linear regression is a technique in parametric statistics that is commonly used for analyzing mean response of a variable Y which changes according

More information

In this chapter, you will learn improvement curve concepts and their application to cost and price analysis.

In this chapter, you will learn improvement curve concepts and their application to cost and price analysis. 7.0 - Chapter Introduction In this chapter, you will learn improvement curve concepts and their application to cost and price analysis. Basic Improvement Curve Concept. You may have learned about improvement

More information

GEOENGINE MSc in Geomatics Engineering (Master Thesis) Anamelechi, Falasy Ebere

GEOENGINE MSc in Geomatics Engineering (Master Thesis) Anamelechi, Falasy Ebere Master s Thesis: ANAMELECHI, FALASY EBERE Analysis of a Raster DEM Creation for a Farm Management Information System based on GNSS and Total Station Coordinates Duration of the Thesis: 6 Months Completion

More information

Geometry and Measurement

Geometry and Measurement The student will be able to: Geometry and Measurement 1. Demonstrate an understanding of the principles of geometry and measurement and operations using measurements Use the US system of measurement for

More information

Reflection and Refraction

Reflection and Refraction Equipment Reflection and Refraction Acrylic block set, plane-concave-convex universal mirror, cork board, cork board stand, pins, flashlight, protractor, ruler, mirror worksheet, rectangular block worksheet,

More information

Solving Simultaneous Equations and Matrices

Solving Simultaneous Equations and Matrices Solving Simultaneous Equations and Matrices The following represents a systematic investigation for the steps used to solve two simultaneous linear equations in two unknowns. The motivation for considering

More information

Physics Lab Report Guidelines

Physics Lab Report Guidelines Physics Lab Report Guidelines Summary The following is an outline of the requirements for a physics lab report. A. Experimental Description 1. Provide a statement of the physical theory or principle observed

More information

NEW MEXICO Grade 6 MATHEMATICS STANDARDS

NEW MEXICO Grade 6 MATHEMATICS STANDARDS PROCESS STANDARDS To help New Mexico students achieve the Content Standards enumerated below, teachers are encouraged to base instruction on the following Process Standards: Problem Solving Build new mathematical

More information

Local outlier detection in data forensics: data mining approach to flag unusual schools

Local outlier detection in data forensics: data mining approach to flag unusual schools Local outlier detection in data forensics: data mining approach to flag unusual schools Mayuko Simon Data Recognition Corporation Paper presented at the 2012 Conference on Statistical Detection of Potential

More information

Session 7 Bivariate Data and Analysis

Session 7 Bivariate Data and Analysis Session 7 Bivariate Data and Analysis Key Terms for This Session Previously Introduced mean standard deviation New in This Session association bivariate analysis contingency table co-variation least squares

More information

Data Exploration Data Visualization

Data Exploration Data Visualization Data Exploration Data Visualization What is data exploration? A preliminary exploration of the data to better understand its characteristics. Key motivations of data exploration include Helping to select

More information

COMPARISONS OF CUSTOMER LOYALTY: PUBLIC & PRIVATE INSURANCE COMPANIES.

COMPARISONS OF CUSTOMER LOYALTY: PUBLIC & PRIVATE INSURANCE COMPANIES. 277 CHAPTER VI COMPARISONS OF CUSTOMER LOYALTY: PUBLIC & PRIVATE INSURANCE COMPANIES. This chapter contains a full discussion of customer loyalty comparisons between private and public insurance companies

More information

ABSTRACT OF THE DOCTORAL THESIS BY Cătălin Ovidiu Obuf Buhăianu

ABSTRACT OF THE DOCTORAL THESIS BY Cătălin Ovidiu Obuf Buhăianu ABSTRACT OF THE DOCTORAL THESIS BY Cătălin Ovidiu Obuf Buhăianu Thesis submitted to: NATIONAL UNIVERSITY OF PHYSICAL EDUCATION AND SPORTS, Bucharest, Romania, 2011 Thesis Advisor: Prof. Dr. Adrian Gagea

More information

On Correlating Performance Metrics

On Correlating Performance Metrics On Correlating Performance Metrics Yiping Ding and Chris Thornley BMC Software, Inc. Kenneth Newman BMC Software, Inc. University of Massachusetts, Boston Performance metrics and their measurements are

More information

http://www.jstor.org This content downloaded on Tue, 19 Feb 2013 17:28:43 PM All use subject to JSTOR Terms and Conditions

http://www.jstor.org This content downloaded on Tue, 19 Feb 2013 17:28:43 PM All use subject to JSTOR Terms and Conditions A Significance Test for Time Series Analysis Author(s): W. Allen Wallis and Geoffrey H. Moore Reviewed work(s): Source: Journal of the American Statistical Association, Vol. 36, No. 215 (Sep., 1941), pp.

More information

Exploratory data analysis (Chapter 2) Fall 2011

Exploratory data analysis (Chapter 2) Fall 2011 Exploratory data analysis (Chapter 2) Fall 2011 Data Examples Example 1: Survey Data 1 Data collected from a Stat 371 class in Fall 2005 2 They answered questions about their: gender, major, year in school,

More information

1/27/2013. PSY 512: Advanced Statistics for Psychological and Behavioral Research 2

1/27/2013. PSY 512: Advanced Statistics for Psychological and Behavioral Research 2 PSY 512: Advanced Statistics for Psychological and Behavioral Research 2 Introduce moderated multiple regression Continuous predictor continuous predictor Continuous predictor categorical predictor Understand

More information

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Final Exam Review MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) A researcher for an airline interviews all of the passengers on five randomly

More information

Polarization of Light

Polarization of Light Polarization of Light References Halliday/Resnick/Walker Fundamentals of Physics, Chapter 33, 7 th ed. Wiley 005 PASCO EX997A and EX999 guide sheets (written by Ann Hanks) weight Exercises and weights

More information

Experiment #1, Analyze Data using Excel, Calculator and Graphs.

Experiment #1, Analyze Data using Excel, Calculator and Graphs. Physics 182 - Fall 2014 - Experiment #1 1 Experiment #1, Analyze Data using Excel, Calculator and Graphs. 1 Purpose (5 Points, Including Title. Points apply to your lab report.) Before we start measuring

More information

Pre-Algebra 2008. Academic Content Standards Grade Eight Ohio. Number, Number Sense and Operations Standard. Number and Number Systems

Pre-Algebra 2008. Academic Content Standards Grade Eight Ohio. Number, Number Sense and Operations Standard. Number and Number Systems Academic Content Standards Grade Eight Ohio Pre-Algebra 2008 STANDARDS Number, Number Sense and Operations Standard Number and Number Systems 1. Use scientific notation to express large numbers and small

More information

Nonparametric Two-Sample Tests. Nonparametric Tests. Sign Test

Nonparametric Two-Sample Tests. Nonparametric Tests. Sign Test Nonparametric Two-Sample Tests Sign test Mann-Whitney U-test (a.k.a. Wilcoxon two-sample test) Kolmogorov-Smirnov Test Wilcoxon Signed-Rank Test Tukey-Duckworth Test 1 Nonparametric Tests Recall, nonparametric

More information

Expression. Variable Equation Polynomial Monomial Add. Area. Volume Surface Space Length Width. Probability. Chance Random Likely Possibility Odds

Expression. Variable Equation Polynomial Monomial Add. Area. Volume Surface Space Length Width. Probability. Chance Random Likely Possibility Odds Isosceles Triangle Congruent Leg Side Expression Equation Polynomial Monomial Radical Square Root Check Times Itself Function Relation One Domain Range Area Volume Surface Space Length Width Quantitative

More information

APPENDIX N. Data Validation Using Data Descriptors

APPENDIX N. Data Validation Using Data Descriptors APPENDIX N Data Validation Using Data Descriptors Data validation is often defined by six data descriptors: 1) reports to decision maker 2) documentation 3) data sources 4) analytical method and detection

More information

1) Write the following as an algebraic expression using x as the variable: Triple a number subtracted from the number

1) Write the following as an algebraic expression using x as the variable: Triple a number subtracted from the number 1) Write the following as an algebraic expression using x as the variable: Triple a number subtracted from the number A. 3(x - x) B. x 3 x C. 3x - x D. x - 3x 2) Write the following as an algebraic expression

More information

MEASURES OF VARIATION

MEASURES OF VARIATION NORMAL DISTRIBTIONS MEASURES OF VARIATION In statistics, it is important to measure the spread of data. A simple way to measure spread is to find the range. But statisticians want to know if the data are

More information

Social Costs of Accidents in Sweden

Social Costs of Accidents in Sweden Social Costs of Accidents in Sweden Social Costs of Accidents in Sweden Social costs of accidents in Sweden Swedish Civil Contingencies Agency (MSB) MSB:s contact: Linda Ryen, +46 (0)10-240 56 64 Layout:

More information

Name: Date: Use the following to answer questions 2-3:

Name: Date: Use the following to answer questions 2-3: Name: Date: 1. A study is conducted on students taking a statistics class. Several variables are recorded in the survey. Identify each variable as categorical or quantitative. A) Type of car the student

More information

NCSS Statistical Software Principal Components Regression. In ordinary least squares, the regression coefficients are estimated using the formula ( )

NCSS Statistical Software Principal Components Regression. In ordinary least squares, the regression coefficients are estimated using the formula ( ) Chapter 340 Principal Components Regression Introduction is a technique for analyzing multiple regression data that suffer from multicollinearity. When multicollinearity occurs, least squares estimates

More information

KEANSBURG SCHOOL DISTRICT KEANSBURG HIGH SCHOOL Mathematics Department. HSPA 10 Curriculum. September 2007

KEANSBURG SCHOOL DISTRICT KEANSBURG HIGH SCHOOL Mathematics Department. HSPA 10 Curriculum. September 2007 KEANSBURG HIGH SCHOOL Mathematics Department HSPA 10 Curriculum September 2007 Written by: Karen Egan Mathematics Supervisor: Ann Gagliardi 7 days Sample and Display Data (Chapter 1 pp. 4-47) Surveys and

More information

Evaluation of a New Method for Measuring the Internet Degree Distribution: Simulation Results

Evaluation of a New Method for Measuring the Internet Degree Distribution: Simulation Results Evaluation of a New Method for Measuring the Internet Distribution: Simulation Results Christophe Crespelle and Fabien Tarissan LIP6 CNRS and Université Pierre et Marie Curie Paris 6 4 avenue du président

More information

Problem: CSI: The Experience - Educator s Guide

Problem: CSI: The Experience - Educator s Guide Problem: At a nearby construction zone, workers have made a startling discovery. They uncovered several bones that look like they were buried some time ago. You are part of a team of forensic anthropologists

More information

For example, estimate the population of the United States as 3 times 10⁸ and the

For example, estimate the population of the United States as 3 times 10⁸ and the CCSS: Mathematics The Number System CCSS: Grade 8 8.NS.A. Know that there are numbers that are not rational, and approximate them by rational numbers. 8.NS.A.1. Understand informally that every number

More information

AN EXPERT SYSTEM TO ANALYZE HOMOGENEITY IN FUEL ELEMENT PLATES FOR RESEARCH REACTORS

AN EXPERT SYSTEM TO ANALYZE HOMOGENEITY IN FUEL ELEMENT PLATES FOR RESEARCH REACTORS AN EXPERT SYSTEM TO ANALYZE HOMOGENEITY IN FUEL ELEMENT PLATES FOR RESEARCH REACTORS Cativa Tolosa, S. and Marajofsky, A. Comisión Nacional de Energía Atómica Abstract In the manufacturing control of Fuel

More information

New Hash Function Construction for Textual and Geometric Data Retrieval

New Hash Function Construction for Textual and Geometric Data Retrieval Latest Trends on Computers, Vol., pp.483-489, ISBN 978-96-474-3-4, ISSN 79-45, CSCC conference, Corfu, Greece, New Hash Function Construction for Textual and Geometric Data Retrieval Václav Skala, Jan

More information

Vocabulary Cards and Word Walls Revised: June 29, 2011

Vocabulary Cards and Word Walls Revised: June 29, 2011 Vocabulary Cards and Word Walls Revised: June 29, 2011 Important Notes for Teachers: The vocabulary cards in this file match the Common Core, the math curriculum adopted by the Utah State Board of Education,

More information

High Resolution Fingerprint Matching Using Level 3 Features

High Resolution Fingerprint Matching Using Level 3 Features High Resolution Fingerprint Matching Using Level 3 Features Anil K. Jain and Yi Chen Michigan State University Fingerprint Features Latent print examiners use Level 3 all the time We do not just count

More information

Technical Drawing Specifications Resource A guide to support VCE Visual Communication Design study design 2013-17

Technical Drawing Specifications Resource A guide to support VCE Visual Communication Design study design 2013-17 A guide to support VCE Visual Communication Design study design 2013-17 1 Contents INTRODUCTION The Australian Standards (AS) Key knowledge and skills THREE-DIMENSIONAL DRAWING PARALINE DRAWING Isometric

More information

Statistical Rules of Thumb

Statistical Rules of Thumb Statistical Rules of Thumb Second Edition Gerald van Belle University of Washington Department of Biostatistics and Department of Environmental and Occupational Health Sciences Seattle, WA WILEY AJOHN

More information

Statistics 151 Practice Midterm 1 Mike Kowalski

Statistics 151 Practice Midterm 1 Mike Kowalski Statistics 151 Practice Midterm 1 Mike Kowalski Statistics 151 Practice Midterm 1 Multiple Choice (50 minutes) Instructions: 1. This is a closed book exam. 2. You may use the STAT 151 formula sheets and

More information

Common Core Unit Summary Grades 6 to 8

Common Core Unit Summary Grades 6 to 8 Common Core Unit Summary Grades 6 to 8 Grade 8: Unit 1: Congruence and Similarity- 8G1-8G5 rotations reflections and translations,( RRT=congruence) understand congruence of 2 d figures after RRT Dilations

More information

NUMERICAL ANALYSIS OF THE EFFECTS OF WIND ON BUILDING STRUCTURES

NUMERICAL ANALYSIS OF THE EFFECTS OF WIND ON BUILDING STRUCTURES Vol. XX 2012 No. 4 28 34 J. ŠIMIČEK O. HUBOVÁ NUMERICAL ANALYSIS OF THE EFFECTS OF WIND ON BUILDING STRUCTURES Jozef ŠIMIČEK email: jozef.simicek@stuba.sk Research field: Statics and Dynamics Fluids mechanics

More information

Chapter 7 Section 7.1: Inference for the Mean of a Population

Chapter 7 Section 7.1: Inference for the Mean of a Population Chapter 7 Section 7.1: Inference for the Mean of a Population Now let s look at a similar situation Take an SRS of size n Normal Population : N(, ). Both and are unknown parameters. Unlike what we used

More information

Chapter 5: Analysis of The National Education Longitudinal Study (NELS:88)

Chapter 5: Analysis of The National Education Longitudinal Study (NELS:88) Chapter 5: Analysis of The National Education Longitudinal Study (NELS:88) Introduction The National Educational Longitudinal Survey (NELS:88) followed students from 8 th grade in 1988 to 10 th grade in

More information

TRINITY COLLEGE. Faculty of Engineering, Mathematics and Science. School of Computer Science & Statistics

TRINITY COLLEGE. Faculty of Engineering, Mathematics and Science. School of Computer Science & Statistics UNIVERSITY OF DUBLIN TRINITY COLLEGE Faculty of Engineering, Mathematics and Science School of Computer Science & Statistics BA (Mod) Enter Course Title Trinity Term 2013 Junior/Senior Sophister ST7002

More information

January 26, 2009 The Faculty Center for Teaching and Learning

January 26, 2009 The Faculty Center for Teaching and Learning THE BASICS OF DATA MANAGEMENT AND ANALYSIS A USER GUIDE January 26, 2009 The Faculty Center for Teaching and Learning THE BASICS OF DATA MANAGEMENT AND ANALYSIS Table of Contents Table of Contents... i

More information

DESCRIPTIVE STATISTICS. The purpose of statistics is to condense raw data to make it easier to answer specific questions; test hypotheses.

DESCRIPTIVE STATISTICS. The purpose of statistics is to condense raw data to make it easier to answer specific questions; test hypotheses. DESCRIPTIVE STATISTICS The purpose of statistics is to condense raw data to make it easier to answer specific questions; test hypotheses. DESCRIPTIVE VS. INFERENTIAL STATISTICS Descriptive To organize,

More information

Determination of g using a spring

Determination of g using a spring INTRODUCTION UNIVERSITY OF SURREY DEPARTMENT OF PHYSICS Level 1 Laboratory: Introduction Experiment Determination of g using a spring This experiment is designed to get you confident in using the quantitative

More information

Robot Perception Continued

Robot Perception Continued Robot Perception Continued 1 Visual Perception Visual Odometry Reconstruction Recognition CS 685 11 Range Sensing strategies Active range sensors Ultrasound Laser range sensor Slides adopted from Siegwart

More information

Palmprint Recognition. By Sree Rama Murthy kora Praveen Verma Yashwant Kashyap

Palmprint Recognition. By Sree Rama Murthy kora Praveen Verma Yashwant Kashyap Palmprint Recognition By Sree Rama Murthy kora Praveen Verma Yashwant Kashyap Palm print Palm Patterns are utilized in many applications: 1. To correlate palm patterns with medical disorders, e.g. genetic

More information

CHAPTER FIVE. 5. Equations of Lines in R 3

CHAPTER FIVE. 5. Equations of Lines in R 3 118 CHAPTER FIVE 5. Equations of Lines in R 3 In this chapter it is going to be very important to distinguish clearly between points and vectors. Frequently in the past the distinction has only been a

More information

E190Q Lecture 5 Autonomous Robot Navigation

E190Q Lecture 5 Autonomous Robot Navigation E190Q Lecture 5 Autonomous Robot Navigation Instructor: Chris Clark Semester: Spring 2014 1 Figures courtesy of Siegwart & Nourbakhsh Control Structures Planning Based Control Prior Knowledge Operator

More information

Dimensionality Reduction: Principal Components Analysis

Dimensionality Reduction: Principal Components Analysis Dimensionality Reduction: Principal Components Analysis In data mining one often encounters situations where there are a large number of variables in the database. In such situations it is very likely

More information

with functions, expressions and equations which follow in units 3 and 4.

with functions, expressions and equations which follow in units 3 and 4. Grade 8 Overview View unit yearlong overview here The unit design was created in line with the areas of focus for grade 8 Mathematics as identified by the Common Core State Standards and the PARCC Model

More information

Gamma Distribution Fitting

Gamma Distribution Fitting Chapter 552 Gamma Distribution Fitting Introduction This module fits the gamma probability distributions to a complete or censored set of individual or grouped data values. It outputs various statistics

More information

ANNEX 2: Assessment of the 7 points agreed by WATCH as meriting attention (cover paper, paragraph 9, bullet points) by Andy Darnton, HSE

ANNEX 2: Assessment of the 7 points agreed by WATCH as meriting attention (cover paper, paragraph 9, bullet points) by Andy Darnton, HSE ANNEX 2: Assessment of the 7 points agreed by WATCH as meriting attention (cover paper, paragraph 9, bullet points) by Andy Darnton, HSE The 7 issues to be addressed outlined in paragraph 9 of the cover

More information

The Map Grid of Australia 1994 A Simplified Computational Manual

The Map Grid of Australia 1994 A Simplified Computational Manual The Map Grid of Australia 1994 A Simplified Computational Manual The Map Grid of Australia 1994 A Simplified Computational Manual 'What's the good of Mercator's North Poles and Equators, Tropics, Zones

More information

TABLE TENNIS TABLE TENNIS

TABLE TENNIS TABLE TENNIS 1 The Official Special Olympics Sports Rules for Table Tennis shall govern all Special Olympics competitions. As an international sports program, Special Olympics has created these rules based upon International

More information

HISTOGRAMS, CUMULATIVE FREQUENCY AND BOX PLOTS

HISTOGRAMS, CUMULATIVE FREQUENCY AND BOX PLOTS Mathematics Revision Guides Histograms, Cumulative Frequency and Box Plots Page 1 of 25 M.K. HOME TUITION Mathematics Revision Guides Level: GCSE Higher Tier HISTOGRAMS, CUMULATIVE FREQUENCY AND BOX PLOTS

More information

Multivariate Analysis of Ecological Data

Multivariate Analysis of Ecological Data Multivariate Analysis of Ecological Data MICHAEL GREENACRE Professor of Statistics at the Pompeu Fabra University in Barcelona, Spain RAUL PRIMICERIO Associate Professor of Ecology, Evolutionary Biology

More information

Optical Illusions Essay Angela Wall EMAT 6690

Optical Illusions Essay Angela Wall EMAT 6690 Optical Illusions Essay Angela Wall EMAT 6690! Optical illusions are images that are visually perceived differently than how they actually appear in reality. These images can be very entertaining, but

More information

CSU, Fresno - Institutional Research, Assessment and Planning - Dmitri Rogulkin

CSU, Fresno - Institutional Research, Assessment and Planning - Dmitri Rogulkin My presentation is about data visualization. How to use visual graphs and charts in order to explore data, discover meaning and report findings. The goal is to show that visual displays can be very effective

More information

Prentice Hall Mathematics Courses 1-3 Common Core Edition 2013

Prentice Hall Mathematics Courses 1-3 Common Core Edition 2013 A Correlation of Prentice Hall Mathematics Courses 1-3 Common Core Edition 2013 to the Topics & Lessons of Pearson A Correlation of Courses 1, 2 and 3, Common Core Introduction This document demonstrates

More information

Evaluating System Suitability CE, GC, LC and A/D ChemStation Revisions: A.03.0x- A.08.0x

Evaluating System Suitability CE, GC, LC and A/D ChemStation Revisions: A.03.0x- A.08.0x CE, GC, LC and A/D ChemStation Revisions: A.03.0x- A.08.0x This document is believed to be accurate and up-to-date. However, Agilent Technologies, Inc. cannot assume responsibility for the use of this

More information

Pennsylvania System of School Assessment

Pennsylvania System of School Assessment Pennsylvania System of School Assessment The Assessment Anchors, as defined by the Eligible Content, are organized into cohesive blueprints, each structured with a common labeling system that can be read

More information

Spring Force Constant Determination as a Learning Tool for Graphing and Modeling

Spring Force Constant Determination as a Learning Tool for Graphing and Modeling NCSU PHYSICS 205 SECTION 11 LAB II 9 FEBRUARY 2002 Spring Force Constant Determination as a Learning Tool for Graphing and Modeling Newton, I. 1*, Galilei, G. 1, & Einstein, A. 1 (1. PY205_011 Group 4C;

More information

Chapter 9. Two-Sample Tests. Effect Sizes and Power Paired t Test Calculation

Chapter 9. Two-Sample Tests. Effect Sizes and Power Paired t Test Calculation Chapter 9 Two-Sample Tests Paired t Test (Correlated Groups t Test) Effect Sizes and Power Paired t Test Calculation Summary Independent t Test Chapter 9 Homework Power and Two-Sample Tests: Paired Versus

More information

A Determination of g, the Acceleration Due to Gravity, from Newton's Laws of Motion

A Determination of g, the Acceleration Due to Gravity, from Newton's Laws of Motion A Determination of g, the Acceleration Due to Gravity, from Newton's Laws of Motion Objective In the experiment you will determine the cart acceleration, a, and the friction force, f, experimentally for

More information

Simple Predictive Analytics Curtis Seare

Simple Predictive Analytics Curtis Seare Using Excel to Solve Business Problems: Simple Predictive Analytics Curtis Seare Copyright: Vault Analytics July 2010 Contents Section I: Background Information Why use Predictive Analytics? How to use

More information

LOGNORMAL MODEL FOR STOCK PRICES

LOGNORMAL MODEL FOR STOCK PRICES LOGNORMAL MODEL FOR STOCK PRICES MICHAEL J. SHARPE MATHEMATICS DEPARTMENT, UCSD 1. INTRODUCTION What follows is a simple but important model that will be the basis for a later study of stock prices as

More information

(I) s(t) = s 0 v 0 (t t 0 ) + 1 2 a (t t 0) 2 (II). t 2 = t 0 + 2 v 0. At the time. E kin = 1 2 m v2 = 1 2 m (a (t t 0) v 0 ) 2

(I) s(t) = s 0 v 0 (t t 0 ) + 1 2 a (t t 0) 2 (II). t 2 = t 0 + 2 v 0. At the time. E kin = 1 2 m v2 = 1 2 m (a (t t 0) v 0 ) 2 Mechanics Translational motions of a mass point One-dimensional motions on the linear air track LD Physics Leaflets P1.3.3.8 Uniformly accelerated motion with reversal of direction Recording and evaluating

More information

REPORT 2014 Eastern Europe and MENA

REPORT 2014 Eastern Europe and MENA Find out how companies and jobseekers use social media in the job market. REPORT 2014 Eastern Europe and MENA 1 The Use of Social Media in the Matching Between Supply and Demand within the Labor Market.

More information

American Society of Agricultural and Biological Engineers

American Society of Agricultural and Biological Engineers ASAE S580.1 NOV2013 Testing and Reporting Solar Cooker Performance American Society of Agricultural and Biological Engineers ASABE is a professional and technical organization, of members worldwide, who

More information

Common Core State Standards for Mathematics Accelerated 7th Grade

Common Core State Standards for Mathematics Accelerated 7th Grade A Correlation of 2013 To the to the Introduction This document demonstrates how Mathematics Accelerated Grade 7, 2013, meets the. Correlation references are to the pages within the Student Edition. Meeting

More information

How To Study The Academic Performance Of An Mba

How To Study The Academic Performance Of An Mba Proceedings of the Annual Meeting of the American Statistical Association, August 5-9, 2001 WORK EXPERIENCE: DETERMINANT OF MBA ACADEMIC SUCCESS? Andrew Braunstein, Iona College Hagan School of Business,

More information

MOD Core Civilian. Contents Page. A1 Average annual basic salary for all permanent employees by gender and grade 3

MOD Core Civilian. Contents Page. A1 Average annual basic salary for all permanent employees by gender and grade 3 Equal Pay Audit 2014 MOD Core Civilian Non-Industrial Personnel This audit presents a comparison of male to female and White to Black, Asian, Minority Ethnic annualised average salaries in the period 1

More information

THE INFLUENCE OF CLIMATE ON FIRE DAMAGE

THE INFLUENCE OF CLIMATE ON FIRE DAMAGE THE INFLUENCE OF CLIMATE ON FIRE DAMAGE HANS ANDERSSON Liding6, Sweden In his paper "Actuarial Activity in General Insurance in the Northern Countries of Europe" L. Wilhelmsen 1) gives amongst other things

More information

Performance Level Descriptors Grade 6 Mathematics

Performance Level Descriptors Grade 6 Mathematics Performance Level Descriptors Grade 6 Mathematics Multiplying and Dividing with Fractions 6.NS.1-2 Grade 6 Math : Sub-Claim A The student solves problems involving the Major Content for grade/course with

More information

NCSS Statistical Software

NCSS Statistical Software Chapter 06 Introduction This procedure provides several reports for the comparison of two distributions, including confidence intervals for the difference in means, two-sample t-tests, the z-test, the

More information

Simple Random Sampling

Simple Random Sampling Source: Frerichs, R.R. Rapid Surveys (unpublished), 2008. NOT FOR COMMERCIAL DISTRIBUTION 3 Simple Random Sampling 3.1 INTRODUCTION Everyone mentions simple random sampling, but few use this method for

More information

After reading this lesson you will be able to: 12.3 IMPORTANCE OF ROOF 12.4 TYPES OF ROOF IN A HOUSE

After reading this lesson you will be able to: 12.3 IMPORTANCE OF ROOF 12.4 TYPES OF ROOF IN A HOUSE 86 :: Certificate in Construction Supervision (CIVIL) 12 ROOF 12.1 INTRODUCTION The structure provided to cover the house surface (floor) is known as roof. For different situation and requirement, it is

More information

STATISTICAL ANALYSIS OF UBC FACULTY SALARIES: INVESTIGATION OF

STATISTICAL ANALYSIS OF UBC FACULTY SALARIES: INVESTIGATION OF STATISTICAL ANALYSIS OF UBC FACULTY SALARIES: INVESTIGATION OF DIFFERENCES DUE TO SEX OR VISIBLE MINORITY STATUS. Oxana Marmer and Walter Sudmant, UBC Planning and Institutional Research SUMMARY This paper

More information

Exercise 1.12 (Pg. 22-23)

Exercise 1.12 (Pg. 22-23) Individuals: The objects that are described by a set of data. They may be people, animals, things, etc. (Also referred to as Cases or Records) Variables: The characteristics recorded about each individual.

More information

MD5-26 Stacking Blocks Pages 115 116

MD5-26 Stacking Blocks Pages 115 116 MD5-26 Stacking Blocks Pages 115 116 STANDARDS 5.MD.C.4 Goals Students will find the number of cubes in a rectangular stack and develop the formula length width height for the number of cubes in a stack.

More information

MATHS LEVEL DESCRIPTORS

MATHS LEVEL DESCRIPTORS MATHS LEVEL DESCRIPTORS Number Level 3 Understand the place value of numbers up to thousands. Order numbers up to 9999. Round numbers to the nearest 10 or 100. Understand the number line below zero, and

More information

12-1 Representations of Three-Dimensional Figures

12-1 Representations of Three-Dimensional Figures Connect the dots on the isometric dot paper to represent the edges of the solid. Shade the tops of 12-1 Representations of Three-Dimensional Figures Use isometric dot paper to sketch each prism. 1. triangular

More information

The Life-Cycle Motive and Money Demand: Further Evidence. Abstract

The Life-Cycle Motive and Money Demand: Further Evidence. Abstract The Life-Cycle Motive and Money Demand: Further Evidence Jan Tin Commerce Department Abstract This study takes a closer look at the relationship between money demand and the life-cycle motive using panel

More information

Assessment Anchors and Eligible Content

Assessment Anchors and Eligible Content M07.A-N The Number System M07.A-N.1 M07.A-N.1.1 DESCRIPTOR Assessment Anchors and Eligible Content Aligned to the Grade 7 Pennsylvania Core Standards Reporting Category Apply and extend previous understandings

More information

15.062 Data Mining: Algorithms and Applications Matrix Math Review

15.062 Data Mining: Algorithms and Applications Matrix Math Review .6 Data Mining: Algorithms and Applications Matrix Math Review The purpose of this document is to give a brief review of selected linear algebra concepts that will be useful for the course and to develop

More information

NEW YORK STATE TEACHER CERTIFICATION EXAMINATIONS

NEW YORK STATE TEACHER CERTIFICATION EXAMINATIONS NEW YORK STATE TEACHER CERTIFICATION EXAMINATIONS TEST DESIGN AND FRAMEWORK September 2014 Authorized for Distribution by the New York State Education Department This test design and framework document

More information

Study of the Human Eye Working Principle: An impressive high angular resolution system with simple array detectors

Study of the Human Eye Working Principle: An impressive high angular resolution system with simple array detectors Study of the Human Eye Working Principle: An impressive high angular resolution system with simple array detectors Diego Betancourt and Carlos del Río Antenna Group, Public University of Navarra, Campus

More information

Point Biserial Correlation Tests

Point Biserial Correlation Tests Chapter 807 Point Biserial Correlation Tests Introduction The point biserial correlation coefficient (ρ in this chapter) is the product-moment correlation calculated between a continuous random variable

More information

Experimental Evaluation of the Discharge Coefficient of a Centre-Pivot Roof Window

Experimental Evaluation of the Discharge Coefficient of a Centre-Pivot Roof Window Experimental Evaluation of the Discharge Coefficient of a Centre-Pivot Roof Window Ahsan Iqbal #1, Alireza Afshari #2, Per Heiselberg *3, Anders Høj **4 # Energy and Environment, Danish Building Research

More information

Welcome to Math 7 Accelerated Courses (Preparation for Algebra in 8 th grade)

Welcome to Math 7 Accelerated Courses (Preparation for Algebra in 8 th grade) Welcome to Math 7 Accelerated Courses (Preparation for Algebra in 8 th grade) Teacher: School Phone: Email: Kim Schnakenberg 402-443- 3101 kschnakenberg@esu2.org Course Descriptions: Both Concept and Application

More information

Descriptive Statistics

Descriptive Statistics Descriptive Statistics Primer Descriptive statistics Central tendency Variation Relative position Relationships Calculating descriptive statistics Descriptive Statistics Purpose to describe or summarize

More information

Data Analysis Tools. Tools for Summarizing Data

Data Analysis Tools. Tools for Summarizing Data Data Analysis Tools This section of the notes is meant to introduce you to many of the tools that are provided by Excel under the Tools/Data Analysis menu item. If your computer does not have that tool

More information