In statistics, stratified sampling is a method of sampling from a population. In statistical surveys, when subpopulations within an overall population vary, it could be advantageous to sample each subpopulation independently. Stratification is the process of dividing members of the population into homogeneous subgroups before sampling; the strata should be mutually exclusive: every element in the population must be assigned to only one stratum. The strata should be collectively exhaustive: no population element can be excluded. Simple random sampling or systematic sampling is applied within each stratum; the objective is to improve the precision of the sample by reducing sampling error. It can produce a weighted mean that has less variability than the arithmetic mean of a simple random sample of the population. In computational statistics, stratified sampling is a method of variance reduction when Monte Carlo methods are used to estimate population statistics from a known population. Assume that we need to estimate average number of votes for each candidate in an election.
Assume that country has 3 towns: Town A has 1 million factory workers, Town B has 2 million office workers and Town C has 3 million retirees. We can choose to get a random sample of size 60 over the entire population but there is some chance that the random sample turns out to be not well balanced across these towns and hence is biased causing a significant error in estimation. Instead if we choose to take a random sample of 10, 20 and 30 from Town A, B and C then we can produce a smaller error in estimation for the same total size of sample. Proportionate allocation uses a sampling fraction in each of the strata, proportional to that of the total population. For instance, if the population consists of X total individuals, m of which are male and f female the relative size of the two samples should reflect this proportion. Optimum allocation - The sampling fraction of each stratum is proportionate to both the proportion and the standard deviation of the distribution of the variable. Larger samples are taken in the strata with the greatest variability to generate the least possible overall sampling variance.
A real-world example of using stratified sampling would be for a political survey. If the respondents needed to reflect the diversity of the population, the researcher would seek to include participants of various minority groups such as race or religion, based on their proportionality to the total population as mentioned above. A stratified survey could thus claim to be more representative of the population than a survey of simple random sampling or systematic sampling; the reasons to use stratified sampling rather than simple random sampling include If measurements within strata have lower standard deviation, stratification gives smaller error in estimation. For many applications, measurements become more manageable and/or cheaper when the population is grouped into strata, it is desirable to have estimates of population parameters for groups within the population. If the population density varies within a region, stratified sampling will ensure that estimates can be made with equal accuracy in different parts of the region, that comparisons of sub-regions can be made with equal statistical power.
For example, in Ontario a survey taken throughout the province might use a larger sampling fraction in the less populated north, since the disparity in population between north and south is so great that a sampling fraction based on the provincial sample as a whole might result in the collection of only a handful of data from the north. Stratified sampling is not useful when the population cannot be exhaustively partitioned into disjoint subgroups, it would be a misapplication of the technique to make subgroups' sample sizes proportional to the amount of data available from the subgroups, rather than scaling sample sizes to subgroup sizes. Data representing each subgroup are taken to be of equal importance if suspected variation among them warrants stratified sampling. If subgroup variances differ and the data needs to be stratified by variance, it is not possible to make each subgroup sample size proportional to subgroup size within the total population. For an efficient way to partition sampling resources among groups that vary in their means and costs, see "optimum allocation".
The problem of stratified sampling in the case of unknown class priors can have deleterious effect on the performance of any analysis on the dataset, e.g. classification. In that regard, minimax sampling ratio can be used to make the dataset robust with respect to uncertainty in the underlying data generating process. Combining sub-strata to ensure adequate numbers can lead to Simpson's paradox, where trends that exist in different groups of data disappear or reverse when the groups are combined; the mean and variance of stratified random sampling are given by: x ¯ = 1 N ∑ h = 1 L N h x h ¯ s x ¯ 2 = ∑ h = 1 L 2 ( N h − n
Science is a systematic enterprise that builds and organizes knowledge in the form of testable explanations and predictions about the universe. The earliest roots of science can be traced to Ancient Egypt and Mesopotamia in around 3500 to 3000 BCE, their contributions to mathematics and medicine entered and shaped Greek natural philosophy of classical antiquity, whereby formal attempts were made to explain events of the physical world based on natural causes. After the fall of the Western Roman Empire, knowledge of Greek conceptions of the world deteriorated in Western Europe during the early centuries of the Middle Ages but was preserved in the Muslim world during the Islamic Golden Age; the recovery and assimilation of Greek works and Islamic inquiries into Western Europe from the 10th to 13th century revived natural philosophy, transformed by the Scientific Revolution that began in the 16th century as new ideas and discoveries departed from previous Greek conceptions and traditions. The scientific method soon played a greater role in knowledge creation and it was not until the 19th century that many of the institutional and professional features of science began to take shape.
Modern science is divided into three major branches that consist of the natural sciences, which study nature in the broadest sense. There is disagreement, however, on whether the formal sciences constitute a science as they do not rely on empirical evidence. Disciplines that use existing scientific knowledge for practical purposes, such as engineering and medicine, are described as applied sciences. Science is based on research, conducted in academic and research institutions as well as in government agencies and companies; the practical impact of scientific research has led to the emergence of science policies that seek to influence the scientific enterprise by prioritizing the development of commercial products, health care, environmental protection. Science in a broad sense existed in many historical civilizations. Modern science is distinct in its approach and successful in its results, so it now defines what science is in the strictest sense of the term. Science in its original sense was a word for a type of knowledge, rather than a specialized word for the pursuit of such knowledge.
In particular, it was the type of knowledge which people can communicate to share. For example, knowledge about the working of natural things was gathered long before recorded history and led to the development of complex abstract thought; this is shown by the construction of complex calendars, techniques for making poisonous plants edible, public works at national scale, such as those which harnessed the floodplain of the Yangtse with reservoirs and dikes, buildings such as the Pyramids. However, no consistent conscious distinction was made between knowledge of such things, which are true in every community, other types of communal knowledge, such as mythologies and legal systems. Metallurgy was known in prehistory, the Vinča culture was the earliest known producer of bronze-like alloys, it is thought that early experimentation with heating and mixing of substances over time developed into alchemy. Neither the words nor the concepts "science" and "nature" were part of the conceptual landscape in the ancient near east.
The ancient Mesopotamians used knowledge about the properties of various natural chemicals for manufacturing pottery, glass, metals, lime plaster, waterproofing. The Mesopotamians had intense interest in medicine and the earliest medical prescriptions appear in Sumerian during the Third Dynasty of Ur. Nonetheless, the Mesopotamians seem to have had little interest in gathering information about the natural world for the mere sake of gathering information and only studied scientific subjects which had obvious practical applications or immediate relevance to their religious system. In the classical world, there is no real ancient analog of a modern scientist. Instead, well-educated upper-class, universally male individuals performed various investigations into nature whenever they could afford the time. Before the invention or discovery of the concept of "nature" by the Pre-Socratic philosophers, the same words tend to be used to describe the natural "way" in which a plant grows, the "way" in which, for example, one tribe worships a particular god.
For this reason, it is claimed these men were the first philosophers in the strict sense, the first people to distinguish "nature" and "convention." Natural philosophy, the precursor of natural science, was thereby distinguished as the knowledge of nature and things which are true for every community, the name of the specialized pursuit of such knowledge was philosophy – the realm of the first philosopher-physicists. They were speculators or theorists interested in astronomy. In contrast, trying to use knowledge of nature to imitate nature was seen by classical scientists as a more appropriate interest for lower class artisans; the early Greek philosophers of the Milesian school, founded by Thales of Miletus and continued by his successors A
In statistics, quality assurance, survey methodology, sampling is the selection of a subset of individuals from within a statistical population to estimate characteristics of the whole population. Statisticians attempt for the samples to represent the population in question. Two advantages of sampling are lower cost and faster data collection than measuring the entire population; each observation measures one or more properties of observable bodies distinguished as independent objects or individuals. In survey sampling, weights can be applied to the data to adjust for the sample design in stratified sampling. Results from probability theory and statistical theory are employed to guide the practice. In business and medical research, sampling is used for gathering information about a population. Acceptance sampling is used to determine if a production lot of material meets the governing specifications. Successful statistical practice is based on focused problem definition. In sampling, this includes defining the "population".
A population can be defined as including all people or items with the characteristic one wishes to understand. Because there is rarely enough time or money to gather information from everyone or everything in a population, the goal becomes finding a representative sample of that population. Sometimes what defines. For example, a manufacturer needs to decide whether a batch of material from production is of high enough quality to be released to the customer, or should be sentenced for scrap or rework due to poor quality. In this case, the batch is the population. Although the population of interest consists of physical objects, sometimes it is necessary to sample over time, space, or some combination of these dimensions. For instance, an investigation of supermarket staffing could examine checkout line length at various times, or a study on endangered penguins might aim to understand their usage of various hunting grounds over time. For the time dimension, the focus may be on discrete occasions.
In other cases, the examined'population' may be less tangible. For example, Joseph Jagger studied the behaviour of roulette wheels at a casino in Monte Carlo, used this to identify a biased wheel. In this case, the'population' Jagger wanted to investigate was the overall behaviour of the wheel, while his'sample' was formed from observed results from that wheel. Similar considerations arise when taking repeated measurements of some physical characteristic such as the electrical conductivity of copper; this situation arises when seeking knowledge about the cause system of which the observed population is an outcome. In such cases, sampling theory may treat the observed population as a sample from a larger'superpopulation'. For example, a researcher might study the success rate of a new'quit smoking' program on a test group of 100 patients, in order to predict the effects of the program if it were made available nationwide. Here the superpopulation is "everybody in the country, given access to this treatment" – a group which does not yet exist, since the program isn't yet available to all.
Note that the population from which the sample is drawn may not be the same as the population about which information is desired. There is large but not complete overlap between these two groups due to frame issues etc.. Sometimes they may be separate – for instance, one might study rats in order to get a better understanding of human health, or one might study records from people born in 2008 in order to make predictions about people born in 2009. Time spent in making the sampled population and population of concern precise is well spent, because it raises many issues and questions that would otherwise have been overlooked at this stage. In the most straightforward case, such as the sampling of a batch of material from production, it would be most desirable to identify and measure every single item in the population and to include any one of them in our sample. However, in the more general case this is not possible or practical. There is no way to identify all rats in the set of all rats. Where voting is not compulsory, there is no way to identify which people will vote at a forthcoming election.
These imprecise populations are not amenable to sampling in any of the ways below and to which we could apply statistical theory. As a remedy, we seek a sampling frame which has the property that we can identify every single element and include any in our sample; the most straightforward type of frame is a list of elements of the population with appropriate contact information. For example, in an opinion poll, possible sampling frames include an electoral register and a telephone directory. A probability sample is a sample in which every unit in the population has a chance of being selected in the sample, this probability can be determined; the combination of these traits makes it possible to produce unbiased estimates of population totals, by weighting sampled units according to their probability of selection. Example: We want to estimate the total income of adults living in a given street. We visit each household in that street, identify all adults living there, randomly select one adult from each household..
We interview the selected person and find their income
Biometrics is the technical term for body measurements and calculations. It refers to metrics related to human characteristics. Biometrics authentication is used in computer science as a form of identification and access control, it is used to identify individuals in groups that are under surveillance. Biometric identifiers are the distinctive, measurable characteristics used to label and describe individuals. Biometric identifiers are categorized as physiological versus behavioral characteristics. Physiological characteristics are related to the shape of the body. Examples include, but are not limited to fingerprint, palm veins, face recognition, DNA, palm print, hand geometry, iris recognition and odour/scent. Behavioral characteristics are related to the pattern of behavior of a person, including but not limited to typing rhythm and voice; some researchers have coined the term behaviometrics to describe the latter class of biometrics. More traditional means of access control include token-based identification systems, such as a driver's license or passport, knowledge-based identification systems, such as a password or personal identification number.
Since biometric identifiers are unique to individuals, they are more reliable in verifying identity than token and knowledge-based methods. Many different aspects of human physiology, chemistry or behavior can be used for biometric authentication; the selection of a particular biometric for use in a specific application involves a weighting of several factors. Jain et al. identified seven such factors to be used when assessing the suitability of any trait for use in biometric authentication. Universality means. Uniqueness means the trait should be sufficiently different for individuals in the relevant population such that they can be distinguished from one another. Permanence relates to the manner. More a trait with'good' permanence will be reasonably invariant over time with respect to the specific matching algorithm. Measurability relates to the ease of measurement of the trait. In addition, acquired data should be in a form that permits subsequent processing and extraction of the relevant feature sets.
Performance relates to the accuracy and robustness of technology used. Acceptability relates to how well individuals in the relevant population accept the technology such that they are willing to have their biometric trait captured and assessed. Circumvention relates to the ease with which a trait might be imitated using an artifact or substitute. Proper biometric use is application dependent. Certain biometrics will be better than others based on the required levels of convenience and security. No single biometric will meet all the requirements of every possible application; the block diagram illustrates the two basic modes of a biometric system. First, in verification mode the system performs a one-to-one comparison of a captured biometric with a specific template stored in a biometric database in order to verify the individual is the person they claim to be. Three steps are involved in the verification of a person. In the first step, reference models for all the users are generated and stored in the model database.
In the second step, some samples are matched with reference models to generate the genuine and impostor scores and calculate the threshold. Third step is the testing step; this process may use a smart card, username or ID number to indicate which template should be used for comparison.'Positive recognition' is a common use of the verification mode, "where the aim is to prevent multiple people from using the same identity". Second, in identification mode the system performs a one-to-many comparison against a biometric database in an attempt to establish the identity of an unknown individual; the system will succeed in identifying the individual if the comparison of the biometric sample to a template in the database falls within a set threshold. Identification mode can be used either for'positive recognition' or for'negative recognition' of the person "where the system establishes whether the person is who she denies to be"; the latter function can only be achieved through biometrics since other methods of personal recognition such as passwords, PINs or keys are ineffective.
The first time an individual uses a biometric system is called enrollment. During the enrollment, biometric information from an individual is stored. In subsequent uses, biometric information is detected and compared with the information stored at the time of enrollment. Note that it is crucial that storage and retrieval of such systems themselves be secure if the biometric system is to be robust; the first block is the interface between the system. Most of the times it is an image acquisition system, but it can change according to the characteristics desired; the second block performs all the necessary pre-processing: it has to remove artifacts from the sensor, to enhance the input, to use some kind of normalization, etc. In the third block necessary features are extracted; this step is an important step. A vector of numbers or an image with particular properties is used to create a template. A template is a synthesis of the relevant characteristics
Humanities are academic disciplines that study aspects of human society and culture. In the Renaissance, the term contrasted with divinity and referred to what is now called classics, the main area of secular study in universities at the time. Today, the humanities are more contrasted with natural, sometimes social, sciences as well as professional training; the humanities use methods that are critical, or speculative, have a significant historical element—as distinguished from the empirical approaches of the natural sciences, unlike the sciences, it has no central discipline. The humanities include ancient and modern languages, philosophy, human geography, politics and art. Scholars in the humanities are humanists; the term "humanist" describes the philosophical position of humanism, which some "antihumanist" scholars in the humanities reject. The Renaissance scholars and artists were called humanists; some secondary schools offer humanities classes consisting of literature, global studies and art.
Human disciplines like history and cultural anthropology study subject matters that the manipulative experimental method does not apply to—and instead use the comparative method and comparative research. Anthropology is a science of the totality of human existence; the discipline deals with the integration of different aspects of the social sciences and human biology. In the twentieth century, academic disciplines have been institutionally divided into three broad domains; the natural sciences seek to derive general laws through verifiable experiments. The humanities study local traditions, through their history, literature and arts, with an emphasis on understanding particular individuals, events, or eras; the social sciences have attempted to develop scientific methods to understand social phenomena in a generalizable way, though with methods distinct from those of the natural sciences. The anthropological social sciences develop nuanced descriptions rather than the general laws derived in physics or chemistry, or they may explain individual cases through more general principles, as in many fields of psychology.
Anthropology does not fit into one of these categories, different branches of anthropology draw on one or more of these domains. Within the United States, anthropology is divided into four sub-fields: archaeology, physical or biological anthropology, anthropological linguistics, cultural anthropology, it is an area, offered at most undergraduate institutions. The word anthropos is from the Greek for "human being" or "person". Eric Wolf described sociocultural anthropology as "the most scientific of the humanities, the most humanistic of the sciences"; the goal of anthropology is to provide a holistic account of human nature. This means that, though anthropologists specialize in only one sub-field, they always keep in mind the biological, linguistic and cultural aspects of any problem. Since anthropology arose as a science in Western societies that were complex and industrial, a major trend within anthropology has been a methodological drive to study peoples in societies with more simple social organization, sometimes called "primitive" in anthropological literature, but without any connotation of "inferior".
Today, anthropologists use terms such as "less complex" societies, or refer to specific modes of subsistence or production, such as "pastoralist" or "forager" or "horticulturalist", to discuss humans living in non-industrial, non-Western cultures, such people or folk remaining of great interest within anthropology. The quest for holism leads most anthropologists to study a people in detail, using biogenetic and linguistic data alongside direct observation of contemporary customs. In the 1990s and 2000s, calls for clarification of what constitutes a culture, of how an observer knows where his or her own culture ends and another begins, other crucial topics in writing anthropology were heard, it is possible to view all human cultures as part of one large. These dynamic relationships, between what can be observed on the ground, as opposed to what can be observed by compiling many local observations remain fundamental in any kind of anthropology, whether cultural, linguistic or archaeological.
Archaeology is the study of human activity through the analysis of material culture. The archaeological record consists of artifacts, biofacts or ecofacts, cultural landscapes. Archaeology can be considered a branch of the humanities, it has various goals, which range from understanding culture history to reconstructing past lifeways to documenting and explaining changes in human societies through time. Archaeology is thought of as a branch of anthropology in the United States, while in Europe, it is viewed as a discipline in its own right, or grouped under other related disciplines such as history. Classics, in the Western academic tradition, refers to the studies of the cultures of classical antiquity, namely Ancient Greek and Latin and the Ancient Greek and Roman cultures. Classical studies is considered one of the cornerstones of the humanities; the influence of classical ideas on many humanities disciplines, such as philosophy and literature, remains strong. History is systematically collected information about the past.
When used as the name of a field of study, history refers to the study and interpretation of the record of humans, societies and any to
Survivorship bias or survival bias is the logical error of concentrating on the people or things that made it past some selection process and overlooking those that did not because of their lack of visibility. This can lead to false conclusions in several different ways, it is a form of selection bias. Survivorship bias can lead to overly optimistic beliefs because failures are ignored, such as when companies that no longer exist are excluded from analyses of financial performance, it can lead to the false belief that the successes in a group have some special property, rather than just coincidence. For example, if three of the five students with the best college grades went to the same high school, that can lead one to believe that the high school must offer an excellent education; this could be true, but the question cannot be answered without looking at the grades of all the other students from that high school, not just the ones who "survived" the top-five selection process. In finance, survivorship bias is the tendency for failed companies to be excluded from performance studies because they no longer exist.
It causes the results of studies to skew higher because only companies which were successful enough to survive until the end of the period are included. For example, a mutual fund company's selection of funds today will include only those that are successful now. Many losing funds are merged into other funds to hide poor performance. In theory, 90% of extant funds could truthfully claim to have performance in the first quartile of their peers, if the peer group includes funds that have closed. In 1996, Elton and Blake showed that survivorship bias is larger in the small-fund sector than in large mutual funds, they estimate the size of the bias across the U. S. mutual fund industry as 0.9% per annum, where the bias is defined and measured as: "Bias is defined as average α for surviving funds minus average α for all funds". Additionally, in quantitative backtesting of market performance or other characteristics, survivorship bias is the use of a current index membership set rather than using the actual constituent changes over time.
Consider a backtest to 1990 to find the average performance of S&P 500 members who have paid dividends within the previous year. To use the current 500 members only and create a historical equity line of the total return of the companies that met the criteria would be adding survivorship bias to the results. S&P maintains an index of healthy companies, removing companies that no longer meet their criteria as a representative of the large-cap U. S. stock market. Companies that had healthy growth on their way to inclusion in the S&P 500 would be counted as if they were in the index during that growth period, which they were not. Instead there may have been another company in the index, losing market capitalization and was destined for the S&P 600 Small-cap Index, removed and would not be counted in the results. Using the actual membership of the index and applying entry and exit dates to gain the appropriate return during inclusion in the index would allow for a bias-free output. Michael Shermer in Scientific American and Larry Smith of the University of Waterloo have described how advice about commercial success distorts perceptions of it by ignoring all of the businesses and college dropouts that failed.
Journalist and author David McRaney observes that the "advice business is a monopoly run by survivors. When something becomes a non-survivor, it is either eliminated, or whatever voice it has is muted to zero". In his book The Black Swan, financial writer Nassim Taleb called the data obscured by survivorship bias "silent evidence." Diogenes was asked concerning paintings of those who had escaped shipwreck: "Look, you who think the gods have no care of human things, what do you say to so many persons preserved from death by their especial favour?", to which Diogenes replied: "Why, I say that their pictures are not here who were cast away, who are by much the greater number." Susan Mumm has described how survival bias leads historians to study organisations that are still in existence more than those which have closed. This means large, successful organisations such as the Women's Institute, which were well organised and still have accessible archives for historians to work from, are studied more than smaller charitable organisations though these may have done a great deal of work.
A held opinion in many populations is that machinery and goods manufactured in previous generations is better built and lasts longer than similar contemporary items.. Again, because of the selective pressures of time and use, it is inevitable that only those items which were built to last will have survived into the present day. Therefore, most of the old machinery still seen functioning well in the present day must have been built to a standard of quality necessary to survive. All of the machinery and goods that have failed over the intervening years are no longer visible to the general population as they have been junked, recycled, or otherwise disposed of. Though survivorship bias may explain a significant portion of the common perception that older manufacturing processes were more rigorous, there are other processes that may explain that perception, such as planned obsolescence and overengineering, it is difficult to directly compare and determine whether manufacturing has become overall better or worse
In statistics, sampling bias is a bias in which a sample is collected in such a way that some members of the intended population are less to be included than others. It results in a biased sample, a non-random sample of a population in which all individuals, or instances, were not likely to have been selected. If this is not accounted for, results can be erroneously attributed to the phenomenon under study rather than to the method of sampling. Medical sources sometimes refer to sampling bias as ascertainment bias. Ascertainment bias has the same definition, but is still sometimes classified as a separate type of bias. Sampling bias is classified as a subtype of selection bias, sometimes termed sample selection bias, but some classify it as a separate type of bias. A distinction, albeit not universally accepted, of sampling bias is that it undermines the external validity of a test, while selection bias addresses internal validity for differences or similarities found in the sample at hand. In this sense, errors occurring in the process of gathering the sample or cohort cause sampling bias, while errors in any process thereafter cause selection bias.
However, selection bias and sampling bias are used synonymously. Selection from a specific real area. For example, a survey of high school students to measure teenage use of illegal drugs will be a biased sample because it does not include home-schooled students or dropouts. A sample is biased if certain members are underrepresented or overrepresented relative to others in the population. For example, a "man on the street" interview which selects people who walk by a certain location is going to have an overrepresentation of healthy individuals who are more to be out of the home than individuals with a chronic illness; this may be an extreme form of biased sampling, because certain members of the population are excluded from the sample. Self-selection bias, possible whenever the group of people being studied has any form of control over whether to participate. Participants' decision to participate may be correlated with traits that affect the study, making the participants a non-representative sample.
For example, people who have strong opinions or substantial knowledge may be more willing to spend time answering a survey than those who do not. Another example is online and phone-in polls, which are biased samples because the respondents are self-selected; those individuals who are motivated to respond individuals who have strong opinions, are overrepresented, individuals that are indifferent or apathetic are less to respond. This leads to a polarization of responses with extreme perspectives being given a disproportionate weight in the summary; as a result, these types of polls are regarded as unscientific. Pre-screening of trial participants, or advertising for volunteers within particular groups. For example, a study to "prove" that smoking does not affect fitness might recruit at the local fitness center, but advertise for smokers during the advanced aerobics class, for non-smokers during the weight loss sessions. Exclusion bias results from exclusion of particular groups from the sample, e.g. exclusion of subjects who have migrated into the study area.
Excluding subjects who move out of the study area during follow-up is rather equivalent of dropout or nonresponse, a selection bias in that it rather affects the internal validity of the study. Healthy user bias, when the study population is healthier than the general population. For example, someone in poor health is unlikely to have a job as manual laborer. Berkson's fallacy, when the study population is selected from a hospital and so is less healthy than the general population; this can result in a spurious negative correlation between diseases: a hospital patient without diabetes is more to have another given disease such as cholecystitis, since they must have had some reason to enter the hospital in the first place. Overmatching, matching for an apparent confounder, a result of the exposure; the control group becomes more similar to the cases in regard to exposure than does the general population. Survivorship bias, in which only "surviving" subjects are selected, ignoring those that fell out of view.
For example, using the record of current companies as an indicator of business climate or economy ignores the businesses that failed and no longer exist. Malmquist bias, an effect in observational astronomy which leads to the preferential detection of intrinsically bright objects; the study of medical conditions begins with anecdotal reports. By their nature, such reports only include those referred for treatment. A child who can't function in school is more to be diagnosed with dyslexia than a child who struggles but passes. A child examined for one condition is more to be tested for and diagnosed with other conditions, skewing comorbidity statistics; as certain diagnoses become associated with behavior problems or intellectual disability, parents try to prevent their children from being stigmatized with those diagnoses, introducing further bias. Studies selected from whole populations are showing that many conditions are much more common and much milder than believed. Geneticists are limited in.
As an example, consider a h