Matching To Sample Generalization Essay

What is a 'Representative Sample'

A representative sample is a small quantity of something that accurately reflects the larger entity. An example is when a small number of people accurately reflect the members of an entire population. In a classroom of 30 students, in which half the students are male and half are female, a representative sample might include six students: three males and three females.

BREAKING DOWN 'Representative Sample'

When a sample is not representative, the result is known as a sampling error. Using the classroom example again, a sample that includes six students, all of whom are male, would not be a representative sample.

A representative sample parallels the key variables and characteristics under examination. Some examples include sex, age, education level, socioeconomic status or marital status. Using a larger sample size increases the likelihood that the sample more accurately reflects what actually exists in the population. Any information collection with biased tendencies is unable to generate a representative sample.

Reasons to Use a Representative Sample

A representative sample allows the collected results to be generalized to a larger population. For most marketing or psychology studies, it is impractical in terms of time, finances and effort to collect data on every person in the target population. This is especially impractical for large population such as an entire country or race.

Risks of Using Samples

The use of sample groups poses risks, as the sample may not accurately reflect the views of the general population. One of the largest risks is developing a sample that is not truly representative. This most likely occurs because the population group is too small. For example, when comparing data relating to gender, a representative sample must include individuals of different ages, economic status and geographical locations. Such information typically requires a diversification of information-collecting sites.

Random Sampling and Purposive Sampling

Random sampling involves choosing respondents from the target population at random, to minimize bias in a representative sample. While this method is more expensive and requires more upfront information, the information yielded is typically of higher quality. Purposive sampling is more widely used, and occurs when the managers target individuals matching certain criteria for information extraction. Ideal interview candidates receive profiles. Although this leads to the potential of bias in the representative sample, the information is easier to collect, and the sampler has more control when creating the representative sample.

True Representative Samples Cannot Exist

When developing a survey, the manager must utilize controls to track and monitor who has provided input, whether the information is usable, and whether it can be interpreted. Random sampling ensures every member of the population has equal probability of selection and inclusion in the sample group. However, sample bias is always present and can never truly be eliminated. For example, individuals who are too busy to participate will be under-represented in the representative sample, as they are less likely to provide feedback.

For the term in the context of mathematical formal logic, see Universal generalization.

For other uses, see Generalization (disambiguation).

A generalization (or generalisation) is the formulation of general concepts from specific instances by abstracting common properties. Generalizations posit the existence of a domain or set of elements, as well as one or more common characteristics shared by those elements (thus creating a conceptual model). As such, they are the essential basis of all valid deductive inferences. The process of verification is necessary to determine whether a generalization holds true for any given situation.

Generalization is the process of identifying the parts of a whole, as belonging to the whole. The parts, completely unrelated may be brought together as a group, belonging to the whole by establishing a common relation between them.

It must be stated that, the parts cannot be generalized into a whole until a common relation is established among all the parts. But this does not mean that the parts are unrelated, only that no common relation has been established yet for the generalization.

The concept of generalization has broad application in many connected disciplines, sometimes having a specialized context or meaning.

Of any two related concepts, such as A and B, A is a "generalization" of B, and B is a special case of A, if and only if

  • every instance of concept B is also an instance of concept A; and
  • there are instances of concept A which are not instances of concept B.

For instance, animal is a generalization of bird because every bird is an animal, and there are animals which are not birds (dogs, for instance). (See also: Specialisation (biology)).

Hypernym and hyponym[edit]

See also: Semantic change

The connection of generalization to specialization (or particularization) is reflected in the contrasting words hypernym and hyponym. A hypernym as a generic stands for a class or group of equally ranked items—for example, tree stands for equally ranked items such as peach and oak, and ship stands for equally ranked items such as cruiser and steamer. In contrast, a hyponym is one of the items included in the generic, such as peach and oak which are included in tree, and cruiser and steamer which are included in ship. A hypernym is superordinate to a hyponym, and a hyponym is subordinate to a hypernym.

Examples[edit]

Biological generalization[edit]

An animal is a generalization of a mammal, a bird, a fish, an amphibian and a reptile.

Cartographic generalization of geo-spatial data[edit]

Main article: Cartographic generalization

Generalization has a long history in cartography as an art of creating maps for different scale and purpose. Cartographic generalization is the process of selecting and representing information of a map in a way that adapts to the scale of the display medium of the map. In this way, every map has, to some extent, been generalized to match the criteria of display. This includes small cartographic scale maps, which cannot convey every detail of the real world. Cartographers must decide and then adjust the content within their maps to create a suitable and useful map that conveys geospatial information within their representation of the world.

Generalization is meant to be context-specific. That is to say, correctly generalized maps are those that emphasize the most important map elements while still representing the world in the most faithful and recognizable way. The level of detail and importance in what is remaining on the map must outweigh the insignificance of items that were generalized, as to preserve the distinguishing characteristics of what makes the map useful and important.

Geometric generalizations[edit]

A polygon is a generalization of a 3-sided triangle, a 4-sided quadrilateral, and so on to n sides.

A hypercube is a generalization of a 2-dimensional square, a 3-dimensional cube, and so on to ndimensions.

A quadric, such as a hypersphere, ellipsoid, paraboloid, or hyperboloid, is a generalization of a conic section to higher dimensions.

See also[edit]

When the mind makes a generalization, it extracts the essence of a concept based on its analysis of similarities from many discrete objects. The resulting simplification enables higher-level thinking.

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