Statistical Science

Definition

The process of posing questions and then seeking to answer them by collecting and analyzing suitable data is an essential component of research in a remarkably diverse array of fields.

Statistics Division

Descriptive Statistics

Inferential Statistics

capture general trends within the data and are calculated and expressed as the mean, median, and mode. Measures of spread describe how the data are distributed and relate to each other. Measures of spread are often visually represented in tables, pie and bar charts, and histograms to aid in the understanding of the trends within the data.

Inferential statistics are produced through complex mathematical calculations that allow scientists to infer trends about a larger population based on a study of a sample taken from it. This information about a population is not stated as a number. Instead, scientists express these parameters as a range of potential numbers, along with a degree of confidence.

Importance and aplications

Is to determine, for a given question, the type of data that is needed, the way it should be collected and how it should be analyzed in order to best answer that question.
It can be aplicated to agriculture, medical research, industrial research, forensic science, market research, environmental science, political science and quality assurance. Basically every topic you can imagine.

Definition of population and sample

Population

Sample

A population is any specific collection of objects of interest. A sample is any subset or subcollection of the population, including the case that the sample consists of the whole population, in which case it is termed a census.

A measurement is a number or attribute computed for each member of a population or of a sample. The measurements of sample elements are collectively called the sample data.

Variables and types

Measurement scales

Types of sampling

There are four levels of measurement: Nominal, Ordinal, Interval, and Ratio. These go from lowest level to highest level. Data is classified according to the highest level which it fits. Each additional level adds something the previous level didn't have.

There are five types of sampling: Random, Systematic, Convenience, Cluster, and Stratified.

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Nominal: Categorical data and numbers that are simply used as
identifiers or names represent a nominal scale of measurement.

Ordinal: An ordinal scale of measurement represents an ordered
series of relationships or rank order.

Interval: A scale which represents quantity and has equal units
but for which zero represents simply an additional point of
measurement is an interval scale.

Ratio: The ratio scale of measurement is similar to the interval
scale in that it also represents quantity and has equality of units.

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Random sampling is analogous to putting everyone's name into a hat and drawing out several names. Each element in the population has an equal chance of occuring. While this is the preferred way of sampling, it is often difficult to do. It requires that a complete list of every element in the population be obtained.

Systematic sampling is easier to do than random sampling. In systematic sampling, the list of elements is "counted off".

Convenience sampling is very easy to do, but it's probably the worst technique to use. In convenience sampling, readily available data is used. That is, the first people the surveyor runs into.

Cluster sampling is accomplished by dividing the population into groups -- usually geographically. These groups are called clusters or blocks. The clusters are randomly selected, and each element in the selected clusters are used.

Stratified sampling also divides the population into groups called strata. However, this time it is by some characteristic, not geographically. For instance, the population might be separated into males and females. A sample is taken from each of these strata using either random, systematic, or convenience sampling.