Statistical unit sample) each member of the target population has a known and non-zero probability of inclusion in the sample. A survey based on a probability sample can in theory produce statistical measurements of the target population that are: A probability-based survey sample is created by constructing a list of the target population, called the sampling frame, a randomized process for selecting units from the sample frame, called a selection procedure, and a method of contacting selected units to enable them to complete the survey, called a data collection method or mode. For some target populations this process may be 	Survey sampling
23173880	easy; for example, sampling the employees of a company by using payroll lists. However, in large, disorganized populations simply constructing a suitable sample frame is often a complex and expensive task. Common methods of conducting a probability sample of the household population in the United States are Area Probability Sampling, Random Digit Dial telephone sampling, and more recently, Address-Based Sampling. Within probability sampling, there are specialized techniques such as stratified sampling and cluster sampling that improve the precision or efficiency of the sampling process without altering the fundamental principles of probability sampling. Stratification is the process of dividing members 	Survey sampling
23173881	of the population into homogeneous subgroups before sampling, based on auxiliary information about each sample unit. The strata should be mutually exclusive: every element in the population must be assigned to only one stratum. The strata should also be collectively exhaustive: no population element can be excluded. Then methods such as simple random sampling or systematic sampling can be applied within each stratum. Stratification often improves the representativeness of the sample by reducing sampling error. Bias in probability sampling. Bias in surveys is undesirable, but often unavoidable. The major types of bias that may occur in the sampling process are	Survey sampling
23173882	: Non-probability sampling. Many surveys are not based on probability samples, but rather on finding a suitable collection of respondents to complete the survey. Some common examples of non-probability sampling are: In non-probability samples the relationship between the target population and the survey sample is immeasurable and potential bias is unknowable. Sophisticated users of non-probability survey samples tend to view the survey as an experimental condition, rather than a tool for population measurement, and examine the results for internally consistent relationships. Further reading. The textbook by Groves et alia provides an overview of survey methodology, including recent 	Survey sampling
23173883	literature on questionnaire development (informed by cognitive psychology) : The other books focus on the statistical theory of survey sampling and require some knowledge of basic statistics, as discussed in the following textbooks: The elementary book by Scheaffer et alia uses quadratic equations from high-school algebra: More mathematical statistics is required for Lohr, for Särndal et alia, and for Cochran (classic): The historically important books by Deming and Kish remain valuable for insights for social scientists (particularly about the U.S. census and the Institute for Social Research at the University of Michigan): Survey sampling In statistics, survey sampling describes the 	Survey sampling
23173884	Statistical theory Statistical theory The theory of statistics provides a basis for the whole range of techniques, in both study design and data analysis, that are used within applications of statistics. The theory covers approaches to statistical-decision problems and to statistical inference, and the actions and deductions that satisfy the basic principles stated for these different approaches. Within a given approach, statistical theory gives ways of comparing statistical procedures; it can find a best possible procedure within a given context for given statistical problems, or can provide guidance on the choice between alternative procedures. Apart from philosophical considerations about how to 	Statistical theory
23173885	make statistical inferences and decisions, much of statistical theory consists of mathematical statistics, and is closely linked to probability theory, to utility theory, and to optimization. Scope. Statistical theory provides an underlying rationale and provides a consistent basis for the choice of methodology used in applied statistics. Modelling. Statistical models describe the sources of data and can have different types of formulation corresponding to these sources and to the problem being studied. Such problems can be of various kinds: Statistical models, once specified, can be tested to see whether they provide useful inferences for new data sets. Data collection. Statistical 	Statistical theory
23173886	theory provides a guide to comparing methods of data collection, where the problem is to generate informative data using optimization and randomization while measuring and controlling for observational error. Optimization of data collection reduces the cost of data while satisfying statistical goals, while randomization allows reliable inferences. Statistical theory provides a basis for good data collection and the structuring of investigations in the topics of: Summarising data. The task of summarising statistical data in conventional forms (also known as descriptive statistics) is considered in theoretical statistics as a problem of defining what aspects of statistical samples need to be described 	Statistical theory
23173887	and how well they can be described from a typically limited sample of data. Thus the problems theoretical statistics considers include: Interpreting data. Besides the philosophy underlying statistical inference, statistical theory has the task of considering the types of questions that data analysts might want to ask about the problems they are studying and of providing data analytic techniques for answering them. Some of these tasks are: When a statistical procedure has been specified in the study protocol, then statistical theory provides well-defined probability statements for the method when applied to all populations that could have arisen from the 	Statistical theory
23173888	randomization used to generate the data. This provides an objective way of estimating parameters, estimating confidence intervals, testing hypotheses, and selecting the best. Even for observational data, statistical theory provides a way of calculating a value that can be used to interpret a sample of data from a population, it can provide a means of indicating how well that value is determined by the sample, and thus a means of saying corresponding values derived for different populations are as different as they might seem; however, the reliability of inferences from post-hoc observational data is often worse than for planned 	Statistical theory
23173889	randomized generation of data. Applied statistical inference. Statistical theory provides the basis for a number of data-analytic approaches that are common across scientific and social research. Interpreting data is done with one of the following approaches: Many of the standard methods for those approaches rely on certain statistical assumptions (made in the derivation of the methodology) actually holding in practice. Statistical theory studies the consequences of departures from these assumptions. In addition it provides a range of robust statistical techniques that are less dependent on assumptions, and it provides methods checking whether particular assumptions are reasonable for a given 	Statistical theory
23173890	data set. Statistical theory The theory of statistics provides a basis for the whole range of techniques, in both study design and data analysis, that are used within applications of statistics. The theory covers approaches to statistical-decision problems and to statistical inference, and the actions and deductions that satisfy the basic principles stated for these different approaches. Within a given approach, statistical theory gives ways of comparing statistical procedures; it can find a best possible procedure within a given context for given statistical problems, or can provide guidance on the choice between alternative procedures. Apart from philosophical considerations about 	Statistical theory
23173891	Statistical unit Statistical unit In statistics, a unit is one member of a set of entities being studied. It is the main source for the mathematical abstraction of a random variable". Common examples of a unit would be a single person, animal, plant, manufactured item, or country that belongs to a larger collection of such entities being studied. Experimental and sampling units. Units are often referred to as being either experimental units, sampling units or units of observation: For example, in an experiment on educational methods, methods may be applied to classrooms of students. This would make the classroom as the experimental  unit. Measurements of progress may be obtained from individual students, as observational units. But the treatment (teaching method) being applied to the class would not be applied independently to the individual students. Hence the student could not be regarded as the experimental unit. The class, or the teacher by method combination if the teacher had multiple classes, would be the appropriate experimental unit. Implementation. In most statistical studies, the goal is to generalize from the observed units to a larger set consisting of all comparable units that exist but are not directly observed. For example, if we randomly sample 100  people and ask them which candidate they intend to vote for in an election, our main interest is in the voting behavior of all eligible voters, not exclusively on the 100 observed units. In some cases, the observed units may not form a sample from any meaningful population, but rather constitute a convenience sample, or may represent the entire population of interest. In this situation, we may study the units descriptively, or we may study their dynamics over time. But it typically does not make sense to talk about generalizing to a larger population of such units. Studies involving countries  or business firms are often of this type. Clinical trials also typically use convenience samples, however the aim is often to make inferences about the effectiveness of treatments in other patients, and given the inclusion and exclusion criteria for some clinical trials, the sample may not be representative of the majority of patients with the condition or disease. In simple data sets, the units are in one-to-one correspondence with the data values. In more complex data sets, multiple measurements are made for each unit. For example, if blood pressure measurements are made daily for a week on each  subject in a study, there would be seven data values for each statistical unit. Multiple measurements taken on an individual are not independent (they will be more alike compared to measurements taken on different individuals). Ignoring these dependencies during the analysis can lead to an inflated sample size or pseudoreplication. While a "unit" is often the lowest level at which observations are made, in some cases, a "unit" can be further decomposed as a statistical assembly. Many statistical analyses use quantitative data that have units of measurement. This is a distinct and non-overlapping use of the term "unit." Units  of collection and analysis. Statistical units are divided into two. They are: Statistical unit In statistics, a unit is one member of a set of entities being studied. It is the main source for the mathematical abstraction of a "random variable". Common examples of a unit would be a single person, animal, plant, manufactured item, or country that belongs to a larger collection of such entities being studied. Experimental and sampling units. Units are often referred to as being either experimental units, sampling units or units of observation: For example, in an experiment on educational methods, methods may be applied