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# examples quota sampling

From Wikipedia

Quota sampling

Quota sampling is a method for selecting survey participants. In quota sampling, a population is first segmented into mutually exclusive sub-groups, just as in stratified sampling. Then judgment is used to select the subjects or units from each segment based on a specified proportion. For example, an interviewer may be told to sample 200 females and 300 males between the age of 45 and 60. This means that individuals can put a demand on who they want to sample (targeting)

This second step makes the technique non-probability sampling. In quota sampling, the selection of the sample is non-random unlike random sampling and can often be found unreliable. For example interviewers might be tempted to interview those people in the street who look most helpful, or may choose to use accidental sampling to question those closest to them, for time-keeping sake. The problem is that these samples may be biased because not everyone gets a chance of selection. This non-random element is its greatest weakness and quota versus probability has been a matter of controversy for many years.

Quota sampling is useful when time is limited, a sampling frame is not available, the research budget is very tight or when detailed accuracy is not important. You can also choose how many of each category is selected.

A quota sample is a convenience sample, with an effort made to ensure a certain distribution of demographic variables. Subjects are recruited as they arrive, and the researcher assigns them to demographic groups based on variables like age and gender. When the quota for a given demographic group is filled, the researcher stops recruiting subjects from that particular group.

This is the non probability version of stratified sampling. Subsets are chosen and then either convenience or judgment sampling is used to choose people from each subset.

Stratified sampling is probably the most commonly used probability method. Subsets of the population are created so that each subset has a common characteristic, such as gender. Random sampling chooses a number of subjects from each subset.

Sample mean and sample covariance

The sample mean or empirical mean and the sample covariance are statistics computed from a collection of data.

## Sample mean and covariance

Given a random sample \textstyle \mathbf{x}_{1},\ldots,\mathbf{x}_{N} from an \textstyle n-dimensional random variable \textstyle \mathbf{X} (i.e., realizations of \textstyle N independent random variables with the same distribution as \textstyle \mathbf{X}), the sample mean is

\mathbf{\bar{x}}=\frac{1}{N}\sum_{k=1}^{N}\mathbf{x}_k.

In coordinates, writing the vectors as columns,

\mathbf{x}_{k}=\left[ \begin{array} [c]{c}x_{1k}\\ \vdots\\ x_{nk}\end{array} \right] ,\quad\mathbf{\bar{x}}=\left[ \begin{array} [c]{c}\bar{x}_1 \\ \vdots\\ \bar{x}_n \end{array} \right] ,

the entries of the sample mean are

The sample covariance of \textstyle \mathbf{x}_{1},\ldots,\mathbf{x}_{N} is the n-by-nmatrix \textstyle \mathbf{Q}=\left[ q_{ij}\right] with the entries given by

q_{ij}=\frac{1}{N-1}\sum_{k=1}^{N}\left( x_{ik}-\bar{x}_i \right) \left( x_{jk}-\bar{x}_j \right) .

The sample mean and the sample covariance matrix are unbiased estimates of the mean and the covariance matrix of the random variable \textstyle \mathbf{X}. The reason why the sample covariance matrix has \textstyle N-1 in the denominator rather than \textstyle N is essentially that the population mean E(X) is not known and is replaced by the sample mean \textstyle\bar{x}. If the population mean E(X) is known, the analogous unbiased estimate

q_{ij}=\frac{1}{N}\sum_{k=1}^N \left( x_{ik}-E(X_i)\right) \left( x_{jk}-E(X_j)\right)

with the population mean indeed does have \textstyle N. This is an example why in probability and statistics it is essential to distinguish between upper case letters (random variables) and lower case letters (realizations of the random variables).

q_{ij}=\frac{1}{N}\sum_{k=1}^N \left( x_{ik}-\bar{x}_i \right) \left( x_{jk}-\bar{x}_j \right)

for the Gaussian distribution case has N as well. The ratio of 1/N to 1/(N&nbsp;&minus;&nbsp;1) approaches 1 for large&nbsp;N, so the maximum likelihood estimate approximately equals the unbiased estimate when the sample is large.

## Weighted samples

In a weighted sample, each vector \textstyle \textbf{x}_{k} is assigned a weight \textstyle w_k \geq0. Without loss of generality, assume that the weights are normalized:

\sum_{k=1}^{N}w_k = 1.

(If they are not, divide the weights by their sum.) Then the weighted mean \textstyle \mathbf{\bar{x}} and the weighted covariance matrix \textstyle \mathbf{Q}=\left[ q_{ij}\right] are given by

\mathbf{\bar{x}}=\sum_{k=1}^N w_k \mathbf{x}_k

and

q_{ij}=\frac{\sum_{k=1}^N w_k \left( x_{ki}-\bar{x}_i \right) \left( x_{kj}-\bar{x}_j \right) }{1-\sum_{k=1}^{N}w_k^2}.

If all weights are the same, \textstyle w_{k}=1/N, the weighted mean and covariance reduce to the sample mean and covariance above.

## Criticism

The sample mean and sample covariance are widely used in statistics and applications, and are extremely common measures of location and dispersion, respectively, likely the most common: they are easily calculated and possess desirable characteristics.

However, they suffer from certain drawbacks; notably, they are not robust statistics, meaning that they are thrown off by outliers. As robustness is often a desired trait, particularly in real-world applications, robust alternatives may prove desirable, notably quantile-based statistics such the sample median for location, and interquartile range (IQR) for dispersion. Other alternatives include trimming and Winsorising, as in the trimmed mean and the Winsorized mean.

Accidental sampling

Accidental sampling is a type of nonprobability sampling which involves the sample being drawn from that part of the population which is close to hand. That is, a sample population selected because it is readily available and convenient. The researcher using such a sample cannot scientifically make generalizations about the total population from this sample because it would not be representative enough. For example, if the interviewer was to conduct such a survey at a shopping center early in the morning on a given day, the people that he/she could interview would be limited to those given there at that given time, which would not represent the views of other members of society in such an area, if the survey was to be conducted at different times of day and several times per week. This type of sampling is most useful for pilot testing.

Sampling risk

In auditing, sampling is an inevitable means of testing. However, sampling is always associated with sampling risks which auditors have to control.

Sampling risk represents the possibility that auditor's conclusion based on a sample is different from that reached if the entire population were subject to audit procedure. The auditor may conclude that material misstatements exist, in fact they do not; or material misstatements do not exist but in fact they do exist. Auditor can lower the sampling risk by increasing the sampling size.

Non-sampling risk includes factors that cause auditors to reach a conclusion other than the sampling size. Misinterpretation of evidence and inappropriate procedures are good examples. Changing of the sampling size would not reduce non-sampling risk.

Answers:easier to do since the data taker is given a certain quota to fill in a given sub-population and but he/she is free to choose which individual or unit to take data from. fast and cheap. but give up some of the statistical strength of randomness.

Question:I'm doing Sociology coursework and need a definition.

Question:And can you please explain the situation which can lead to the method of systematic sampling being biased. WIll choose a best answer. Thanks In Advance