# Sampling and Probability (DOC)

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```					Sampling and Probability Target Population – The entire group for which a study is performed. Matched Samples – Samples in which the members are paired or matched by the researcher or in samples that are taken multiple times on the same subjects under different circumstances. Independent Samples – Samples taken from a population that have no affect on one another. Random Sampling – A sampling method where a sample is chosen from a population on a random basis or by chance thus reducing the chance of bias in the sample. Each member of the population has a known but possibly non-equal chance of being selected. Simple Random Sampling – This is a Random Sampling method where the selection of members is made by chance where every member has an equal chance of being selected. Stratified Sampling – A sampling method where the members are selected equally from among the different strata or sub-groups of a population to ensure accurate representation of the population. Cluster Sampling – A sampling method whereby the population is divided into clusters and a random sample of the clusters is taken. All observations of a cluster are included in the sample. Quota Sampling – A sampling method where the members are pre-defined from a specified member type and thus is not a random sample and is not representative of the population. Spatial Sampling – An area of survey sampling concerned with sampling in two dimensions. Sampling Variability – The difference or variance in two or more samples taken from the same population. Standard Error – The deviation of the values of a given function of the data over all possible samples of the same size. Bias – A term referring to how far the average statistics lie from the actual parameter being estimated. Precision – A measure of how close an estimator is expected to be to the value of the parameter. Outcome – The result of an experiment involving uncertainty. Sample Space – An exhaustive list of all possible outcomes of an experiment usually denoted by S. Event – Any collection of outcomes of an experiment. Relative Frequency – Another term for proportion and is calculated by dividing the number of times an event occurs by the total number of times an experiment is carried out. Probability – Provides a quantitative description of the likely occurrence of a particular event. Subjective Probability – A reasonable assessment by an individual concerning the likelihood a particular event will occur. Independent Events – Events that have no correlation or affect on one another.

Mutually Exclusive Events – Events that can not occur together. Addition Rule – A rule used to determine the probability that event A or event B occurs or both occur. Multiplication Rule – A rule used to determine the probability that event A and event B both occur. Conditional Probability – A probability calculated given the current conditions. With a change in conditions the probability may change. Law of Total Probability – A calculation to express the state that a probability of and event C occurring will be affected by the probabilities of events A and B of which C is a subset. Bayes’ Theorem – A result that allows new information to be used to update the conditional probability of an event. Random Variable – A function that associates a unique numerical value with every outcome of an experiment. The value of the variable will vary as the experiment is repeated. Expected Value – An expected value of a random variable indicates its average or central value. Variance – A non-negative number which gives an idea of how widely spread the values of a random variable are likely to be. Probability Distribution – A list of probabilities associated with each of the values of a discrete random variable. Cumulative Distribution Function – A function giving the probability that the random variable X is less than or equal to x, for every value x. Probability Density Function – A function which can be integrated to obtain the probability that the random variable takes a value in a given interval. Discrete Random Variable – A random variable that can only take on a countable number of distinct values. Continuous Random Variable – A random variable which takes an infinite number of possible values. Probability-Probability (P-P) Plot – Used to see if a given set of data follows some specified distribution. Quantile-Quantile (QQ) Plot – Used to see if a given set of data follows some specified distribution. Normal Distribution – A method of modeling continuous random variables. Poisson Distribution – A method of modeling discrete random variables. Binomial Distribution – A method of modeling discrete random variables. Geometric Distribution – A method of modeling discrete random variables. Uniform Distribution – A method of modeling continuous random variables and discrete random variables. Independent Random Variables – These are random variables that do not have any influence on one another. Central Limit Theorem – States that data that are affected by many small and unrelated random affects are normally distributed.

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