Basic STAT Commonly Used Terms #STATSNOB

• The population is the entire group that the researchers are interested in. Because it is usually too costly to gather the data for the entire population, researchers will collect data from a sample, representing a subset of the population.
•  A parameter is a true quantity for the entire population, while a statistic is what is calculated from the sample. A parameter is about a population and a statistic is about a sample. Remember: p goes with p and s goes with s.
•  Two common summary quantities are mean (for numerical variables) and proportion (for categorical variables).
• Finding a good estimate for a population parameter requires a random sample; do not generalize from anecdotal evidence.
•  There are two primary types of data collection: observational studies and experiments. In an experiment, researchers impose a treatment to look for a causal relationship between the treatment and the response. In an observational study, researchers simply collect data without imposing any treatment.
• Remember: Correlation is not causation! In other words, an association between two variables does not imply that one causes the other. Proving a causal relationship requires a well-designed experiment.
•  In an observational study, one must always consider the existence of confounding factors. A confounding factor is a “spoiler variable” that could explain an observed relationship between the explanatory variable and the response. Remember: For a variable to be confounding it must be associated with both the explanatory variable and the response variable.
• When taking a sample from a population, avoid convenience samples and volunteer samples, which likely introduce bias. Instead, use a random sampling method.
•  Generalizations from a sample can be made to a population only if the sample is random. Furthermore, the generalization can be made only to the population from which the sample was randomly selected, not to a larger or different population.
• Random sampling from the entire population of interest avoids the problem of under-coverage bias. However, response bias and non-response bias can be present in any type of sample, random or not.
•  In a simple random sample, every individual as well as every group of individuals has the same probability of being in the sample. A common way to select a simple random sample is to number each individual of the population from 1 to N. Using a random digit table or a random number generator, numbers are randomly selected without replacement and the corresponding individuals become part of the sample.
•  A systematic random sample involves choosing from of a population using a random starting point, and then selecting members according to a fixed, periodic interval (such as every 10th member).
•  A stratified random sample involves randomly sampling from every strata, where the strata should correspond to a variable thought to be associated with the variable of interest.
• This ensures that the sample will have appropriate representation from each of the different strata and reduces variability in the sample estimates.
•  A cluster random sample involves randomly selecting a set of clusters, or groups, and then collecting data on all individuals in the selected clusters. This can be useful when sampling clusters is more convenient and less expensive than sampling individuals, and it is an effective strategy when each cluster is approximately representative of the population.
• Remember: Individual strata should be homogeneous (self-similar), while individual clusters should be heterogeneous (diverse). For example, if smoking is correlated with what is being estimated, let one stratum be all smokers and the other be all non-smokers, then randomly select an appropriate number of individuals from each strata. Alternately, if age is correlated with the variable being estimated, one could randomly select a subset of clusters, where each cluster has mixed age groups.

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