Explain and give a full and correct answer how confusing the two (population and a sample) can lead to incorrect statistical inferences.

Comparing two groups
asked 2021-01-31
Explain and give a full and correct answer how confusing the two (population and a sample) can lead to incorrect statistical inferences.

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In statistics, statistical inference is the process of drawing conclusions from data that is subject to random variation, for example, observational errors or sampling variation.[1] More substantially, the terms statistical inference, statistical induction and inferential statistics are used to describe systems of procedures that can be used to draw conclusions from datasets arising from systems affected by random variation,[2] such as observational errors, random sampling, or random experimentation.[1] Initial requirements of such a system of procedures for inference and induction are that the system should produce reasonable answers when applied to well-defined situations and that it should be general enough to be applied across a range of situations. The outcome of statistical inference may be an answer to the question "what should be done next?", where this might be a decision about making further experiments or surveys, or about drawing a conclusion before implementing some organizational or governmental policy. Contents [show] [edit]Introduction [edit]Scope For the most part, statistical inference makes propositions about populations, using data drawn from the population of interest via some form of random sampling. More generally, data about a random process is obtained from its observed behavior during a finite period of time. Given a parameter or hypothesis about which one wishes to make inference, statistical inference most often uses: a statistical model of the random process that is supposed to generate the data, which is known when randomization has been used, and a particular realization of the random process, i.e., a set of data. The conclusion of a statistical inference is a statistical proposition.[citation needed] Some common forms of statistical proposition are: an estimate, i.e., a particular value that best approximates some parameter of interest, a confidence interval (or set estimate), i.e., an interval constructed using a dataset drawn from a population so that, under repeated sampling of such datasets, such intervals would contain the true parameter value with the probability at the stated confidence level, a credible interval, i.e., a set of values containing, for example, 95% of posterior belief, rejection of a hypothesis[3] clustering or classification of data points into groups [edit]Comparison to descriptive statistics Statistical inference is generally distinguished from descriptive statistics. In simple terms, descriptive statistics can be thought of as being just a straightforward presentation of facts, in which modeling decisions made by a data analyst have had minimal influence. [edit]Models/Assumptions Main articles: Statistical model and Statistical assumptions Any statistical inference requires some assumptions. A statistical model is a set of assumptions concerning the generation of the observed data and similar data. Descriptions of statistical models usually emphasize the role of population quantities of interest, about which we wish to draw inference.[4] Descriptive statistics are typically used as a preliminary step before more formal inferences are drawn.[5] [edit]Degree of models/assumptions Statisticians distinguish between three levels of modeling assumptions, Fully parametric: The probability distributions describing the data-generation process are assumed to be fully described by a family of probability distributions involving only a finite number of unknown parameters.[4] For example, one may assume that the distribution of population values is truly Normal, with unknown mean and variance, and that datasets are generated by 'simple' random sampling. The family of generalized linear models is a widely used and flexible class of parametric models. Non-parametric: The assumptions made about the process generating the data are much less than in parametric statistics and may be minimal.[6] For example, every continuous probability distribution has a median, which may be estimated using the sample median or the Hodges–Lehmann–Sen estimator, which has good properties when the data arise from simple random sampling. Semi-parametric: This term typically implies assumptions 'in between' fully and non-parametric approaches. For example, one may assume that a population distribution has a finite mean. Furthermore, one may assume that the mean response level in the population depends in a truly linear manner on some covariate (a parametric assumption) but not make any parametric assumption describing the variance around that mean (i.e.)
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