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Introduction to Inferential Statistics 2: Population and Parameter Estimation

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Abstract

The chapter considers the critical distinction of sample and population, and it covers the interplay of sampling on the one hand and parameter estimation on the other hand. We explore the relationship between sample statistics and hypothetical population parameters based on a simulation. Finally, we describe criteria that an estimator must fulfill to be a ”good estimator”.

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Notes

  1. 1.

    Indeed, several psychological theories such as the power law of motor learning have been demonstrated using cigar rolling as an example (Crossman 1959; Fitts and Posner 1967; see Rosenbaum and Janczyk 2019, for more information on Crossman).

  2. 2.

    Other measures of central tendency could also be used in theory, such as the mode or the median. However, as we will see later, it is mainly the arithmetic mean that meets common quality criteria (see Sect. 3.3).

  3. 3.

    Remember that this is an unrealistic situation in most cases: If we actually knew the population parameters, we would no longer need parameter estimation or inferential statistics. We could then rely on descriptive statistics alone to arrive at perfectly correct statements about the population.

  4. 4.

    Because there is only a finite number of possible means in this example (i.e., the set Ω′ is finitely large), \(\boldsymbol {\bar {X}}\) is a discrete random variable.

References

  • Crossman, E. R. F. W. (1959). A theory of the acquisition of speed-skill. Ergonomics, 2, 153–166.

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  • Fitts, P. M., & Posner, M. I. (1967). Human performance. Prentice-Hall.

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  • Rosenbaum, D. A., & Janczyk, M. (2019). Who is or was E. R. F. W. Crossman, the champion of the Power Law of Learning and the developer of an influential model of aiming? Psychonomic Bulletin & Review, 26, 1449–1463.

    Article  Google Scholar 

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Authors and Affiliations

  1. Research Methods and Cognitive Psychology, University of Bremen, Bremen, Germany

    Markus Janczyk

  2. General Psychology, Trier University, Trier, Germany

    Roland Pfister

Authors
  1. Markus Janczyk
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  2. Roland Pfister
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Janczyk, M., Pfister, R. (2023). Introduction to Inferential Statistics 2: Population and Parameter Estimation. In: Understanding Inferential Statistics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-66786-6_3

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