Central Tendency Errors

Examples of Central Tendency Errors in the following topics:

• Evaluating Performance: Who, What, and How

  • Detriments of the PA system include the possible hindrance of quality control, stress for both employees and management, errors in judgment, legal issues arising from improper evaluations, and the implementation of inappropriate performance goals.
  • The most common problems in this area are leniency errors, halo effect errors, and central tendency errors.
  • Employee comparison methods attempt to evade the leniency and central tendency errors.

• Evaluating Employee Performance

  • Detriments of the PA system include the possible hindrance of quality control, stress for both employees and management, errors in judgment, legal issues arising from improper evaluations, and the implementation of inappropriate performance goals.
  • Judgmental evaluation:One of the primary drawbacks of employee performance evaluation is the tendency for positive feedback despite negative behavior.
  • This method eliminates central-tendency and leniency errors but still allows for halo-effect errors to occur.

• Exercises

  • You had calculated the following measures of central tendency: the mean, the median, and the mean trimmed 25%.
  • Which of these measures of central tendency will change when you correct the recording error?
  • Which of the following measures of central tendency or variability can you determine?
  • Consider spread as well as central tendency.
  • Which measure of central tendency is most often used for returns on investment?

• Hypotheses about one mean or density

  • Of the various properties of the distribution of a single variable (e.g. central tendency, dispersion, skewness), we are usually most interested in central tendency.
  • If we are working with the distribution of relations among actors in a network, and our measure of tie-strength is binary (zero/one), the mean or central tendency is also the proportion of all ties that are present, and is the "density."
  • If we are working with the distribution of relations among actors in a network, and our measure of tie-strength is valued, central tendency is usually indicated by the average strength of the tie across all the relations.
  • Using this alternative standard error based on random draws from the observed sample, our test statistic is -3.7943.
  • Using them results in the worst kind of inferential error -- the false positive, or rejecting the null when we shouldn't.

• Mean: The Average

  • The term central tendency relates to the way in which quantitative data tend to cluster around some value.
  • The term central tendency relates to the way in which quantitative data tend to cluster around some value.
  • A measure of central tendency is any of a variety of ways of specifying this "central value".
  • Central tendency is contrasted with statistical dispersion (spread), and together these are the most used properties of distributions.
  • Statistics that measure central tendency can be used in descriptive statistics as a summary statistic for a data set, or as estimators of location parameters of a statistical model.

• Regressing position on attributes

  • Our dependent attribute, as before, is the eigenvector centrality of the individual political donors.
  • Workers groups do appear to have higher eigenvector centrality, even controlling for total coalition participation (.075), but this tendency may be a random result (a one-tailed significance is only p = .102).
  • What differs here is the recognition that the actors are not independent, so that estimation of standard errors by simulation, rather than by standard formula, is necessary.
  • Multiple regression of eigenvector centrality with permutation based significance tests
  • Dialog for Tools>Testing Hypotheses>Node-level>Regression for California donor's eigenvector centrality

• Attribution

  • One of the central concerns of social psychology is understanding the ways in which people explain, or "attribute," events and behavior.
  • People are susceptible to bias and error when making attributions about themselves and others.
  • The fundamental attribution error is so powerful that people often overlook even obvious situational influences on behavior.
  • Self-serving bias is the tendency of individuals to make internal attributions when their actions have a positive outcome but external attributions when their actions have a negative outcome.
  • One consequence of Westerners’ tendency to provide internal explanations for others' behavior is victim-blaming (Jost & Major, 2001).

• Estimating the Accuracy of an Average

  • Note that the standard error and the standard deviation of small samples tend to systematically underestimate the population standard error and deviations because the standard error of the mean is a biased estimator of the population standard error.
  • In particular, the standard error of a sample statistic (such as sample mean) is the estimated standard deviation of the error in the process by which it was generated.
  • If the standard error of several individual quantities is known, then the standard error of some function of the quantities can be easily calculated in many cases.
  • As the sample size tends to infinity, the central limit theorem guarantees that the sampling distribution of the mean is asymptotically normal.
  • Evaluate the accuracy of an average by finding the standard error of the mean.

• Median

  • A measure of central tendency (also referred to as measures of center or central location) is a summary measure that attempts to describe a whole set of data with a single value that represents the middle or center of its distribution.
  • There are three main measures of central tendency: the mode, the median and the mean .
  • Each of these measures describes a different indication of the typical or central value in the distribution.
  • The median is less affected by outliers and skewed data than the mean, and is usually the preferred measure of central tendency when the distribution is not symmetrical.
  • Identify the median in a data set and distinguish it's properties from other measures of central tendency.

• Comparing Measures of Central Tendency

  • How do the various measures of central tendency compare with each other?
  • Measures of central tendency are shown in Table 1.
  • Table 2 shows the measures of central tendency for these data.
  • No single measure of central tendency is sufficient for data such as these.
  • Measures of central tendency for baseball salaries (in thousands of dollars)