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Related Concept Videos

Multiple Comparison Tests01:13

Multiple Comparison Tests

Multiple comparison test, abbreviated as MCT, is a post hoc analysis generally performed after comparing multiple samples with one or more tests. An MCT will help identify a significantly different sample among multiple samples or a factor among multiple factors.
It would be easy to compare two samples using a significance alpha level of 0.05. In other words, there is only one sample pair to be compared. However, it would be difficult to identify a significantly different sample if the number...
Comparing Experimental Results: Student's t-Test01:09

Comparing Experimental Results: Student's t-Test

The t-test is a statistical method used to compare the sample mean with a population mean or compare two means from two data sets. The test statistic is calculated from the standard deviation, mean, and number of measurements in the data set at a selected confidence interval and then compared to a table of critical values at this confidence level. If the test statistic is smaller than the critical value, the null hypothesis is accepted. In this case, we state that the difference between the...
Bonferroni Test01:10

Bonferroni Test

The Bonferroni test is a statistical test named after Carlo Emilio Bonferroni, an Italian mathematician best known for Bonferroni inequalities. This statistical test is a type of multiple comparison test to determine which means are different than the rest. Bonferroni test can minimize the Type 1 error by reducing the significance level alpha, which otherwise increases with sample pairs.
The means of different samples are first paired in all possible combinations.
The null hypothesis of the...
Comparison Tests01:28

Comparison Tests

An infinite series composed of positive terms may either approach a finite value or increase without bound. Determining which outcome occurs is a central task in calculus, and comparison tests provide structured methods for making this determination. Rather than evaluating a series directly, these tests relate it to another series whose behavior is already known, allowing conclusions to be drawn through logical comparison.The direct comparison test applies to series with positive terms. If each...
Test for Homogeneity01:23

Test for Homogeneity

The goodness–of–fit test can be used to decide whether a population fits a given distribution, but it will not suffice to decide whether two populations follow the same unknown distribution. A different test, called the test for homogeneity, can be used to conclude whether two populations have the same distribution. To calculate the test statistic for a test for homogeneity, follow the same procedure as with the test of independence. The hypotheses for the test for homogeneity can be stated as...
Statistical Methods to Analyze Parametric Data: Student t-Test and Goodness-of-Fit Test01:09

Statistical Methods to Analyze Parametric Data: Student t-Test and Goodness-of-Fit Test

In parametric statistics, two fundamental tests stand out for their utility and wide application: the Student's t-test and goodness-of-fit tests. These tests provide researchers with a robust method for drawing insights from data, testing hypotheses, and making informed decisions based on their findings.
The Student's t-test is a statistical test that examines if there is a statistically significant difference between the means of two groups. This test is instrumental when dealing with data...

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A Psychophysics Paradigm for the Collection and Analysis of Similarity Judgments
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Manipulability of comparative tests.

Wojciech Olszewski1, Alvaro Sandroni

  • 1Department of Economics, Northwestern University, 2001 Sheridan Road, Evanston, IL 60208, USA. wo@northwestern.edu

Proceedings of the National Academy of Sciences of the United States of America
|March 18, 2009
PubMed
Summary

Uninformed experts can create convincing false forecasts that may pass statistical tests. This challenges the ability of data alone to discredit strategic but unknowing forecasters.

Area of Science:

  • Decision theory
  • Probability theory
  • Statistical inference

Background:

  • Experts often claim knowledge of future event probabilities.
  • Assessing expert reliability is challenging when true probabilities are unknown.
  • Existing tests aim to control Type I errors in expert evaluation.

Purpose of the Study:

  • To investigate if uninformed experts can produce forecasts that evade rejection by statistical tests.
  • To determine the limitations of data-driven evaluation for strategic, uninformed forecasters.

Main Methods:

  • Simulating a testing scenario where experts provide probability forecasts for all future events.
  • Analyzing the conditions under which uninformed experts' false forecasts can pass a test designed to control Type I errors.

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  • Considering scenarios with strategic experts who may not possess true knowledge.
  • Main Results:

    • Uninformed experts can generate false forecasts that are likely to pass the test, irrespective of future data.
    • The testing procedure, even with controlled Type I error, may fail to discredit strategic, uninformed experts.
    • Observed data may be insufficient to definitively identify and reject experts lacking genuine predictive ability.

    Conclusions:

    • Statistical tests controlling Type I error may not be sufficient to debunk uninformed but strategic experts.
    • The effectiveness of data in discrediting experts depends on their actual knowledge, not just their strategic forecasting.
    • Further research is needed on methods to reliably assess expert claims in situations of uncertainty.