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Related Concept Videos

Determination of Expected Frequency01:08

Determination of Expected Frequency

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Suppose one wants to test independence between the two variables of a contingency table. The values in the table constitute the observed frequencies of the dataset. But how does one determine the expected frequency of the dataset? One of the important assumptions is that the two variables are independent, which means the variables do not influence each other. For independent variables, the statistical probability of any event involving both variables is calculated by multiplying the individual...
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Regression Toward the Mean01:52

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Regression toward the mean (“RTM”) is a phenomenon in which extremely high or low values—for example, and individual’s blood pressure at a particular moment—appear closer to a group’s average upon remeasuring. Although this statistical peculiarity is the result of random error and chance, it has been problematic across various medical, scientific, financial and psychological applications. In particular, RTM, if not taken into account, can interfere when...
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Expected Value01:15

Expected Value

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The expected value is known as the "long-term" average or mean. This means that over the long term of experimenting over and over, you would expect this average. The expected average is represented by the symbol μ. It is calculated as follows:
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Testing a Claim about Standard Deviation01:19

Testing a Claim about Standard Deviation

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A complete procedure to test a claim about population standard deviation or population variance is explained here.
The hypothesis testing for the claim of population standard deviation (or variance) requires the data and samples to be random and unbiased. The population distribution also must be normal. There is no specific requirement on the sample size as the estimation is based on the chi-square distribution.
As a first step, the hypothesis (null and alternative) concerning the claim about...
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Expected Frequencies in Goodness-of-Fit Tests01:19

Expected Frequencies in Goodness-of-Fit Tests

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A goodness-of-fit test is conducted to determine whether the observed frequency values are statistically similar to the frequencies expected for the dataset. Suppose the expected frequencies for a dataset are equal such as when predicting the frequency of any number appearing when casting a die. In that case, the expected frequency is the ratio of the total number of observations (n)  to the number of categories (k).
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Types of Biopharmaceutical Studies: Controlled and Non-Controlled Approaches01:23

Types of Biopharmaceutical Studies: Controlled and Non-Controlled Approaches

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Biopharmaceutical studies constitute a vital field aiming to enhance drug delivery methods and refine therapeutic approaches, drawing upon diverse interdisciplinary knowledge. In research methodologies, the choice between controlled and non-controlled studies significantly influences the study's reliability and accuracy.
Non-controlled studies, commonly employed for initial exploration, lack a control group, rendering them susceptible to biases and external influences. In contrast,...
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Related Experiment Video

Updated: Dec 6, 2025

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach
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Accounting for Expected Adjusted Effect.

Kimmo Sorjonen1, Bo Melin1, Michael Ingre1,2,3

  • 1Department of Clinical Neuroscience, Karolinska Institutet, Stockholm, Sweden.

Frontiers in Psychology
|October 12, 2020
PubMed
Summary

Adjusting for confounders may not prevent false findings, especially with large sample sizes and unreliable confounder measurement. New equations can help quantify and mitigate this risk in regression analysis.

Keywords:
adjustmentconfounderexpected effectregression analysisreliabilitysimulationtype 1-error

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Area of Science:

  • Statistics
  • Epidemiology
  • Biostatistics

Background:

  • Confounder adjustment is crucial in statistical analysis to prevent biased results.
  • However, adjustment does not always eliminate spurious findings or Type 1 errors.

Purpose of the Study:

  • To investigate the conditions under which confounder adjustment fails in traditional regression methods.
  • To present methods for calculating and potentially attenuating the risk of spurious findings.

Main Methods:

  • A simulation study was conducted using traditional regression methods.
  • The study examined the impact of sample size, confounder reliability, and predictor/outcome reliability.

Main Results:

  • The risk of spurious findings is amplified by large sample sizes, low confounder measurement reliability, and high predictor/outcome reliability.
  • Equations were derived to calculate the expected adjusted effect and required confounder reliability.

Conclusions:

  • Confounder adjustment in regression analysis can be unreliable under specific conditions.
  • The derived equations offer a way to assess and potentially reduce the risk of Type 1 errors in observational studies.