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Related Concept Videos

P-value01:10

P-value

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P-value is one of the most crucial concepts in statistics.
P-value stands for the probability value.  P-value is the probability that, if the null hypothesis is true, the results from another randomly selected sample will be as extreme or more extreme as the results obtained from the given sample.
A large P-value calculated from the data indicates to  not reject the null hypothesis. But a higher P-value does not mean that the null hypothesis is true. The smaller the P-value, the more...
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Decision Making: P-value Method01:09

Decision Making: P-value Method

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The process of hypothesis testing based on the P-value method includes calculating the P- value using the sample data and interpreting it.
First, a specific claim about the population parameter is proposed. The claim is based on the research question and is stated in a simple form. Further, an opposing statement to the claim  is also stated. These statements can act as null and alternative hypotheses:  a null hypothesis would be a neutral statement while the alternative hypothesis can...
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Detection of Gross Error: The Q Test01:00

Detection of Gross Error: The Q Test

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When one or more data points appear far from the rest of the data, there is a need to determine whether they are outliers and whether they should be eliminated from the data set to ensure an accurate representation of the measured value. In many cases, outliers arise from gross errors (or human errors) and do not accurately reflect the underlying phenomenon. In some cases, however, these apparent outliers reflect true phenomenological differences. In these cases, we can use statistical methods...
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z Scores and Area Under the Curve01:17

z Scores and Area Under the Curve

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z scores are the standardized values obtained after converting a normal distribution into a standard normal distribution. A z score is measured in units of the standard deviation. The z score tells you how many standard deviations the value x is above (to the right of) or below (to the left of) the mean, μ. Values of x that are larger than the mean have positive z scores, and values of x that are smaller than the mean have negative z scores. If x equals the mean, then x has a z score of...
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Fisher's Exact Test01:08

Fisher's Exact Test

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Fisher's exact test is a statistical significance test widely used to analyze 2x2 contingency tables, particularly in situations where sample sizes are small. Unlike the chi-squared test, which approximates P-values and assumes minimum expected frequencies of at least five in each cell, Fisher's exact test calculates the exact probability (P-value) of observing the data or more extreme results under the null hypothesis. This feature makes it especially valuable when the assumptions of...
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Testing a Claim about Mean: Unknown Population SD01:21

Testing a Claim about Mean: Unknown Population SD

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A complete procedure of testing a hypothesis about a population mean when the population standard deviation is unknown is explained here.
Estimating a population mean requires the samples to be approximately normally distributed. The data should be collected from the randomly selected samples having no sampling bias. There is no specific requirement for sample size. But if the sample size is less than 30, and we don't know the population standard deviation, a different approach is used;...
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Detection of Rare Genomic Variants from Pooled Sequencing Using SPLINTER
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p-value approximations for spatial scan statistics using extreme value distributions.

Inkyung Jung1, Goeun Park

  • 1Department of Biostatistics, Yonsei University College of Medicine, Seoul, 120-752, Korea.

Statistics in Medicine
|October 28, 2014
PubMed
Summary
This summary is machine-generated.

This study introduces extreme value distributions for more accurate p-value approximations in spatial scan statistics, improving disease cluster detection. This method enhances statistical significance evaluation in geographic disease surveillance without extensive Monte Carlo simulations.

Keywords:
Gumbel distributionMonte Carlo hypothesis testinggeneralized extreme value distribution

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Area of Science:

  • Epidemiology and Biostatistics
  • Geographic Information Systems (GIS) in Public Health
  • Spatial Statistics and Disease Surveillance

Background:

  • Spatial scan statistics are crucial for identifying disease clusters in geographic surveillance.
  • Traditional Monte Carlo hypothesis testing for statistical significance requires numerous replications, impacting efficiency.
  • Existing Gumbel-based p-value approximations show promise but are limited to specific statistical models.

Purpose of the Study:

  • To evaluate generalized extreme value distributions for approximating the null distribution of spatial scan statistics.
  • To compare the accuracy of extreme value distribution approximations against Gumbel distribution approximations.
  • To assess these approximations across various statistical models, including multinomial and ordinal, beyond Poisson and Bernoulli.

Main Methods:

  • Utilized simulation studies to generate data for spatial scan statistics.
  • Applied generalized extreme value (GEV) and Gumbel distributions to approximate the null distribution.
  • Assessed p-value approximation accuracy for multinomial, ordinal, Poisson, and Bernoulli models.

Main Results:

  • Extreme value distributions, including GEV, provide viable approximations for spatial scan statistic null distributions.
  • These approximations offer a more efficient alternative to Monte Carlo methods for determining statistical significance.
  • The assessment demonstrated the applicability of these methods across a broader range of disease surveillance models.

Conclusions:

  • Generalized extreme value distributions offer a robust and efficient method for p-value approximation in spatial scan statistics.
  • This approach enhances the statistical rigor and practicality of geographic disease surveillance.
  • Future research can leverage these approximations for improved cluster detection and public health decision-making.