Related Experiment Video
Updated: Jun 9, 2026
Candidate Gene Testing in Clinical Cohort Studies with Multiplexed Genotyping and Mass Spectrometry
Published on: June 21, 2018
Estimation of P-value of MAX test with double triangle diagram for 2 x 3 SNP case-control tables
Katsura Hirosawa1, Takahisa Kawaguchi, Fumihiko Matsuda
1Center for Genomic Medicine, Graduate School of Medicine, Kyoto University, Kyoto, Japan.
Abstract:
Single nucle otide polymorphisms (SNPs) are the most popular markers in genetic epidemiology. Multiple tests have been applied to evaluate genetic effect of SNPs, such as Pearson's test with two degrees of freedom, three tests with one degree of freedom (chi(2) tests for dominant and recessive modes and Cockran-Armitage trend test for additive mode) as well as MAX3 test and MAX test, which are combination of four tests mentioned earlier. Because MAX test is a combination of Pearson's test of two degrees of freedom and two tests of one degree of freedom, the probability density function (pdf) of MAX statistics does not match pdf of chi(2) distribution of either one or two degrees of freedom. In order to calculate P-value of MAX test, we introduced a new diagram, Double Triangle Diagram, which was an extension of de Finetti diagram in population genetics which characterized all of the tests for 2 x 3 tables. In the diagram the contour lines of MAX statistics were consisted of elliptic curves and two tangent lines to the ellipses in the space. We normalized the ellipses into regular circles and expressed P-value of MAX test in an integral form. Although a part of the integral was not analytically solvable, it was calculable with arbitrary accuracy by dividing the area under pdf into finite rectangles. We confirmed that P-values from our method took uniform distribution from 0 to 1 in three example marginal count sets and concluded that our method was appropriate to give P-value of MAX test for 2 x 3 tables.
Related Concept Videos
01:09Decision Making: P-value Method
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 have a...
01:10P-value
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 unlikely...
01:24Testing a Claim about Population Proportion
There are two methods of testing a claim about a population proportion: (1) Using the sample proportion from the data where a binomial distribution is approximated to the normal distribution and (2) Using the binomial probabilities calculated from the data.
The first method uses normal distribution as an approximation to the binomial distribution. The requirements are as follows: sample size is large...
02:46Chi-square Analysis
The chi-square test was developed by Pearson in 1990.
The first step of performing a Chi-square analysis is to establish a null hypothesis, which assumes that there is no real...
01:23McNemar's Test
01:08Determination of Expected Frequency