Related Experiment Video
Updated: Mar 17, 2026
13:55
Combined Immunofluorescence and DNA FISH on 3D-preserved Interphase Nuclei to Study Changes in 3D Nuclear Organization
Published on: February 3, 2013
19.1K
Generalized Sequential Probability Ratio Test for Separate Families of Hypotheses
Xiaoou Li1, Jingchen Liu1, Zhiliang Ying1
1Department of Statistics, Columbia University, New York, NY 10027, USA.
Sequential Analysis
|July 16, 2016
Summary
This study introduces a generalized sequential probability ratio test for hypothesis testing. The new method is asymptotically optimal, minimizing sample size for precise error control.
Area of Science:
- Statistics
- Hypothesis Testing
Background:
- Sequential analysis offers efficient data collection for hypothesis testing.
- Traditional sequential probability ratio tests have limitations in certain complex scenarios.
Purpose of the Study:
- To generalize the sequential probability ratio test for testing separate families of hypotheses.
- To establish the asymptotic optimality of the proposed generalized test.
Main Methods:
- Utilizing a generalized likelihood ratio statistic.
- Implementing a stopping rule based on the first boundary crossing of this statistic.
Main Results:
- The proposed sequential test is asymptotically optimal.
- The test achieves asymptotically the shortest expected sample size.
- Optimality is demonstrated as maximal error probabilities approach zero.
Conclusions:
- The generalized sequential probability ratio test provides an efficient and optimal approach for hypothesis testing.
- This method is particularly valuable when dealing with separate families of hypotheses and strict error bounds.
Related Concept Videos
01:23Test for Homogeneity
2.5K
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...
2.5K
01:10Bonferroni Test
3.5K
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...
The means of different samples are first paired in all possible combinations.
The null hypothesis of the...
3.5K
01:11Types of Hypothesis Testing
29.3K
There are three types of hypothesis tests: right-tailed, left-tailed, and two-tailed.
When the null and alternative hypotheses are stated, it is observed that the null hypothesis is a neutral statement against which the alternative hypothesis is tested. The alternative hypothesis is a claim that instead has a certain direction. If the null hypothesis claims that p = 0.5, the alternative hypothesis would be an opposing statement to this and can be put either p > 0.5, p < 0.5, or p...
When the null and alternative hypotheses are stated, it is observed that the null hypothesis is a neutral statement against which the alternative hypothesis is tested. The alternative hypothesis is a claim that instead has a certain direction. If the null hypothesis claims that p = 0.5, the alternative hypothesis would be an opposing statement to this and can be put either p > 0.5, p < 0.5, or p...
29.3K
01:24Testing a Claim about Population Proportion
4.0K
A complete procedure for testing a claim about a population proportion is provided here.
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...
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...
4.0K
01:14Decision Making: Traditional Method
5.7K
The process of hypothesis testing based on the traditional method includes calculating the critical value, testing the value of the test statistic using the sample data, and interpreting these values.
First, a specific claim about the population parameter is decided based on the research question and is stated in a simple form. Further, an opposing statement to this claim is also stated. These statements can act as null and alternative hypotheses, out of which a null hypothesis would be a...
First, a specific claim about the population parameter is decided based on the research question and is stated in a simple form. Further, an opposing statement to this claim is also stated. These statements can act as null and alternative hypotheses, out of which a null hypothesis would be a...
5.7K
01:16Hypothesis Test for Test of Independence
8.3K
The test of independence is a chi-square-based test used to determine whether two variables or factors are independent or dependent. This hypothesis test is used to examine the independence of the variables. One can construct two qualitative survey questions or experiments based on the variables in a contingency table. The goal is to see if the two variables are unrelated (independent) or related (dependent). The null and alternative hypotheses for this test are:
H0: The two variables (factors)...
H0: The two variables (factors)...
8.3K