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Sequential testing is a statistical method that allows for the evaluation of data as it is collected, rather than waiting for all data to be gathered before analysis. This approach enables researchers to make decisions or adjust hypotheses in real-time, potentially reducing the number of observations needed and increasing the efficiency of the study.
Hypothesis testing is a statistical method used to make decisions about the properties of a population based on a sample. It involves formulating a null hypothesis and an alternative hypothesis, then using sample data to determine which hypothesis is more likely to be true.
Statistical significance is a measure that helps determine if the results of an experiment or study are likely to be genuine and not due to random chance. It is typically assessed using a p-value, with a common threshold of 0.05, indicating that there is less than a 5% probability that the observed results occurred by chance.
Type I and Type II errors are statistical errors that occur in hypothesis testing, where a Type I error (false positive) involves rejecting a true null hypothesis, and a Type II error (false negative) involves failing to reject a false null hypothesis. Balancing these errors is crucial in research, as reducing one often increases the other, impacting the validity and reliability of study results.
Power analysis is a statistical method used to determine the minimum sample size required for a study to detect an effect of a given size with a certain degree of confidence. It helps researchers avoid underpowered studies that may fail to identify meaningful effects or overpowered studies that waste resources.
Stopping rules are predefined criteria that dictate when a statistical analysis or experiment should be terminated to avoid misleading results or unnecessary resource expenditure. They are crucial in ensuring the integrity and validity of findings, particularly in clinical trials and sequential analysis, by preventing data-driven decisions that could inflate type I error rates.
Bayesian statistics is a statistical paradigm that updates the probability for a hypothesis as more evidence or information becomes available, using Bayes' theorem as its foundation. It contrasts with frequentist statistics by incorporating prior knowledge or beliefs, expressed as a prior distribution, into the analysis to produce a posterior distribution that reflects both the prior information and the new data.
Frequentist statistics is an approach to statistical inference that interprets probability as the long-run frequency of events and emphasizes the use of data from repeated sampling. It relies heavily on hypothesis testing, confidence intervals, and p-values to draw conclusions about population parameters based on sample data.
The likelihood ratio is a statistical measure used to compare the probability of observed data under two different hypotheses, often the null and alternative hypotheses. It is a crucial tool in hypothesis testing and model selection, helping to assess the strength of evidence against the null hypothesis.
Confidence intervals provide a range of values, derived from sample data, that is likely to contain the true population parameter with a specified level of confidence. They are crucial in inferential statistics as they account for sampling variability and help in making informed decisions based on data analysis.
The Holm-Bonferroni Method is a statistical technique used to control the family-wise error rate when performing multiple hypothesis tests. It is a stepwise method that sequentially adjusts p-values, providing a more powerful alternative to the traditional Bonferroni correction by allowing for a less conservative adjustment.
A test schedule is an organized plan that outlines the timing and sequence of specific tests, ensuring efficient resource allocation and adherence to project timelines. Its primary purpose is to coordinate testing activities, maintain order, and avoid potential conflicts in complex environments, such as software development or educational settings.
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