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Co-integration and error correction

A Type I error (sometimes called a Type 1 error), is the incorrect rejection of a true null hypothesis. The alpha symbol, α, is usually used to denote a Type I error.

The most common way to control the familywise error rate is with the Bonferroni correction. You find the critical value (alpha) for an individual test by dividing the familywise error rate (usually 0.05) by the number of tests. Thus if you are doing 100 statistical tests, the critical value for an individual test would be 0.05/100=0.0005, and you would only consider individual tests with P

Error-correcting codes have a certain ..

Multiple comparisons problem - Wikipedia

CORRECTION: Some scientists and philosophers have tried to draw a line between "hard" sciences (e.g., chemistry and physics) and "soft" ones (e.g., psychology and sociology). The thinking was that hard science used more rigorous, quantitative methods than soft science did and so were more trustworthy. In fact, the rigor of a scientific study has much more to do with the investigator's approach than with the discipline. Many psychology studies, for example, are carefully controlled, rely on large sample sizes, and are highly quantitative. To learn more about how rigorous and fair tests are designed, regardless of discipline, check out our side trip .

CORRECTION: Perhaps because the Scientific Method and popular portrayals of science emphasize , many people think that science can't be done an experiment. In fact, there are ways to test almost any scientific idea; experimentation is only one approach. Some ideas are best tested by setting up a in a lab, some by making detailed observations of the natural world, and some with a combination of strategies. To study detailed examples of how scientific ideas can be tested fairly, with and without experiments, check out our side trip .

Family-wise error rate - Wikipedia

Correction drill
Choose a confident student who will not mind having mistakes corrected. Explain that you are going to correct him as he speaks, and that the purpose behind this is not to humiliate, but to help. The student should speak, e.g. tell a story about himself. You repeat each sentence. If there are mistakes, you repeat the sentence correctly and the rest of the class does the same after you. The rationale is 1) students get to hear how they should sound, 2) the rest of the class is involved, and they listen to the original and the teacher’s improvement. 3) By using intonation to show interest, approval, disapproval, and surprise in a light-hearted way, which can be echoed by the class, you focus on meaning as well as form. Example:

*I used this simple statement as an example of Type I and Type II errors. I haven’t actually researched this statement, so as well as committing numerous errors myself, I’m probably also guilty of sloppy science!

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Tips and strategies for teaching the nature and process …

Misleading stereotypes of scientists

You conduct your research by polling local residents at a retirement community and to your surprise you find out that most people do believe in urban legends. The problem is, you didn’t account for the fact that your sampling method introduced some bias…retired folks are less likely to have access to tools like Smartphones than the general population. So you incorrectly fail to reject the false null hypothesis that most people do believe in urban legends (in other words, most people do not, and you failed to prove that). You’ve committed an egregious Type II error, the penalty for which is banishment from the scientific community.

MISCONCEPTION: Science is a solitary pursuit

The Bonferroni correction is appropriate when a single false positive in a set of tests would be a problem. It is mainly useful when there are a fairly small number of multiple comparisons and you're looking for one or two that might be significant. However, if you have a large number of multiple comparisons and you're looking for many that might be significant, the Bonferroni correction may lead to a very high rate of false negatives. For example, let's say you're comparing the expression level of 20,000 genes between liver cancer tissue and normal liver tissue. Based on previous studies, you are hoping to find dozens or hundreds of genes with different expression levels. If you use the Bonferroni correction, a P value would have to be less than 0.05/20000=0.0000025 to be significant. Only genes with huge differences in expression will have a P value that low, and could miss out on a lot of important differences just because you wanted to be sure that your results did not include a single false negative.

Hypothesis Testing -- from Wolfram MathWorld

Basically, place the correction at the end of the formula you want to use. For example, the of the mean formula is:

And with the correction, the formula is:

Type I and Type II Errors: Easy Definition, Examples

That was a clear explanation of type 1 and type 2 error, thank you for that .
one thing i felt regarding the example of type 2 error, could have been a better one because being an Asian i not familiar with the term ( urban legend researcher) or (urban legend ) so a much more generalized example will be helpful for people like me
than you

Finite Population Correction Factor FPC: Formula, …

Errors are produced as a result of the lack or misinterpretation of knowledge, which, in turn, may be a product of the learner’s stage of language development, or inadequate teaching or learning. Errors cannot be corrected and need to be dealt with by teaching or reteaching. Errors are often noticed in less-guided practice activities when the same error is made by a number of learners, leading the teacher to realize that something has gone wrong in earlier stages of the teaching/learning process. Mistakes, on the other hand, are products of the learner’s efforts to produce language despite prior knowledge. They may be due a variety of factors including over-enthusiasm, over-generalization of rules, interference from the mother tongue, and once the cause has been established, can be dealt with by a number of correction techniques.

Multiple comparisons - Handbook of Biological Statistics

When standardized observations and forecasts are used as RMSE inputs, there is a direct relationship with the For example, if the correlation coefficient is 1, the RMSE will be 0, because all of the points lie on the regression line (and therefore there are no errors).

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