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Principle of insufficient reason (laplace)
| Glossary of Statistical Terms |
Laplace`s principle of insufficient reason says that if there is no reason to believe that the possible outcomes of an experiment are not equally likely, one should assume that the outcomes are equally likely. this is an example of a fallacy called appeal to ignorance.
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Insufficient, английский
Недостаточный
Experiment, английский
- What distinguishes an experiment from an observational study is that in an experiment, the experimenter decides who receives the treatment.
- Эксперимент
- A scientific test conducted under set conditions the scientists did some experiments to try the new drug on a small sample of people.
- N экспе- римент (см. тж. test) associative ~ псхлнгв. ассоциативный экспе- римент psycholinguistic ~ психолингвистический экс- перимент
- Эксперимент; опыт, опытное исследование
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Regression, linear regression, английский
Linear regression fits a line to a scatterplot in such a way as to minimize the sum of the squares of the residuals. the resulting regression line, together with the standard deviations of the two variables or their correlation coefficient, can be a reasonable summary of a scatterplot if the scatterplot is roughly football-shaped. in other cases, it is a poor summary. if we are regressing the variable y on the variable x, and if y is plotted on the vertical axis and x is plotted on the horizontal axis, the regression line passes through the point of averages, and has slope equal to the correlation coefficient times the sd of y divided by the sd of x. this page shows a scatterplot, with a button to plot the regression line.
Continuity correction, английский
In using the normal approximation to the binomial probability histogram, one can get more accurate answers by finding the area under the normal curve corresponding to half-integers, transformed to standard units. this is clearest if we are seeking the chance of a particular number of successes. for example, suppose we seek to approximate the chance of 10 successes in 25 independent trials, each with probability p = 40% of success. the number of successes in this scenario has a binomial distribution with parameters n = 25 and p = 40%. the expected number of successes is np = 10, and the standard error is (np(1−p))½ = 6½ = 2.45. if we consider the area under the normal curve at the point 10 successes, transformed to standard units, we get zero: the area under a point is always zero. we get a better approximation by considering 10 successes to be the range from 9 1/2 to 10 1/2 successes. the only possible number of successes between 9 1/2 and 10 1/2 is 10, so this is exactly right for the binomial distribution. because the normal curve is continuous and a binomial random variable is discrete, we need to "smear out" the binomial probability over an appropriate range. the lower endpoint of the range, 9 1/2 successes, is (9.5 − 10)/2.45 = −0.20 standard units. the upper endpoint of the range, 10 1/2 successes, is (10.5 − 10)/2.45 = +0.20 standard units. the area under the normal curve between −0.20 and +0.20 is about 15.8%. the true binomial probability is 25c10×(0.4)10×(0.6)15 = 16%. in a similar way, if we seek the normal approximation to the probability that a binomial random variable is in the range from i successes to k successes, inclusive, we should find the area under the normal curve from i−1/2 to k+1/2 successes, transformed to standard units. if we seek the probability of more than i successes and fewer than k successes, we should find the area under the normal curve corresponding to the range i+1/2 to k−1/2 successes, transformed to standard units. if we seek the probability of more than i but no more than k successes, we should find the area under the normal curve corresponding to the range i+1/2 to k+1/2 successes, transformed to standard units. if we seek the probability of at least i but fewer than k successes, we should find the area under the normal curve corresponding to the range i−1/2 to k−1/2 successes, transformed to standard units. including or excluding the half-integer ranges at the ends of the interval in this manner is called the continuity correction.
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