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A likelihood ratio of greater than 1 for a test in a population indicates that a positive test result is evidence that a condition is present. If the likelihood ratio for a test in a population is not clearly better than one, the test will not provide good evidence: the post-test probability will not be meaningfully different from the pretest ...
Thus the likelihood-ratio test tests whether this ratio is significantly different from one, or equivalently whether its natural logarithm is significantly different from zero. The likelihood-ratio test, also known as Wilks test , [ 2 ] is the oldest of the three classical approaches to hypothesis testing, together with the Lagrange multiplier ...
For the figure that shows high sensitivity and low specificity, there are 3 FN and 8 FP. Using the fact that positive results = true positives (TP) + FP, we get TP = positive results - FP, or TP = 40 - 8 = 32. The number of sick people in the data set is equal to TP + FN, or 32 + 3 = 35. The sensitivity is therefore 32 / 35 = 91.4%.
Diagram relating pre- and post-test probabilities, with the green curve (upper left half) representing a positive test, and the red curve (lower right half) representing a negative test, for the case of 90% sensitivity and 90% specificity, corresponding to a likelihood ratio positive of 9, and a likelihood ratio negative of 0.111.
The positive predictive value (PPV), or precision, is defined as = + = where a "true positive" is the event that the test makes a positive prediction, and the subject has a positive result under the gold standard, and a "false positive" is the event that the test makes a positive prediction, and the subject has a negative result under the gold standard.
The likelihood ratio is central to likelihoodist statistics: the law of likelihood states that the degree to which data (considered as evidence) supports one parameter value versus another is measured by the likelihood ratio. In frequentist inference, the likelihood ratio is the basis for a test statistic, the so-called likelihood-ratio test.
On the Nasdaq, 2,178 stocks rose and 2,163 fell as advancing issues outnumbered decliners by a 1.01-to-1 ratio. The S&P 500 posted one new 52-week high and 8 new lows while the Nasdaq Composite ...
One can take ratios of a complementary pair of ratios, yielding four likelihood ratios (two column ratio of ratios, two row ratio of ratios). This is primarily done for the column (condition) ratios, yielding likelihood ratios in diagnostic testing. Taking the ratio of one of these groups of ratios yields a final ratio, the diagnostic odds ...