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Tobin's q [a] (or the q ratio, and Kaldor's v), is the ratio between a physical asset's market value and its replacement value. It was first introduced by Nicholas Kaldor in 1966 in his paper: Marginal Productivity and the Macro-Economic Theories of Distribution: Comment on Samuelson and Modigliani .
However, at 95% confidence, Q = 0.455 < 0.466 = Q table 0.167 is not considered an outlier. McBane [ 1 ] notes: Dixon provided related tests intended to search for more than one outlier, but they are much less frequently used than the r 10 or Q version that is intended to eliminate a single outlier.
Mathematically, the markup rule can be derived for a firm with price-setting power by maximizing the following expression for profit: = () where Q = quantity sold, P(Q) = inverse demand function, and thereby the price at which Q can be sold given the existing demand C(Q) = total cost of producing Q.
The first quartile (Q 1) is defined as the 25th percentile where lowest 25% data is below this point. It is also known as the lower quartile. The second quartile (Q 2) is the median of a data set; thus 50% of the data lies below this point. The third quartile (Q 3) is the 75th percentile where
The Q-statistic or q-statistic is a test statistic: . The Box-Pierce test outputs a Q-statistic (uppercase) which follows the chi-squared distribution . The Ljung-Box test is a modified version of the Box-Pierce test which provides better small sample properties
In statistics, the Q-function is the tail distribution function of the standard normal distribution. [ 1 ] [ 2 ] In other words, Q ( x ) {\displaystyle Q(x)} is the probability that a normal (Gaussian) random variable will obtain a value larger than x {\displaystyle x} standard deviations.
The q-value can be interpreted as the false discovery rate (FDR): the proportion of false positives among all positive results. Given a set of test statistics and their associated q-values, rejecting the null hypothesis for all tests whose q-value is less than or equal to some threshold ensures that the expected value of the false discovery rate is .
First, with a data sample of length n, the data analyst may run the regression over only q of the data points (with q < n), holding back the other n – q data points with the specific purpose of using them to compute the estimated model’s MSPE out of sample (i.e., not using data that were used in the model estimation process).