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Q–Q plot for first opening/final closing dates of Washington State Route 20, versus a normal distribution. [5] Outliers are visible in the upper right corner. A Q–Q plot is a plot of the quantiles of two distributions against each other, or a plot based on estimates of the quantiles. The pattern of points in the plot is used to compare the ...
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 .
To apply a Q test for bad data, arrange the data in order of increasing values and calculate Q as defined: Q = gap range {\displaystyle Q={\frac {\text{gap}}{\text{range}}}} Where gap is the absolute difference between the outlier in question and the closest number to it.
The Q-function is well tabulated and can be computed directly in most of the mathematical software packages such as R and those available in Python, MATLAB and Mathematica. Some values of the Q-function are given below for reference.
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
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 cumulative distribution function (shown as F(x)) gives the p values as a function of the q values. The quantile function does the opposite: it gives the q values as a function of the p values. Note that the portion of F(x) in red is a horizontal line segment.
An appropriate value of p in the ARMA(p, q) model can be found by plotting the partial autocorrelation functions. Similarly, q can be estimated by using the autocorrelation functions. Both p and q can be determined simultaneously using extended autocorrelation functions (EACF). [9]