Statistics median

Another way is the robust parameter estimation on the basis of median statistics (see Sect. 4.1.2 Danzer [1989] Danzer and Currie [1998]). For this, all possible slopes between all the calibration points bij = (yj — yi)/(xj — X ) for j > i are calculated. After arranging the b j according to increasing values, the average slope can be estimated as the median by... 

Application of robust statistics, especially methods of median statistics, for quantitative description of widely varying values may give information which can often be interpreted better than the results from normal parametric statistical methods. 

The purpose of this study is the use of median statistics for quantitative and interpretable recording of the traffic-related impact of lead on soils [EINAX et al., 1991]. ... 

The methods of robust statistics have recently been used for the quantitative description of series of measurements that comprise few data together with some outliers [DAVIES, 1988 RUTAN and CARR, 1988]. Advantages over classical outlier tests, such as those according to DIXON [SACHS, 1992] or GRUBBS [SCHEFFLER, 1986], occur pri-marly when outliers towards both the maximum and the minimum are found simultaneously. Such cases almost always occur in environmental analysis without being outliers in the classical sense which should be eliminated from the set of data. The foundations of robust statistics, particularly those of median statistics, are described in detail by TUKEY [1972], HUBER [1981], and HAMPEL et al. [1986] and in an overview also by DANZER [1989] only a brief presentation of the various computation steps shall be given here. 

Distribution Averages. The most commonly used quantities for describing the average diameter of a particle population are the mean, mode, median, and geometric mean. The mean diameter, d, is statistically calculated and in one form or another represents the size of a particle population. It is usefiil for comparing various populations of particles. 

The probabihty-density function for the normal distribution cui ve calculated from Eq. (9-95) by using the values of a, b, and c obtained in Example 10 is also compared with precise values in Table 9-10. In such symmetrical cases the best fit is to be expected when the median or 50 percentile Xm is used in conjunction with the lower quartile or 25 percentile Xl or with the upper quartile or 75 percentile X[j. These statistics are frequently quoted, and determination of values of a, b, and c by using Xm with Xl and with Xu is an indication of the symmetry of the cui ve. When the agreement is reasonable, the mean v ues of o so determined should be used to calculate the corresponding value of a. 

When a distribufion of particle sizes which must be collected is present, the aclual size distribution must be converted to a mass distribution by aerodynamic size. Frequently the distribution can be represented or approximated by a log-normal distribution (a straight line on a log-log plot of cumulative mass percent of particles versus diameter) wmich can be characterized by the mass median particle diameter dp5o and the standard statistical deviation of particles from the median [Pg.1428]

In general, air quality data are classified as a function of time, location, and magnitude. Several statistical parameters may be used to characterize a group of air pollution concentrations, including the arithmetic mean, the median, and the geometric mean. These parameters may be determined over averaging times of up to 1 year. In addition to these three parameters, a measure of the variability of a data set, such as the standard deviation... 

Data point A numerical estimate of equipment reliability as a mean or median value of a statistical distribution of the equipment s failure rate or probability. 

Median Effective Dose (ED) The statistically derived single dose of a substance that can be expected to cause a defined nonlethal effect in 50% of a given population of organisms under a defined set of e.xperimental conditions. 

Populations are very large collections of values. In practice, experimental pharmacology deals with samples (much smaller collections) from a population. The statistical tools used to deal with samples differ somewhat from those used to deal with populations. When an experimental sample is obtained, the investigator often wants to know about two features of the sample central tendency and variability. The central tendency refers to the most representative estimate of the value, while the variability defines the confidence that the estimate is a true reflection of that value. Central tendency estimates can be the median (value that divides the sample into two equal halves) or the... 

The Interventional Management of Stroke (IMS I) Study was a multicenter, open-labeled, single-arm pilot study in which 80 patients (median NIHSS 18) were enrolled to receive IV rt-PA (0.6 mg/kg, 60 mg maximum, 15% of the dose as a bolus with the remainder administered over 30 minutes) within 3 hours of stroke onset (median time to initiation 140 minutes). " Additional rt-PA was subsequently administered via a microcatheter at the site of the thrombus in 62 of the 80 patients, up to a total dose of 22 mg over 2 hours of infusion or until complete recanalization. Primary comparisons were with similar subsets of the placebo and rt-PA-treated subjects from the NINDS rt-PA Stroke Trial. The 3-month mortality in IMS I subjects (16%) was numerically lower but not statistically different than the mortality of the placebo (24%) or rt-PA-treated subjects (21%) in the NINDS rt-PA Stroke Trial. The rate of symptomatic ICH (6.3%) in IMS I subjects was similar to that of the rt-PA-treated subjects (6.6%) but higher than the rate in the... 

Box plots, also known as box and whisker plots, are commonly used to display univariate statistics for a given variable across another variable. The statistics typically displayed in a box plot are the minimum, first quartile, median, third quartile, and maximum values. Mean values are often included in box plots as well. The following is a sample box plot of a clinical response measure showing how three different drug therapies compare to one another. 

In 1990, Vatten et al.51 in Norway subsequently reviewed data on breast cancer risk from a cohort of 14,593 women with 152 cases of breast cancer during a follow up of 12 years on subjects who were between 35 and 51 years old at the beginning of the study and between 46 and 63 years at the end. They reported no overall statistically significant correlation between breast cancer and coffee consumption, but when body mass index was taken into account, lean women who consumed >5 cups per day had a lower risk than women who drank two cups or less. In obese women, however, there was a positive correlation between coffee intake and breast cancer. In a 1993 study, though, Folsom and associates52 failed to find an association between caffeine and postmenopausal breast cancer in 34,388 women in the Iowa Women s Health Study, with a median caffeine intake of 212 mg/day in women who developed breast cancer and 201 mg/day for women who did not and in Denmark, Ewertz53 studied... 

Comparisons between observed data and model predictions must be made on a consistent basis, i.e., apples with apples and oranges with oranges. Since models provide a continuous timeseries, any type of statistic can be produced such as daily maximums, minimums, averages, medians, etc. However, observed data are usually collected on infrequent intervals so only certain statistics can be reliably estimated. Validation of aquatic chemical fate and transport models is often performed by comparing both simulated and observed concentration values and total chemical loadings obtained from multiplying the flow and the concentration values. Whereas the model supplies flow and concentration values in each time step, the calculated observed loads are usually based on values interpolated between actual flow and sample measurements. The frequency of sample collection will affect the validity of the resulting calculated load. Thus, the model user needs to be aware of how observed chemical loads are calculated in order to assess the veracity of the values. 

If possible, the intake should be expressed both as a statistical mean or median and maximum (e.g., 95th percentile). Ideally, a frequency distribution of exposure for the study area population is the goal. Inmost cases, however, the variability in exposure medium intake rates and pollutant concentrations are unknown and average/maximum values must suffice. 

The median values of REM sleep latency, total time asleep, and SWS (in minutes and as a percentage of total time asleep) were lower, and REM sleep (percent) values were found to be higher, in depressive disorders than in all other psychiatric conditions. However, the statistical differences between depressed patients and other psychiatric categories were far less evident. Indeed, no sleep variable reliably distinguished depressed patients from those with other psychiatric disorders. The investigators concluded that sleep disturbances are associated with most psychiatric disorders, although the most widespread and most severe disturbances are found in patients with depressive disorders (Van Bemmel 1997). 

In general, it can be seen that there is no incentive to price below RP the price of some generics in Germany has risen to RP, which was established as a statistical median of observed prices. 

Another source of acrylonitrile in water is leachate from chemical waste sites. Preliminary data from the Contact Laboratory Program (CLP) Statistical Database indicates that acrylonitrile has been detected in surface water samples collected at two of 862 hazardous-waste sites (including NPL and other sites) being investigated under Superfund. The median concentration of the positive samples was 100 pg/L (CLPSD 1988). Acrylonitrile was detected in 12 groundwater samples collected at 5 sites, also at a median concentration of 100 pg/L. 

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