Standard error of the mean SEM

Table 1 Cytotoxicity towards A2780, A2780cisR, HT29 and A549 cancer cells, and ECRF24 endothelial cells, and intracellular uptake in A2780 cells and logP0/w values of 1 - 3. Errors represent the standard error of the mean (SEM)...

Most commonly, location is described by giving the (arithmetic) mean and dispersion by giving the standard deviation (SD) or the standard error of the mean (SEM). The calculation of the first two of these has already been described. If we again denote the total number of data in a group as N, then the SEM would be calculated as... 

To establish the probability table, the standard error of the mean (SEM) must be calculated as presented earlier or as... 

Table 7.1 Mean values (means) and standard errors of the means (SEM) of relaxation time and maxima of exposition-to-relaxation ratio Max/Max of TCNQ sensor response curves obtained with exhaled air of patients with gastric and duodenal inflammation...

Data were expressed as the mean standard error of the mean (SEM). Differences between means were determined using one-way analysis of variance (ANOVA) followed by the Tukey-Kramer post hoc comparison and two-sided t test. For comparing percentages, nonparametric tests were also applied (Mann-Whitney, Kruskal-Wallis). Differences were considered significant when p < 0.05. 

The larger the sample size, the more likely it is that the sample mean is a good representation of the population mean If the sample were large enough to contain the entire population, the sample mean would be identical to the population mean. In a clinical trial, the sample size is precisely known. Knowledge of the sample SD and the sample size (N) facilitates precise calculation of the sample standard error of the mean (SEM) ... 

Confidence intervals consist of a sample mean the standard error of the mean (SEM) multiplied by a certain factor. Consider the example of adult height. Imagine selecting a sample of 100 adult males and measuring their heights. On the basis of these 100 measurements, the sample mean and the sample SD can be calculated. Then, on the basis of the SD and the size of the sample (N), the SEM can be calculated as shown in Equation 8.1. Imagine the following hypothetical data ... 

The sum of all deviations from the mean — that is, Z (xt — 3c) —will always equal zero. Summing the absolute values of the deviations from the mean results in a quantity that expresses dispersion about the mean. This quantity is divided by n to yield a measure known as the mean deviation or the standard error of the mean (SEM), which expresses the confidence in the resulting mean value ... 

FIGURE 6 Changes in area under the curve (AUC0 i2o) for blood glucose values in rats that received 2U insulin in presence of alkylmaltosides. Data represent mean change in AUC0120 in arbitrary units (AU) + standard error of the mean (SEM) compared with rats that received insulin formulated without alkylmaltoside (n = 3,4). (Reproduced from ref. 66 with permission of John Wiley Sons.)... 

In most analytical experiments where replicate measurements are made on the same matrix, it is assumed that the frequency distribution of the random error in the population follows the normal or Gaussian form (these terms are also used interchangeably, though neither is entirely appropriate). In such cases it may be shown readily that if samples of size n are taken from the population, and their means calculated, these means also follow the normal error distribution ( the sampling distribution of the mean ), but with standard deviation sj /n this is referred to as the standard deviation of the mean (sdm), or sometimes standard error of the mean (sem). It is obviously important to ensure that the sdm and the standard deviation s are carefully distinguished when expressing the results of an analysis. 

Other parameters frequently used are the mean absolute deviation (MAD), as an estimator of the dispersion of groups of single observations, and the standard error of the mean (SEM), which is used to calculate the confidence limits of a mean value. Their formulae are presented in Eqs. 16.6 and 16.7. 

The variability of the mean test result from a group of n patients decreases proportionally to the square root of the number of determinations. The variability of the estimated mean is given by the standard error of the mean (SEM), which is equal to the standard deviation of the patient population divided by the square root of n, the number of patient measurements included in the group mean. Consider the following example, where the s of the patient values is 100 units. As n increases to 16, 25, 100, and 400, the SEM becomes 25, 20, 10, and 5 units, respectively. If the s of the analytical method was 10 units, the distribution of patients would be 10 times as large however, if one considers the mean values of groups of 100 patients, the variability (SEM) of the group mean is approximately equal to the variability... 

Determination of cellular lactate production. Lactate concentration changes were evaluated on culture medium by H nuclear magnetic resonance analysis (NMR Gemini 300 spectrometer, Varian, Palo Alto, CA). Experiments were performed as already reported.6 Statistical analysis. All results were expressed as means standard error of the mean (SEM) taking into consideration at least three different experiments performed in duplicate. The means were compared by analysis of variance (ANOVA), p<0.05 was considered significant. 

Notes-, (a) Based on NHANES III (1988-1994) laboratory sample, weighted to national population, (b) Excluding patients with thyroid disease and goiter, (c) GM - Geometrlo means. Weighted geometric mean standard error of the mean (SEM) and 95% confidence Interval. 

As noted above, each RBA value is calculated as the ratio of two slopes (UEFs), each of which is estimated by linear regression through a set of data points. Because of the variability in the data, uncertainty exists in the estimated slope (UEF) for each material. This uncertainty in the slope is described by the standard error of the mean (SEM) for the slope parameter. 

The variability associated with a mean is smaller than that of a single measurement. The SD associated with the mean [also called the standard error of the mean (SEM) ] is smaller than the SD by a factor equal to the square root of the number of measurements used to calculate the mean. In our example, SEM =10.5/-v/l0= 10.5/3.16 = 3.32. Thus, in our experiment the probability is 95% that the mean change will fall between -6.64 and +6.64. The mean of 12.8 is well outside that range. In fact, 12.8/SEM = 3.85. The probability of obtaining a ratio of 3.85 or larger is now approximately 0.15%. 

Figure 9.8 Individual values with standard error of the mean (SEM) bars, where appropriate, for FDG uptake in healthy subjects and a number of patient groups. In the head injury series, the FDG uptake in the only patient with lung symptoms is shown as a black dot. Although high, this was not the highest point. Individual points in showing FDG uptake in the pneumonic lung are labeled with the number of days since the onset of s3Tnptoms. The double-headed arrow indicates repeat measurements made in an individual patient. [Composite illustration was constructed from results of several studies (23,28,31,32).]...

Log ATow is the logio octanol-water partition coefficient. Included are the mean, standard deviation (sd), and standard error of the mean (sem) for all data. Data from 1, Radding et al. (1976) 2, Leo et al. (1971) 3, Karickhoff et al. (1979) 4, de Bruijn et al. (1989) 5, Hansch and Leo (1979) 6, Konasewich et al. (1982) 7, Krishnamurthy and Wasik (1978) 8, Mackay et al. (1980) 9, Means et al. (1980) 10, Miller et al. (1985) 11, Mills et al. (1982) 12, U.S. EPA Athens, slow stir method 13, Bruggeman et al. (1982) 14, Hammers et al. (1982) 15, De Kock and Lord (1987) 16, D Amboise and Hanai (1982) 17, early-release prototype version of the SPARC model, Karickhoff et al. (1991). Bold indicates mean of many values from this citation MW is molecular weight in daltons. No distinction was made between measured and calculated AT s. Most AowS for a compound are unique however, there is the possibility that some entries occur in two or more citations. 

In the two extreme sectors beyond p 4 A (the tails of the distribution) it falls only 0.26 % of the entire population of experimental data having a true mean given by p. This actually means that just one over 10,000 samples will yield a value below p — 4-A or above p + 4 A. The standard error of the mean (SEM) is the standard deviation of the sample mean estimate of a population mean. SEM is... 

Healthy euthyroid and nongoitrous subjects have been investigated for iodine intake directly and indirectly, by various methodologies including the determination of stable iodine concentration on 24 hr excretion collections (either directly measured on 24 hr urine collections or calculated by the use of the iodine/creatinine or l/Cr ratio), the determination of iodine concentration in the urines, iodine kinetic studies (particularly of the inorganic iodine compartment) and iodine balance studies as well. Most of the values are given as mean standard deviation the standard error of the mean (sem) is specified when used. 

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