Standard error of the mean

Confidence intervals also can be reported using the mean for a sample of size n, drawn from a population of known O. The standard deviation for the mean value. Ox, which also is known as the standard error of the mean, is... 

Vitha, M. F. Carr, P. W. A Laboratory Exercise in Statistical Analysis of Data, /. Chem. Educ. 1997, 74, 998-1000. Students determine the average weight of vitamin E pills using several different methods (one at a time, in sets of ten pills, and in sets of 100 pills). The data collected by the class are pooled together, plotted as histograms, and compared with results predicted by a normal distribution. The histograms and standard deviations for the pooled data also show the effect of sample size on the standard error of the mean. 

Show by a propagation of uncertainty calculation that the standard error of the mean for n determinations is given as s/VTj. 

SEM = standard error of the means. IGF-I = insulin-like growth factor I. 

The estimate of variability for a sample mean is the standard error of the mean ... 

So how does one infer that two samples come from different populations when only small samples are available The key is the discovery of the t-distribution by Gosset in 1908 (publishing under the pseudonym of Student) and development of the concept by Fisher in 1926. This revolutionary concept enables the estimation of ct ( standard deviation of the population) from values of standard errors of the mean and thus to estimate... 

FIGURE 11.2 Paired experimental data. Values of constitutive calcitonin receptor activity [1 -(Tr/Tj) units] in transiently transfected melanophores. Five separate experiments are shown. Points to the left indicate the basal level of constitutive activity before (filled circles) and after (open circles) addition of 100 nM AC512 (calcitonin receptor inverse agonist). Lines join values for each individual experiment. Points to the right are the mean values for constitutive activity in control (filled circles) and after AC512 (open circles) for all five experiments (bars represent standard errors of the mean). Data shown in Table 11.3. 

The mean of several readings (x) will make a more reliable estimate of the true mean (yu) than is given by one observation. The greater the number of measurements (n), the closer will the sample average approach the true mean. The standard error of the mean sx is given by ... 

Fig. 7. vs gp) mean values for bone collagens of herbivores and omnivores including humans from Great Britain, Hungary, Peru and Canada dating from the Neolithic to the mid-15th century AD (adapted from Reynard Hedges 2008). Error bars indicate one standard error of the mean of 10 to 15 samples per species. 

Figure 4.1 Time-course of free-radical production during aerobic (a) or anoxic (b) reperfusion of the isolated rat heart. Radical production was assessed using e.s.r. and quantified as the formation of a Af-tert-butyl-a-phenylnitrone (PBN) spin adduct. After a 35 min stabilization period of aerobic perfusion, hearts were made globally ischaemic for 15 min. Hearts were then reperfused, either with oxygenated buffer (a) (n = 6), or with anoxic buffer, switching to an oxygenated buffer after 10 min (b) (n = 5). The bars represent the standard errors of the means. Redrawn with permission from Garlick et af. (1987).

Table 4.1 Effect of selected thiols, disulphides, amino acids and antioxidants on the time to the onset and the time to reach maximal ischaemic contracture in isolated perfused rat hearts. Hearts were perfused for a control period of 10 min at the end of which global low-flow (10% of control) ischaemia was initiated. The interventions described above were included in the perfusion fluid 5 min prior to the onset and throughout the ischaemic period. The data are shown as means standard errors of the means (n = 6)...

Figure 4.10 Effect of reduced glutathione (GSH) (0-1.0 mM) on Na/K ATPase inhibition associated with the addition of oxidized glutathione (GSSG) (1 me). Experiments were performed using an isolated bovine ventricular Na/K ATPase preparation. Na/K ATPase activity was quantified by the ouabain-sensitive hydrolysis of ATP to yield inorganic phosphate. The data are presented as means standard errors of the means (n = 6).

SEM Standard error of the mean SGAW Specific airway conductance... 

NOTE Values represent the mean standard error of the mean. 

Fig. 4 Mean cumulative urinary excretion of nitrofurantoin after oral administration of a 100-mg macrocrystalline capsule of fasting (O) and nonfasting ( ) subjects and a 100-mg microcrystalline tablet to fasting ( ) and nonfasting ( ) subjects. Vertical bars represent standard errors of the mean. (From Ref. 7.).

FIGURE 1.17 Schild plot for the action of atropine in antagonizing the action of acetylcholine on guinea-pig ileum. Each point gives the mean the standard error of the mean of the number of observations shown. 

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)...

Figure 3 Migration inhibition assessment of ECRF24 and MDA-MB-231 cells after exposure to compound 1 and 3. Wound closure in ECRF24 cultures after 7 h of incubation with concentration ranges of 1 (A) and 3 (B). (C) Typical images of the wound at the beginning of the experiment (culture medium as a control) and after 7 h of incubation with 3, 60 pM. Error bars represent standard error of the mean. P < 0.05.

Scale bar 200 pm. Red arrows indicate the avascular zones. Quantification of digital analysis of the fluorescence angiography images number of branching points (mm2) (B) and mean mesh size (102 pm2) (C) as markers of vessel density for CAM. P < 0.05 was considered to be statistically significant. Error bars represent standard error of the mean. 

The uncertainty in the finite-data free energy values, 5 A A, can be estimated as twice the standard error of the mean, 8AA = 2[Pg.240]

The ratios of the experimental to the calculated values for deposition efficiency for each generation are shown for each of the experiments in Figures 2-4. The error bars represent the standard error derived from the mean measured deposition fraction for the generation. A coefficient of variation was calculated for the measured deposition in each generation which was used to obtain an estimate of the standard error of the ratio. It was assumed that no additional variability in the ratio was introduced by the calculated deposition fraction. The mean ratio for all six sets of cast measurements is shown in Figure 5. The error bars in Figure 5 represent the standard error of the mean of the six experiments. 

Fig. 4.6. The integrated signals of harmonics from an H2 gas (lO.OTorr), a D2 gas (lO.OTorr), and a gas of their mixture (lO.OTorr) measured as a function of the harmonic order q. The signals are normalized to those from the H2 gas and vertical errors represent SEM (standard error of the mean) for 800 laser shots...

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... 

The standard deviation of the collection of all possible means of samples of a given size, called the standard error of the mean, depends on both the standard deviation of the original population and the size of the sample. 

Table 9.21 gives the yields, times to maximum yield, retention times and least detectable amounts of the herbicide esters or ethers prepared using the above method. In no instance was the standard error of the mean yield >2%. The least detectable amount is based on a peak giving a response of twice the background signal. 

Standard error of the mean (SEMI Is a statistical assessment of the increased confidence in a result ighen ft isthe meert of a iiQfinM numw or. replicates rather than a single measurement... 

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