Two Means

We obtain two sets of numbers, and wish to test whether the mean of one set is significantly different from the mean of the other set, or whether the two sets can be regarded as drawn from one population. 

There is frequent need to compare two or more sets of data. For example, sample uniformity can be estimated by analysis of sets of laboratory samples gathered from different parts or at different times or both of the object(s) being measured. Although the means of the various sets can be expected to differ somewhat, how much of a difference indicates nonuniformity or real difference rather than experimental uncertainty. 

The criterion forjudging that Xg and X, are significantly different if lXg-Xbl tSpi/(Ng+Nb)/NgNb where values of t are obtained from Table 12.2. 

Confidence Level, or Probability That X3 - X, is Less Than the Limits Above When Pa l b 

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It should be stressed that these polarized orbital pairs are not the same as hybrid orbitals. The latter are used to deseribe direeted bonding, but polarized orbital pairs are eaeh a mixture of two mean-field orbitals with... 

Thus we are challenged by the problem of measuring a small signal against the background of one much stronger. The problem is usually solved by one of two means (a) lock-in-amplifier detection and (b) a boxcar type of detection (to some extent we can include double-input optical multichannel detection in this category). 

Statistical test for comparing two mean values to see if their difference is too large to be explained by indeterminate error. 

Significance testing for comparing two mean values is divided into two categories depending on the source of the data. Data are said to be unpaired when each mean is derived from the analysis of several samples drawn from the same source. Paired data are encountered when analyzing a series of samples drawn from different sources. 

The analysis of cigarette smoke for 16 different polyaromatic hydrocarbons is described in this experiment. Separations are carried out using a polymeric bonded silica column with a mobile phase of 50% v/v water, 40% v/v acetonitrile, and 10% v/v tetrahydrofuran. A notable feature of this experiment is the evaluation of two means of detection. The ability to improve sensitivity by selecting the optimum excitation and emission wavelengths when using a fluorescence detector is demonstrated. A comparison of fluorescence detection with absorbance detection shows that better detection limits are obtained when using fluorescence. 

This value of fexp is compared with the critical value for f(a, v), where the significance level is the same as that used in the ANOVA calculation, and the degrees of freedom is the same as that for the within-sample variance. Because we are interested in whether the larger of the two means is significantly greater than the other mean, the value of f(a, v) is that for a one-tail significance test. 

A magnetic-sector/TOP hybrid has two means of measuring m/z values, one very accurately in a conventional magnetic/electric-sector sense, and the other somewhat less accurately in a time-of-flight sense. 

The term glass has two meanings, ie, the material and a state of matter. The glassy or vitreous condition is where the atoms of the material have a random orientation. This amorphous or noncrystalline nature leads to physical properties typical of the product caHed glass, including unpredictable breaks, no sharp melting temperature, and no heat of fusion. 

As an idealization of the classified-fines removal operation, assume that two streams are withdrawn from the crystallizer, one corresponding to the product stream and the other a fines removal stream. Such an arrangement is shown schematically in Figure 14. The flow rate of the clear solution in the product stream is designated and the flow rate of the clear solution in the fines removal stream is set as (R — 1) - Furthermore, assume that the device used to separate fines from larger crystals functions so that only crystals below an arbitrary size are in the fines removal stream and that all crystals below size have an equal probabiHty of being removed in the fines removal stream. Under these conditions, the crystal size distribution is characterized by two mean residence times, one for the fines and the other for crystals larger than These quantities are related by the equations... 

Thus the average cost per share for John is the arithmetic mean of pi, po,. . . , pn, whereas that for Mary is the harmonic mean of these n numbers. Since the harmonic mean is less than or equal to the arithmetic mean for any set of positive numbers and the two means are equal only i pi=po = =pn, we conclude that the average cost per share for Mary is less than that for John if two of the prices Pi are distinct. One can also give a proof based on the Gaiichy-Schwarz inequality, To this end, define the vectors... 

Expressing the requirements in terms of requirements that can be verified and validated has two meanings. You need to be able to verify that both the design input requirements and user requirements (if different) have been achieved in the product so they need to be expressed in appropriate terms. The vehicle to contain such requirements is usually a product or service specification. You also need to be able to verify that the design output meets the design input and to achieve this you will need to document your calculations and analyses. 

Comparing two mean values to evaluate metliod/assays. 

COMPARISON OF MORE THAN TWO MEANS (ANALYSIS OF VARIANCE)... 

The comparison of more than two means is a situation that often arises in analytical chemistry. It may be useful, for example, to compare (a) the mean results obtained from different spectrophotometers all using the same analytical sample (b) the performance of a number of analysts using the same titration method. In the latter example assume that three analysts, using the same solutions, each perform four replicate titrations. In this case there are two possible sources of error (a) the random error associated with replicate measurements and (b) the variation that may arise between the individual analysts. These variations may be calculated and their effects estimated by a statistical method known as the Analysis of Variance (ANOVA), where the... 

The calculated value must be compared to a critical q that takes account of the distance that separates the two means in the ordered set if Xmean.u and Xmean.D are adjacent, the column labeled 2 in Table 1.11 must be used. 

Table 1.11. Critical q-Values for Two Means with Index Number Differences...

Two slopes are compared in a similar manner as are two means the simplest case is obtained when both calibrations are carried out using identical calibration concentrations (as is usual when SOPs are followed) the average variance V u is used in a t-test ... 

Enter Data Manually) opens an empty table for manual input of the two means, standard deviations and numbers of determinations. 

Two means are available for learning about the time at which reactions occur. One can vary the conditions of the irradiation— the time, temperature, and y-flux—in order to alter the value of F(t, T,y) of Eq. (4). The other, rather more versatile, approach is to perform various treatment on the... 

The amount to be depreciated may be calculated by two means. If the net salvage value is used the amount that can be depreciated is... 

Ans. You can tell from the context. For example, if a problem asks if a sample is a solution or a mixture, the word mixture means heterogeneous mixture. If it asks whether the sample is a compound or a mixture, it means any kind of mixture. Such usage occurs in ordinary English as well as in technical usage. For example, the word day has two meanings—one a subdivision of the other. How many hours are there in a day What is the opposite of night "... 

If more than two means have to be compared, the (-lest cannot be applied in a multiple way. Instead of this, an indirect comparison by analysis of variance (ANOVA) has to be used, see (3) below. 

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