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The ear lengths measured in table 18.2 are a sample of all ear lengths in the theoretically in nite population of ears in that variety of corn. Statisticians call sample values statistics (and use letters from the Roman alphabet to represent them), whereas they call population values parameters (and use Greek letters for them). The sample value is an estimate of the true value for the population. Thus, in the variance formula (equation 18.2), the sample value, V or s2, is an estimate of the population variance, 2. When sample values are used to estimate parameters, one degree of freedom is lost for each parameter estimated. To determine the sample variance, we divide not by the sample size, but by the degrees of freedom (n 1 in this case, as de ned in chapter 4). The variance for the entire population (assuming we know the population mean, , and all the data values) would be calculated by dividing by n. The sample variance is calculated in table 18.2. The variance has several interesting properties, not the least of which is the fact that it is additive. That is, if we can determine how much a given variable contributes to the total variance, we can subtract that amount of variance from the total, and the remainder is caused by whatever other variables (and their interactions) affect the trait. This property makes the variance extremely important in quantitative genetic theory. The standard deviation is also a measure of variation of a distribution. It is the square root of the variance: s V

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The use of a thermocouple requires special connections, because the junction of the thermocouple wires with other leads (such as voltmeter leads, for example) creates additional thermoelectric junctions that in effect act as additional thermocouples For example, in the J thermocouple circuit of Figure 153, junction J1 is exposed to the temperature to be measured, but junctions J2 and J3 also generate a thermoelectric voltage, which is dependent on the temperature at these junctions, that is, the temperature at the voltmeter connections One would therefore have to know the voltages at these junctions, as well, in order to determine the actual thermoelectric voltage at J1 To obviate this problem, a reference junction at known temperature can be employed; a traditional approach involves the use of a cold junction, so called because it often consists of an ice bath, one of the easiest means of obtaining a known reference temperature Figure 154 depicts a thermocouple measurement using an ice bath The voltage measured in Figure 154 is dependent on the temperature difference T1 Tref , where Tref = 0 C The connections to the voltmeter are made at an isothermal block, kept at a constant temperature; note that the same metal is used in both of the connections to the isothermal block Thus (still assuming a J thermocouple), there is no difference between the thermoelectric voltages at the two copper-iron junctions; these will add to zero at the voltmeter The voltmeter will therefore read a voltage proportional to T1 Tref An ice bath is not always a practical solution Other cold junction temperature compensation techniques employ an additional temperature sensor to determine the actual temperature of the junctions J2 and J3 of Figure 153

(18.3)

Resistance Temperature Detectors (RTDs)

A resistance temperature detector (RTD) is a variable-resistance device whose resistance is a function of temperature RTDs can be made with both positive and negative temperature coef cients and offer greater accuracy and stability than thermocouples Thermistors are part of the RTD family A characteristic of all RTDs is that they are passive devices, that is, they do not provide a useful output unless excited by an external source The change in resistance in an RTD is usually converted to a change in voltage by forcing a current to ow through the device An indirect result of this method is a self-heating error, caused by the i 2 R heating of the device Self-heating of an RTD is usually denoted by the amount of power that will raise the RTD temperature by 1 C Reducing the excitation current can clearly help reduce self-heating, but it also reduces the output voltage The RTD resistance has a fairly linear dependence on temperature; a common de nition of the temperature coef cient of an RTD is related to the change in

The McGraw Hill Companies, 2001

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