Tests of proportions

As for continuous data, a power curve can be generated for a number of scenarios for binary outcomes. As seen in Figure 12.2, the power of a test of proportions (for a fixed value of A) is quite sensitive to the particular assumed value of the response rate in the control (for example, placebo) group. 

The goal of this section is to introduce common statistic tests used in chemical education research (correlation coefficients, /-tests, ANOVAs and ANCOVAs, tests of proportions, and some non-parametric tests), and describe specific examples of studies from the chemical education literature that have used these tests. The list of statistics tests described here is not intended to be exhaustive it simply reflects the statistical tests most commonly used by chemical education researchers. 

Sanger, Phelps, and Fienhold (<5) used independent tests of proportions to analyze the differences in responses from students who viewed a computer animation of a can-crushing demonstration and from students who did not. They found that students who viewed the animation were more likely to provide correct explanations (34% versus 17% z = 3.02, p =. 0025), were more likely to recognize that the condensation of water was important (58% versus 24% z = 4.25, p <. 0001), and less likely to blindly quote ideal gas laws in their predictions (6% versus 33% z = -4.38, p <. 0001). The first two z-values were positive because the animation had a positive effect on the students responses the lastz-value was negative because the animation had a negative effect on the proportion of students blindly quoting gas laws. 

The study performed by Sanger et al. (24) demonstrates the different uses of chi-square tests. The data, which appear in Table I, show the frequency of student responses to a particulate gas-law question that has appeared in several chemical education research studies (24-27), Sanger et al. investigated whether viewing an animated version of the multiple-choice question would change the distribution of student responses. If the researchers were only interested in the proportion of students getting the question right, they could have used a test of proportions, but since they were interested in the distribution of all four choices, a test was used. 

The sample labeled atactic in Fig. 7.10 was prepared by a free-radical mechanism and, hence, is expected to follow zero-order Markov statistics. As a test of this, we examine Fig. 7.9 to see whether the values of p, P, and Pj, which are given by the fractions in Table 7.9, agree with a single set of p values. When this is done, it is apparent that these proportions are consistent with this type... 

Although still preliminary, the study that provides the most detailed test of the theory for the electronic properties of the ID carbon nanotubes, thus far, is the combined STM/STS study by Oik and Heremans[13]. In this STM/STS study, more than nine individual multilayer tubules with diameters ranging from 1.7 to 9.5 nm were examined. The 7-Fplots provide evidence for both metallic and semiconducting tubules[13,14]. Plots of dl/dV indicate maxima in the ID density of states, suggestive of predicted singularities in the ID density of states for carbon nanotubes. This STM/ STS study further shows that the energy gap for the semiconducting tubules is proportional to the inverse tubule diameter l/<7, and is independent of the tubule chirality. 

Couplings for grades J-55, K-55 and N-80 shall conform to the tensile requirements specified in Table 4-142. A tensile test shall be made on each heat of steel from which couplings are produced, and the coupling manufacturer shall maintain a record of such tests. This record shall be open to inspection by the purchaser. Either round specimens proportioned as specified in ASTME 8 Tension Testing of Metallic Materials, or strip specimens shall be used, at the option of the manufacturer. 

Tests of dieldrin against cotton pests have not been as extensive, but the Mississippi 1950 Cotton Insect Control Recommendations state that it kills a larger proportion of immature weevils in squares than any other insecticide tested thus far and is considered very promising for cotton insect control (4). 

Ziegler-Nichols Continuous Cycling (empirical tuning with closed loop test) Increase proportional gain of only a proportional controller until system sustains oscillation. Measure ultimate gain and ultimate period. Apply empirical design relations. 

An investigation of the association of the same molecules with Na+ over a range of temperatures showed that the rate coefficient is proportional to T-" as expected. The present findings of the investigations have provided a test of the available theoretical models and the usual procedures for determining n were not found to be valid. The data were found to be generally in accord with our suggestion that, for weakly bound systems, n is closely related to the number of new vibrational modes in the association complex. 

In contrast to variable testing (comparison of measured values or analytical values), attribute testing means testing of product or process quality (nonconformity test, good-bad test) by samples. Important parameters are the sample size n (the number of units within the random sample) as well as the acceptance criterion naccept, both of which are determined according to the lot size, N, and the proportion of defective items, p, within the lot, namely by the related distribution function or by operational characteristics. 

Many methods have been proposed and are used to study the thermal stability of propellants and to ensure the absence of possible autocatalysed decompositions during storage. None are sufficiently reliable to merit individual description. In practice, stabilisers are added, the usual being diphenylamine for nitrocellulose powders and symmetrical diethyl diphenyl urea (carbamate or centralite) for double base propellants. Provided a reasonable proportion of stabiliser remains, the propellant can be assumed to be free from the possibility of autocatalytic decomposition. The best test of stability is therefore a chemical determination of the stabiliser present. 

Linearity The ability of the method to obtain test results proportional to the concentration of the analyte. 

Development of proportional counters to measure C14/C12 ratios in 10 mg carbon samples was undertaken in the Chemistry Department of Brookhaven National Laboratory in 1975 [10] for two reasons (1) at the time, there was no other possibility in sight to accomplish the generally much-needed objective of small-sample C14 measurement, and (2) there was a particular carbon 14 dating problem at the Smithsonian Institution, which would only be solved if very small carbon samples could be handled. The development and testing of the counters has already been reported [9] in the present paper we discuss the application of those counters to the actual dating problem which concerned the Smithsonian Institution, the dating of the "Frobisher iron bloom". 

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