Q test

On occasion, a data set appears to be skewed by the presence of one or more data points that are not consistent with the remaining data points. Such values are called outliers. The most commonly used significance test for identifying outliers is Dixon s Q-test. The null hypothesis is that the apparent outlier is taken from the same population as the remaining data. The alternative hypothesis is that the outlier comes from a different population, and, therefore, should be excluded from consideration. 

The Q-test compares the difference between the suspected outlier and its nearest numerical neighbor to the range of the entire data set. Data are ranked from smallest to largest so that the suspected outlier is either the first or the last data... 

In this experiment students measure the length of a pestle using a wooden meter stick, a stainless-steel ruler, and a vernier caliper. The data collected in this experiment provide an opportunity to discuss significant figures and sources of error. Statistical analysis includes the Q-test, f-test, and F-test. 

This experiment uses the change in the mass of a U.S. penny to create data sets with outliers. Students are given a sample of ten pennies, nine of which are from one population. The Q-test is used to verify that the outlier can be rejected. Glass data from each of the two populations of pennies are pooled and compared with results predicted for a normal distribution. 

The stretching properties of polymers are investigated by examining the effect of polymer orientation, polymer chain length, stretching rate, and temperature. Homogeneity of polymer films and consistency between lots of polymer films also are investigated. Statistical analysis of data includes Q-tests and f-tests. 

The detection of outliers, particularly when working with a small number of samples, is discussed in the following papers. Efstathiou, G. Stochastic Galculation of Gritical Q-Test Values for the Detection of Outliers in Measurements, /. Chem. Educ. 1992, 69, 773-736. 

Dixon s Q-test statistical test for deciding if an outlier can be removed from a set of data. (p. 93) dropping mercury electrode an electrode in which successive drops of Hg form at the end of a capillary tube as a result of gravity, with each drop providing a fresh electrode surface, (p. 509)... 

A commercially interesting low calorie fat has been produced from sucrose. Proctor Gamble has patented a mixture of penta- to octafatty acid ester derivatives of sucrose under the brand name Olestra. It was approved by the FDA in January 1996 for use as up to 100% replacement for the oil used in preparing savory snacks and biscuits. Olestra, a viscous, bland-tasting Hquid insoluble in water, has an appearance and color similar to refined edible vegetable oils. It is basically inert from a toxicity point of view as it is not metabolized or absorbed. It absorbs cholesterol (low density Hpoprotein) and removes certain fat-soluble vitamins (A, D, E, and K). Hence, Olestra has to be supplemented with these vitamins. No standard LD q tests have been performed on Olestra however, several chronic and subchronic studies were performed at levels of 15% in the diet, and no evidence of toxicity was found. No threshold limit value (TLV), expressed as a maximum exposure per m of air, has been estabhshed, but it is estimated to be similar to that of an inert hpid material at 5 mg/m. ... 

Another method that may be employed to test whether single data points should be included in a sample mean is the Q-test. This simple test determines the confidence with which a data point can or cannot be considered part of the data set. The test calculates a ratio of the gap between the data point and its nearest neighbor and the range of the complete data set ... 

Q-test for rejection of, 252t weighting, 237-239 Degrees of freedom, 241 De-orphanization, 180 Dependent variables, 35, 162 Depolarization thresholds, 16 Descriptive statistics... 

Gan R, Sacco RL, Kargman DE, Roberts JK, Boden-Albala B, Gu Q. Testing the validity of the lacunar h3fpothesis the Northern Manhattan Stroke Study experience. Neurology 1997 48 1204-1211. 

Q Test statistic (estimate) of Dixon s outlier test (4.35)... 

Apply Q-test, reject 0.60 t= 1.21. The difference is significant at less than 90% confidence and the new method may be used. 

The Q test, suggested by Dean and Dixon (1951) is statistically correct and valid, and it may be applied easily as stated below ... 

Example Five determinations of the ampicillin content in capsules of a marketed product gave the following results 0.248, 0.245, 0.265, 0.249 and 0.250 mg per capsule. Apply the Q-test to find out if the 0.265 value can be rejected. 

Note The Q-test administers excellent justification for the outright rejection of abnormally erroneous values however, it fails to eliminate the problem with less deviant suspicious values. 

For small data sets (n < 10), which are often encountered in chemical analysis, a simple method to determine if an outlier is rejectable is the Q test. In this test, a value for Q is calculated and compared to a table of Q values that represent a certain percentage of confidence that the proposed rejection is valid. If the calculated Q value is greater than the value from the table, then the suspect value is rejected and the mean recalculated. If the Q value is less than or equal to the value from the table, then the calculated mean is reported. Q is defined as follows ... 

Determine if any of the values in Example 4.1 should be rejected based on the Q test at the 90% confidence level. 

If the data as a whole appear normally distributed but there is concern that an extreme point is an outlier, it is not necessary to apply the Rankit procedure. The Grubbs s outlier test (1950) is now recommended for testing single outliers, replacing Dixon s Q-test. After identifying a single outlier, which, of course, must be either the maximum or minimum data value, the G statistic is calculated ... 

An outlier is an individual measurement that appears to be statistically different from others when a series of replicate measurements is performed. The Q test is an easy test used to define an outlier. 

If the (2observed > (2theoreticab the outlier may be discarded. The Q test gives a good evaluation of the outlier when the number of observations >5. Different intervals of confidence can be chosen to evaluate theoretical even if a 95% confidence limit is suggested. 

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