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• In Q test the suspected value can be
retained when -----
Answer
A.Qcal > Q lit
B. Qcal < Q lit
C. Qcal = Q lit
D. none of the above
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Answer:
Theory
In a set of replicate measurements of a physical or chemical quantity, one or more of the obtained values may differ considerably from the majority of the rest. In this case there is always a strong motivation to eliminate those deviant values and not to include them in any subsequent calculation (e.g. of the mean value and/or of the standard deviation). This is permitted only if the suspect values can be "legitimately" characterized as outliers.
Usually, an outlier is defined as an observation that is generated from a different model or a different distribution than was the main "body" of data. Although this definition implies that an outlier may be found anywhere within the range of observations, it is natural to suspect and examine as possible outliers only the extreme values.
The rejection of suspect observations must be based exclusively on an objective criterion and not on subjective or intuitive grounds. This can be achieved by using statistically sound tests for "the detection of outliers".
The Dixon's Q-test is the simpler test of this type and it is usually the only one described in textbooks of Analytical Chemistry in the chapters of data treatment. This test allows us to examine if one (and only one) observation from a small set of replicate observations (typically 3 to 10) can be "legitimately" rejected or not.
Q-test is based on the statistical distribution of "subrange ratios" of ordered data samples, drawn from the same normal population. Hence, a normal (Gaussian) distribution of data is assumed whenever this test is applied. In case of the detection and rejection of an outier, Q-test cannot be reapplied on the set of the remaining observations.
How the Q-test is applied
The test is very simple and it is applied as follows:
(1) The N values comprising the set of observations under examination are arranged in ascending order:
x1 < x2 < . . . < xN
(2) The statistic experimental Q-value (Qexp) is calculated. This is a ratio defined as the difference of the suspect value from its nearest one divided by the range of the values (Q: rejection quotient). Thus, for testing x1 or xN (as possible outliers) we use the following Qexp values:
(3) The obtained Qexp value is compared to a critical Q-value (Qcrit) found in tables. This critical value should correspond to the confidence level (CL) we have decided to run the test (usually: CL=95%).