Protein Engineering Protocols - Mycobacteriology research center

Protein Library Design and Screening 149Fig. 7. Decision to accept or reject an experimental result based on the χ 2 test. Thevalue q is calculated for an experimental outcome and is compared with a value of χ 2 ,chosen at the desired level (α) of significance from a table of values. If q χ 2 , the outcome is assigned the value1, and is rejected.Example 2. Three possible outcomes: Suppose an experiment theoreticallyyields outcome A, 20% of the time; outcome B, 30% of the time; and outcomeC, 50% of the time. The experiment is run 20 times by a new student in the lab;the student obtains 8 outcomes A, 6 outcomes B, and only 6 outcomes C. Is thiscredible? Is the student’s technique trustworthy?The statistic is:2 2( 8−20×020 . ) ( 6−20×0. 30)( 6 − 20 × 0.50)q =++20 × 0.20 20 × 0.30 20 × 0.502= 56 .At the level 5%, we have χ 2 0.05 (2) = 5.991 and: q = 5.6 < 5.991 = χ2 0.05 (2)indicates that the statistic q, and the discrepancy with the expected results, arenot so large that we can conclude that there is a flaw in the student’s procedure;the hypothesis cannot be rejected. However, if we are ready to work withα=10%, then χ 2 0.1 (2) = 4.605, and the test becomes: q = 5.6 > 4.605 = χ2 0.1 (2)and we are able to reject the hypothesis that the actual experiment is theintended one.4. Notes1. The answers to Problems A and B (Subheadings 3.1.1.1. and 3.1.1.2.) rely on thetheory of Poisson approximations of sums of Bernoulli random variables, which