By Oscar Kempthorne
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Extra info for Design and Analysis of Experiments
X II We can then find the probability that the inequality t < 7= < t s/Vn is satisfied: namely, the percentage point p corresponding to the value of I in the table of the t distribution with (n Now this inequality can be written as x 1) degrees of freedom. ts/y/n < n < x + ts/y/n, and the probability that the inequality in this form is satisfied is also p. If then, having drawn a sample, we construct the interval x ts/Vn to x + ts/Vn and say that the true mean lies within this interval, the probability that our statement is correct is equal to p.
4. Examination of possible outcomes and reference back to the reasons for the inquiry to be sure the experiment provides the required informa- tion to an adequate extent. 5. Consideration of the possible results from the point of view of the statistical procedures which will be applied to them, to ensure that the conditions necessary for these procedures to be valid are satisfied. 6. Performance of experiment. 7. Application of statistical techniques to the experimental results. 8. Drawing conclusions with measures of the reliability of estimates of any quantities that are evaluated, careful consideration being given to the validity of the conclusions for the population of objects or events to which they are to apply.
Does he mean that he will always be correct? If he does, our experimental procedure is quite simple; we toss pennies successively by some process, which we believe is random and which has been found to give results in accordance with random theory, and we stop the process when he makes a mistake. It should be noted that this hypothesis can never be proved, and it is true of all hypotheses that they can only be dis- proved. As a second example of this point, the law of gravitation states that the attractive force between two bodies of masses, m\ and m2 at distance r apart is y , , where 7 is a constant, but it cannot be proved that the power of r should be 2.