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By Athanasios Papoulis

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Limiting position of distribution of sample averages. 99, etc. where A is the tabulated area. Distribution of the Standard Deviation The form of the distribution of standard deviations is quite dependent upon the number of measurements from which the standard deviation is calculated. table rather than from the table of normal distribution areas. 26 STATISTICAL METHODS bers of measurements the standard deviation tends to be lower on the average than the true standard deviation of the population from which the samples were taken for measure- ment.

34 STATISTICAL METHODS Student's t-Test for Paired Differences The results of an experiment on plasticizers for nylon is given in Table III-2. 3 probability levels not sufficiently improbable to refute the null hypothesis that there is no difference between the plasticizers in their rate of TABLE III-2 Plasticizer Analysis for Two Types of Plasticizers (initial plasticizer content = 20%) After 48 hr. at 60°C After 7 days at 50°C After 48 hr. at 70°C After 7 days at 70°C After 3 mo. Florida exposure....

Partition of Sums of Squares The total sum of squares of a data set (obtained by sum- ming the squares of deviations of all the measurements from their grand mean, 23 (X X)2, may likewise be separated into components and each component assigned to the testing of one and only one hypothesis. The portion of the sum of squares assigned to a particular factor is associated with the number of degrees of freedom assigned to that factor and, if this sum of squares is divided by the corresponding degrees of freedom, the result is an estimate of the basic variance of the population sampled provided the null hypothesis is true.

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