We also have to account for "degrees of freedom," listed as df in the table, but often given the Greek symbol ν. It is, of course, possible to present results with different probabilities of meeting the "real" value, but this corresponds to close to two standard deviations on either side of the "true" mean. In chemistry, we will normally want to report a 95% confidence interval, so select the column indicating P2 = 0.95. To calculate the confidence interval that this description provides, we will use the "two-sided" P2 to choose our probability. You will initially have calculated the mean of the data x̄ and the estimated standard deviation S m from the data set after applying the Q test for discordance, if necessary. The Student t Distribution Table P1 sided 433ff, or in Garland, Nibler & Schoemaker, pp. A full theoretical description is developed in Shafer & Zhang, Ch. Gosset (who went by the pseudonym "Student") requires finding a value of the t distribution for the number of observations that describes the desired probability for which we want to know the "how good?" question. The core problem with reporting a mean and an estimated standard deviation is that while it does describe the statistical behavior of our finite data set, it doesn't directly answer the question of "how good is the answer?" To do this we have to explicitly correct for the finite number of observations: a normal distribution actually presupposes an infinite data set, which we clearly will never have.
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