A measuring technique is biased if the population mean of
replicate measurements made by it diﬀers from the true value of what
is being measured. In ”Selected Values of the Thermodynamic Prop-
erties of the Elements” (American Society for Metals, 1973) a value
of 1246 degrees celcius is given for the melting point of manganese.
Suppose that 4 determinations carried out by the metallurgist gave, in
degrees Celcius: 1247, 1254, 1250, 1253. Taking the published value
to be the true value, would you judge the metallurgist’s results to be
biased if you were prepared to take a 5% risk of making a false accu-
sation of bias? Would your answer be the same if this chance is only
1%? What judgment would you make in this respect if the data were
1261, 1268, 1264, 1267.