Precision

Examples of Precision in the following topics:

• Chance Error

  • Random errors are due to the precision of the equipment , and systematic errors are due to how well the equipment was used or how well the experiment was controlled .
  • A random error makes the measured value both smaller and larger than the true value; they are errors of precision.
  • These are errors incurred as a result of making measurements on imperfect tools which can only have certain degree of precision.
  • This target shows an example of low accuracy (points are not close to center target) but high precision (points are close together).
  • This target shows an example of high accuracy (points are all close to center target) but low precision (points are not close together).

• Using simulation for goodness of fit tests

  • This distribution will be a very precise null distribution for the test statistic X2 if the probabilities are accurate, and we can find the upper tail of this null distribution, using a cutoff of the observed test statistic, to calculate the p-value.
  • The precise null distribution for the juror example from Section 6.3 is shown as a histogram of simulated $X^2_{sim}$ statistics, and the theoretical chi-square distribution is also shown.

• Bias

  • Random errors are due to the precision of the equipment , and systematic errors are due to how well the equipment was used or how well the experiment was controlled .
  • This target shows an example of high accuracy (points are all close to center target) but low precision (points are not close together).
  • This target shows an example of low accuracy (points are not close to center target) but high precision (points are close together).

• Statistical Literacy

  • That definition is sort of correct, but it could be stated more precisely.

• Are Real Dice Fair?

  • Perhaps to mitigate concerns that the pips on the faces of certain styles of dice cause a small bias, casinos use precision dice with flush markings.
  • Precision casino dice may have a polished or sand finish, making them transparent or translucent, respectively.

• Statistical significance versus practical significance

  • When the sample size becomes larger, point estimates become more precise and any real differences in the mean and null value become easier to detect and recognize.

• A sampling distribution for the mean

  • If a point estimate, such as $\bar{x}$, is associated with a normal model and standard error SE, then we use this more precise 95% confidence interval.

• Pooled standard deviation estimate (special topic)

  • In such cases, we can make our t distribution approach slightly more precise by using a pooled standard deviation.

• Introduction to testing for goodness of fit using chi-square

  • While the proportions in the juries do not precisely represent the population proportions, it is unclear whether these data provide convincing evidence that the sample is not representative.

• Creating a test statistic for one-way tables

  • The sample proportion represented from each race among the 275 jurors was not a precise match for any ethnic group.