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A scanner used to measure bone density using dual energy X-ray absorptiometry. Bone density, or bone mineral density, is the amount of bone mineral in bone tissue.The concept is of mass of mineral per volume of bone (relating to density in the physics sense), although clinically it is measured by proxy according to optical density per square centimetre of bone surface upon imaging. [1]
In statistics, a standard normal table, also called the unit normal table or Z table, [1] is a mathematical table for the values of Φ, the cumulative distribution function of the normal distribution.
In statistics, the 68–95–99.7 rule, also known as the empirical rule, and sometimes abbreviated 3sr, is a shorthand used to remember the percentage of values that lie within an interval estimate in a normal distribution: approximately 68%, 95%, and 99.7% of the values lie within one, two, and three standard deviations of the mean, respectively.
In educational assessment, T-score is a standard score Z shifted and scaled to have a mean of 50 and a standard deviation of 10. [ 14 ] [ 15 ] [ 16 ] In bone density measurements, the T-score is the standard score of the measurement compared to the population of healthy 30-year-old adults, and has the usual mean of 0 and standard deviation of 1.
/ is the critical value of the standard normal distribution (e.g., 1.96 for a 95% confidence level). The MDE for when using the (two-sided) z-test formula for comparing two proportions, incorporating critical values for α {\displaystyle \alpha } and 1 − β {\displaystyle 1-\beta } , and the standard errors of the proportions: [ 1 ] [ 2 ]
Each of these confidence intervals covers the corresponding true value f(x) with confidence 0.95. Taken together, these confidence intervals constitute a 95% pointwise confidence band for f(x). In mathematical terms, a pointwise confidence band ^ () with coverage probability 1 − α satisfies the following condition separately for each value of x: