Define and explain logarithmic scales and the role they may play in trend analysis.
What will be an ideal response?
Ans: Logarithmic functions show the power to which some base would have to be raised to obtain that number. We can refer to log base 10 as log10. Therefore, log10 (100) = 2 because 102 = 100. And, log10 (1,000) = 3 because 103 = 1,000. In base 2 logarithms log2 (4) = 2 because 22 = 4. And, log2 (8) = 3 because 23 = 8. If values of x are equally spaced on a logarithmic scale then any logarithmic transformation of these will produce values that are equally spaced on a linear scale.
To conduct a trend analysis the values of x must be equally spaced on a linear scale. However, if the levels of x are equally spaced on a logarithmic scale (i.e., each level of x is the same multiple of the previous level) then these levels can be transformed through a log function to produce intervals that are equally spaced on a linear scale. For example, the values 1, 2, 4, 8, and 16 are not equally spaced on a linear scale, but are equally spaced on a logarithmic scale (xi+1 = 2 * xi). When we transform these values to units of log2, their values are 0, 1, 2, 3, and 4. Now a trend analysis can be applied.
You might also like to view...
Cognitive behavioral therapies originated in the treatment of _____, in which individuals presumably maintain negative thoughts and evaluations of themselves, the world, and the future
a) schizophrenia b) depression c) amnesia d) insomnia
One study (by Willenbring, Levine, and Morely) found that ____% of participants reported that they ate less when under stress, ____% ate more, and ____% reported no stress-related changes in their eating patterns
a. 35, 35, 30 c. 48, 44, 8 b. 75, 25, 25 d. 25, 25, 75
What developmental task of infancy may influence several components of temperament, including rhythmicity, distractibility, intensity of reaction, and attention?
A. learning how to regulate attention and emotions B. coordinating reflexes with purposeful behavior C. understanding the connection between behaviors and social interaction D. developing a sense of trust in the world
The DSM-5’s social anxiety disorder is synonymous with the DSM-IV’s ______.
a. social fear disorder b. Williams syndrome c. hypoactive social interaction disorder d. social phobia