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.

Psychology

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