RelativeResourceManager-3

RelativeResourceManager-3 - PSY 2801 Summer 2009...

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Unformatted text preview: PSY 2801: Summer 2009 z-scores/Normal Distribution Jeff Jones University of Minnesota Jeff Jones Ch 6 Data Transformations Often, your data will make more sense in a different form. For instance, if you have interval data, then the 0 point doesn’t make sense, so it might be more practical to transform your data in order to make the 0 point equal to the mean . Jeff Jones Ch 6 Data Transformations Data Transformations : Any mathematical operation changing the original metric of your data. This mathematical operation is performed to every data point . For instance: y i = f ( x i ) is a transformation, with x i the old data point for person i, y i the new data point for person i, and f ( ) the function performed on every data point . Jeff Jones Ch 6 Notes Notes Notes Data Transformations Examples of Data Transformations: y i = 2 x i y i = ln ( x i ) + 4 y i = x i 44 y i = sin ( x i ) + cos ( x 2 i ) y i = x i-20 2 y i = x 3 i The left column contains linear transformations while the right column contains non-linear transformations . Jeff Jones Ch 6 Linear Transformations Linear Transformations : Any transformation that can be written in the form y i = ax i + b 1 The mean of a linear transformation: ¯ y = a ¯ x + b 2 The variance of a linear transformation: s 2 y = a 2 s 2 x 3 The shape does not change Linear transformations change the mean and the variance of the data. However, the shape doesn’t change → it is as though we are drawing the same picture with a different center and on a different scale. Jeff Jones Ch 6 Linear Transformations This is what happens if we transform data by an arbitrary linear function:-2 2 4 6 8 10 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 Density Plot of Distribution K n = 200 K Density 10 20 30 40 0.02 0.04 0.06 0.08 Density Plot of K Transformed by (K + 3) * pi K Transformed Linearly Jeff Jones Ch 6 Notes Notes Notes Non-Linear Transformations Non-Linear Transformations : Anything that cannot be written in the form of a linear transformation. It could be any function. Linear functions are a class of function (they’re special), so statisticians make note of them and regard anything else as non-linear . Non-Linear Transformations often change the mean, the variance and the shape of the distribution. Jeff Jones Ch 6 Non-Linear Transformations This is what happens if we transform data by an arbitrary non-linear function:-2 2 4 6 8 10 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 Density Plot of Distribution K n = 200 K Density 20 40 60 80 120 0.02 0.04 0.06 0.08 0.12 0.14 Density Plot of K Transformed by K^2 K Transformed Non-Linearly Jeff Jones Ch 6 Non-Linear Transformations This is a different non-linear transformation:-2 2 4 6 8 10 Density Plot of Distribution K n = 200 K-4-2 2 Density Plot of K Transformed by log(K) K Transformed Non-Linearly Jeff Jones Ch 6 Notes Notes Notes Non-Linear Transformations Unlike linear transformations, the predictability of changes via non-linear transformations are not as apparent. non-linear transformations are not as apparent....
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This note was uploaded on 10/08/2010 for the course PSY 2801 taught by Professor Guyer during the Summer '08 term at Minnesota.

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RelativeResourceManager-3 - PSY 2801 Summer 2009...

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