RelativeResourceManager-3

RelativeResourceManager-3 - PSY 2801: Summer 2009...

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Unformatted text preview: PSY 2801: Summer 2009 z-scores/Normal Distribution Je Jones University of Minnesota Je Jones Ch 6 Data Transformations Often, your data will make more sense in a dierent form. For instance, if you have interval data, then the 0 point doesnt make sense, so it might be more practical to transform your data in order to make the 0 point equal to the mean . Je 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 . Je 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 . Je 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 doesnt change it is as though we are drawing the same picture with a dierent center and on a dierent scale. Je 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 Je 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 (theyre 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. Je 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 Je Jones Ch 6 Non-Linear Transformations This is a dierent 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 Je 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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RelativeResourceManager-3 - PSY 2801: Summer 2009...

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