Can standardization hide important information?
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Standardization is an important, useful technique in statistics for comparing and combining different kinds of columnal, numeric data in relational datasets. I came up with the following scenario because I'm unsure whether standardization can end up hiding some important information in the data.
$hspace{10mm}$ Suppose you do a survey where people rank happiness on a scale from 0 to 100. Let's say the mean is 56 and the standard deviation is 10. If you are to standardize this data, then 56 would be scaled to 0 and the standard deviation would be scaled to 1 using:
$$forall x_i epsilon X, hat{x_i} = frac{x_i - mean{X}}{std{X}}=frac{x_i-56}{10}$$
However, you can imagine that this perhaps hides the fact that since the mean is 56, and 50 is (mathematically) what's "neutral," then on average people are a bit happier than "neutral." Standardizing, however, makes 56 become "neutral." I don't know if this is a valid techique, but one could force a mean of 50 and use the same standard deviation to get a new standardization where the mean is $frac{56-50}{10}=+0.6$ points. Which is better?
statistics
asked Jan 17 at 16:18
Jatin MathurJatin Mathur
11
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add a comment |
$begingroup$
Standardization is an important, useful technique in statistics for comparing and combining different kinds of columnal, numeric data in relational datasets. I came up with the following scenario because I'm unsure whether standardization can end up hiding some important information in the data.
$hspace{10mm}$ Suppose you do a survey where people rank happiness on a scale from 0 to 100. Let's say the mean is 56 and the standard deviation is 10. If you are to standardize this data, then 56 would be scaled to 0 and the standard deviation would be scaled to 1 using:
$$forall x_i epsilon X, hat{x_i} = frac{x_i - mean{X}}{std{X}}=frac{x_i-56}{10}$$
However, you can imagine that this perhaps hides the fact that since the mean is 56, and 50 is (mathematically) what's "neutral," then on average people are a bit happier than "neutral." Standardizing, however, makes 56 become "neutral." I don't know if this is a valid techique, but one could force a mean of 50 and use the same standard deviation to get a new standardization where the mean is $frac{56-50}{10}=+0.6$ points. Which is better?
statistics
asked Jan 17 at 16:18
Jatin MathurJatin Mathur
11
$endgroup$
add a comment |
$begingroup$
Standardization is an important, useful technique in statistics for comparing and combining different kinds of columnal, numeric data in relational datasets. I came up with the following scenario because I'm unsure whether standardization can end up hiding some important information in the data.
$hspace{10mm}$ Suppose you do a survey where people rank happiness on a scale from 0 to 100. Let's say the mean is 56 and the standard deviation is 10. If you are to standardize this data, then 56 would be scaled to 0 and the standard deviation would be scaled to 1 using:
$$forall x_i epsilon X, hat{x_i} = frac{x_i - mean{X}}{std{X}}=frac{x_i-56}{10}$$
However, you can imagine that this perhaps hides the fact that since the mean is 56, and 50 is (mathematically) what's "neutral," then on average people are a bit happier than "neutral." Standardizing, however, makes 56 become "neutral." I don't know if this is a valid techique, but one could force a mean of 50 and use the same standard deviation to get a new standardization where the mean is $frac{56-50}{10}=+0.6$ points. Which is better?
statistics
asked Jan 17 at 16:18
Jatin MathurJatin Mathur
11
$endgroup$
Standardization is an important, useful technique in statistics for comparing and combining different kinds of columnal, numeric data in relational datasets. I came up with the following scenario because I'm unsure whether standardization can end up hiding some important information in the data.
$hspace{10mm}$ Suppose you do a survey where people rank happiness on a scale from 0 to 100. Let's say the mean is 56 and the standard deviation is 10. If you are to standardize this data, then 56 would be scaled to 0 and the standard deviation would be scaled to 1 using:
$$forall x_i epsilon X, hat{x_i} = frac{x_i - mean{X}}{std{X}}=frac{x_i-56}{10}$$
However, you can imagine that this perhaps hides the fact that since the mean is 56, and 50 is (mathematically) what's "neutral," then on average people are a bit happier than "neutral." Standardizing, however, makes 56 become "neutral." I don't know if this is a valid techique, but one could force a mean of 50 and use the same standard deviation to get a new standardization where the mean is $frac{56-50}{10}=+0.6$ points. Which is better?
statistics
statistics
asked Jan 17 at 16:18
Jatin MathurJatin Mathur
11
asked Jan 17 at 16:18
Jatin MathurJatin Mathur
11
asked Jan 17 at 16:18
Jatin MathurJatin Mathur
11
asked Jan 17 at 16:18
Jatin MathurJatin Mathur
11
asked Jan 17 at 16:18
Jatin MathurJatin Mathur
11
11
add a comment |
add a comment |
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