Count of items as squared sum over sum of squares
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If I have made 3 identical purchases of (£2, £2, £2) then this formula gives a measure of the number of purchases:
$N = frac{(sum v_i)^2}{sum v_i^2}$
In this example:
$(sum v_i)^2 = 6^2 = 36$ and $sum v_i^2 = 4 + 4 + 4 = 12$ so N is calculated as 3, which happily agrees with the simple count of purchases.
In the example where purchases are (£1, £5, £5) then $(sum v_i)^2 = 11^2 = 121$ and $sum v_i^2 = 1 + 25 + 25 = 51$ so N is calculated as 2.4.
The background to this question is that I've been given this formula to measure an "effective count" and I want understand clearly what it's measuring. I can see that it takes account of variation in the individual values, perhaps reducing an item's weight / importance as it gets further from the simple mean? Is there a standard name for this type of statistical measure of the number of values so that I can read more about it?
statistics
asked Nov 22 at 8:47
David B
1034
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If I have made 3 identical purchases of (£2, £2, £2) then this formula gives a measure of the number of purchases:
$N = frac{(sum v_i)^2}{sum v_i^2}$
In this example:
$(sum v_i)^2 = 6^2 = 36$ and $sum v_i^2 = 4 + 4 + 4 = 12$ so N is calculated as 3, which happily agrees with the simple count of purchases.
In the example where purchases are (£1, £5, £5) then $(sum v_i)^2 = 11^2 = 121$ and $sum v_i^2 = 1 + 25 + 25 = 51$ so N is calculated as 2.4.
The background to this question is that I've been given this formula to measure an "effective count" and I want understand clearly what it's measuring. I can see that it takes account of variation in the individual values, perhaps reducing an item's weight / importance as it gets further from the simple mean? Is there a standard name for this type of statistical measure of the number of values so that I can read more about it?
statistics
asked Nov 22 at 8:47
David B
1034
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
If I have made 3 identical purchases of (£2, £2, £2) then this formula gives a measure of the number of purchases:
$N = frac{(sum v_i)^2}{sum v_i^2}$
In this example:
$(sum v_i)^2 = 6^2 = 36$ and $sum v_i^2 = 4 + 4 + 4 = 12$ so N is calculated as 3, which happily agrees with the simple count of purchases.
In the example where purchases are (£1, £5, £5) then $(sum v_i)^2 = 11^2 = 121$ and $sum v_i^2 = 1 + 25 + 25 = 51$ so N is calculated as 2.4.
The background to this question is that I've been given this formula to measure an "effective count" and I want understand clearly what it's measuring. I can see that it takes account of variation in the individual values, perhaps reducing an item's weight / importance as it gets further from the simple mean? Is there a standard name for this type of statistical measure of the number of values so that I can read more about it?
statistics
asked Nov 22 at 8:47
David B
1034
If I have made 3 identical purchases of (£2, £2, £2) then this formula gives a measure of the number of purchases:
$N = frac{(sum v_i)^2}{sum v_i^2}$
In this example:
$(sum v_i)^2 = 6^2 = 36$ and $sum v_i^2 = 4 + 4 + 4 = 12$ so N is calculated as 3, which happily agrees with the simple count of purchases.
In the example where purchases are (£1, £5, £5) then $(sum v_i)^2 = 11^2 = 121$ and $sum v_i^2 = 1 + 25 + 25 = 51$ so N is calculated as 2.4.
The background to this question is that I've been given this formula to measure an "effective count" and I want understand clearly what it's measuring. I can see that it takes account of variation in the individual values, perhaps reducing an item's weight / importance as it gets further from the simple mean? Is there a standard name for this type of statistical measure of the number of values so that I can read more about it?
statistics
statistics
asked Nov 22 at 8:47
David B
1034
asked Nov 22 at 8:47
David B
1034
asked Nov 22 at 8:47
David B
1034
asked Nov 22 at 8:47
David B
1034
asked Nov 22 at 8:47
David B
1034
1034
add a comment |
add a comment |
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