notes.Rmd

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output: pdf_document
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  actor_id: "esch" 
  data_date: "2021-01-08"
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## Notes

The raw data for this project originates from XXX. For this project, the raw data was scaled and standardized several ways. First, each variable was assigned to a category where a high value equates to a high opportunity ("higher value is better"), or where a high value equates to a low opportunity ("lower is better"). 
<br>

### Z-score
The z-score value represents the number of standard deviations x is from the mean. The z-score calculation is:

Where "higher is better": <br>
$z \, score = \frac{x - mean}{standard\,deviation}\\$

Where "lower is better":  <br>
$z \, score = \frac{x - mean}{standard\,deviation}\times (-1)\\$

### Weights nominal
The weights nominal value represents where x falls nominally in the range of values, on a 0-10 scale. The weights nominal calculation is:

Where "higher is better":  <br>
$weights \, nominal = \frac{x - minimum\,value}{maximum\,value - minimum\,value}\times 10\\$

Where "lower is better":  <br>
$weights \, nominal = 10 - \frac{x - minimum\,value}{maximum\,value - minimum\,value}\times 10\\$


### Weights standard score
The weights standard score normally distributes the z score of x on a 0-10 scale. **This is the primary variable mapped in this tool.** It is calculated according to:

Where "higher is better":  <br>
$weights \, standard\, score = (normal\, distribution\, of\, z\, score)\times 10\\$

Where "lower is better":  <br>
$weights \, standard\, score = 10 - (normal\, distribution\, of\, z\, score)\times 10\\$

### Weights rank
The weights standard score normally distributes the z score of x on a 0-10 scale. It is calculated according to:

Where "higher is better":  <br>
$weights \, rank = \frac{rank\, of\, the\, nominal \,weight\,of\,x}{number \, of \,tracts\, with\,data \, on\,x}\times 10\\$

Where "lower is better": <br>
$weights \, rank = \frac{rank\, of\, the\, nominal \,weight\,of\,x}{number \, of \,tracts\, with\,data \, on\,x}\times 10\\$