Question

We can represent a two-by-two table in JavaScript with a four-element array ( [76, 9, 4, 1] ). We could also use other representations, such as an array containing two two-element arrays ( [[76, 9], [4, 1]] ) or an object with property names like "11" and "01" , but the flat array is simple and makes the expressions that access the table pleasantly short. We’ll interpret the indices to the array as two-bit binary number, where the leftmost (most significant) digit refers to the squirrel variable and the rightmost (least significant) digit refers to the event variable. For example, the binary number 10 refers to the case where Jacques did turn into a squirrel, but the event (say, "pizza") didn’t occur. This happened four times. And since binary 10 is 2 in decimal notation, we will store this number at index 2 of the array.

This is the function that computes the ϕ coefficient from such an array:

function phi(table) {
  return (table[3] * table[0] - table[2] * table[1]) /
    Math.sqrt((table[2] + table[3]) *
              (table[0] + table[1]) *
              (table[1] + table[3]) *
              (table[0] + table[2]));
}

console.log(phi([76, 9, 4, 1]));
// → 0.068599434

This is simply a direct translation of the ϕ formula into JavaScript. Math.sqrt is the square root function, as provided by the Math object in a standard JavaScript environment. We have to sum two fields from the table to get fields like n_1• because the sums of rows or columns are not stored directly in our data structure.

Jacques kept his journal for three months. The resulting data set is available in the coding sandbox for this chapter( eloquentjavascript.net/code#4 ), where it is stored in the JOURNAL variable, and in a downloadable file .

To extract a two-by-two table for a specific event from this journal, we must loop over all the entries and tally up how many times the event occurs in relation to squirrel transformations.

function hasEvent(event, entry) {
  return entry.events.indexOf(event) != -1;
}

function tableFor(event, journal) {
  var table = [0, 0, 0, 0];
  for (var i = 0; i < journal.length; i++) {
    var entry = journal[i], index = 0;
    if (hasEvent(event, entry)) index += 1;
    if (entry.squirrel) index += 2;
    table[index] += 1;
  }
  return table;
}

console.log(tableFor("pizza", JOURNAL));
// → [76, 9, 4, 1]

The hasEvent function tests whether an entry contains a given event. Arrays have an indexOf method that tries to find a given value (in this case, the event name) in the array and returns the index at which it was found or -1 if it wasn’t found. So if the call to indexOf doesn’t return -1, then we know the event was found in the entry.

The body of the loop in tableFor figures out which box in the table each journal entry falls into by checking whether the entry contains the specific event it’s interested in and whether the event happens alongside a squirrel incident. The loop then adds one to the number in the array that corresponds to this box on the table.

We now have the tools we need to compute individual correlations. The only step remaining is to find a correlation for every type of event that was recorded and see whether anything stands out. But how should we store these correlations once we compute them?

This is a book about getting computers to do what you want them to do. Computers are about as common as screwdrivers today, but they contain a lot more hidden complexity and thus are harder to operate and understand. To many, they remain alien, slightly threatening things.