# Significant Variables

A quick peek into potential correlations

Significant variables appear when you filter your data. By selecting a date range, a
category or a number range in any of the columns, you are selecting a subset of all
the possible data points you have. Depending on what variable you used, this filter can
be related to some other variable. Those variables that show a strong correlation with
the selected one are **significant variables**.

These appear on the top left side of the interface upon filtering.

You’ll see 5 groups of tiny rectangles next to a number. These rectangles display a score of how significant the selection you’ve made is with respect to how this variable changed. Those variables that suffer a greater change in their distribution after selecting will have a higher score, meaning they could be quite relevant to whatever selection you’ve made.

Clicking the number will reveal all the variables that belong to this group of significance. In the example, we see all the variables with a score of 4 out of 5.

## How is the score calculated?

When hovering over the five little bars next to each variable, a score appears. This score tells us how significant the distribution of this variable is to the distribution of the current selection we’ve made.

### Manually computing an example

#### Context

Assume we are on a dataset where, among other things, we have a column `month`

which has the numbers 1 – 12 for each month,
and a column `season`

which has the values “Summer”, “Autumn”, “Winter”, “Spring”.

We all know that in the northern hemisphere, Spring happens in March, April and May, approximately. If we select the category “Spring”, we can see that the months 3, 4 and 5 show up these blue spikes, whereas the rest of the months do not.

If we hover over one of these blue bars in this case, this tooltip informs us of several important figures:

- 3.19K represents the number of rows that have this particular value from this particular column (in this case, the value 5 for column
`month`

). Or, basically, the grey-ish bar behind the blue one. - This 3.19K amounts to an ~8.5% of the whole dataset, which has ~37.3K rows.
- Importantly, these 3.19K rows correspond to ~33% of all the 9442 rows we selected when clicking on “Spring”. This makes sense: spring spans across 3 months, so May alone has about a third of all the days that comprise the whole Spring.

If we hover over month 6 instead, this shows up:

There are ~3.07K rows occurring in June, but 0 that have both the value 6 in `month`

AND the value “Spring” in `season`

.

#### Computing

The way we calculate how different the distributions between month and season are would involve going over each of these tooltips, subtracting the two percentage values, getting the absolute value, adding them all up and finally dividing by two.

The full operation would look like this.

- We add up all the absolute value of the differences:

- Finally, we divide the whole result by 2:

if we hover over `month`

in the significant variables section:

We are not proving and demonstrating all the math behind this, since this flies a bit out of the scope for this short explainer. Check the references if you really want to dig into the topic.

## Summing up

This computed the distance of the distributions created by your selection and the distributions that are already present in your data. Each of the different values a variable may have is a distribution on itself that changes when you select particular rows within your data. Studying these distributions and their differences help us understand our data in better ways.

### References

The actual calculation that’s going on corresponds to the total variation distance of probability measures, for those interested in the math behind it.

This article: Is there a difference? goes into great depth with a practical example calculating and interpreting the result.

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