Hello, in this video,
I want to talk with you just a little bit about statistics that we can measure and how we want to think about differences between them.
In the previous video or an earlier video, I talked about how bar charts emphasized relative differences.
So in this one, I'm going to talk just a little bit about what that means.
So are learning outcomes for this video to review a little bit of the statistics or the metrics that we've been talking about,
to talk for you to be able to compute absolute and relative differences and to interpret a relative difference between two quantities.
So as we've talked about, we can compute various statistics over our data means median mode success rates.
We can compute percentiles, counts many.
Basically, any statistic you can think of for that, you can compute over a of a set of numbers we can use as some kind of a statistic or a metric.
And this often serves as the metric for analysis or evaluation. Try to evaluate a program or tried to evaluate a technology.
We have some metric that is measuring its effectiveness.
And we want to see whether it's improved or changed somehow.
So when we compare to values, though, with a few different ways to do it.
So let's take a couple the population estimate in 2018 of Boise in Salt Lake City.
And there's two ways that we few different ways that we can compare it.
Two of them are the absolute difference. Boise has twenty eight thousand more people than Salt Lake City.
The other is the relative difference. Boise has fourteen point five percent or fourteen percent more people than Salt Lake City.
So the absolute value is the difference between two values is actually the absolute value of the difference between two values.
We can also talk about a science difference or a real difference where we don't have the absolute value if we need the direction on the difference.
That becomes useful. But what we're talking about here is the actual difference in the underlying units.
So in our example case, number of people. And but the another way we can do it is to talk about the relative difference.
So this is the it's the difference normalized by.
The reference quantity, and we have to be clear on which ones,
the reference quantity and the reference quantity is the one we're starting from whom we're computing the relative difference.
So, for example, 50 is 25 percent, more than 40 because you take 25 percent of fortius 10 add add that and you get 50.
But 40 is 20 percent is only 20 percent less than 50 because you take 50.
10 is 20 percent a 50, whereas it's 25 percent of 40.
You subtract it. And you get and you get 40.
So this different this order difference is really, really important.
So for the 50, what we've got is we have 50 minus 40, over 40.
That's this one. And we have for the minus 50, over 50, negative 10, over 50.
That's 20 percent. Ten over 40 is 25 percent.
So we need to be really, really careful about the order, another way we can compares with the ratio, we just divide one quantity by the other.
So this is when we say slike this year's sales of 20 million are twice as much as last year's 10 million.
This is an apt. It's an absolute change of one of 10 million and it's a relative change of one hundred percent.
Twenty million is twice as much as one is 10 million.
And it is one hundred percent higher than 10 million.
Now, one thing to think about, if I say this year's returns are two times larger than last year's.
What does that mean? Does it mean it's two times?
Does it mean it's 200 percent more, which would be three times?
Is it clear? I would submit that this way of framing it is ambiguous.
And so we should avoid it. The appropriate comparison really depends on context and problem.
There's not a hard and fast rule when you need one or another.
Relative comparisons are quite common because they they can be compared across a variety of contexts.
But we still also need to pay attention to the underlying absolute difference in what
the act what this what the change being made in this relative change actually is.
One example of a high profile relative change.
If the Netflix prize, which was a run by Netflix a number of years ago, they paid a million dollars to the team that was able to beat It's The Beat,
their internal movie recommender on the metric that they chose by 10 percent.
They wanted a 10 percent improvement. And this metric it was. Lower is better, so they wanted you to.
They wanted to decrease in the metric by 10 percent.
We can also talk about a difference between differences, because if we compute a difference, that difference itself is just another value.
So we could say ten sales grew 10 percent more this year than last year.
So if we define growth as the one year sales minus the other year sales, then we can look at the growth of this year.
And the growth of last year and we can compute the difference and difference.
And so we can have a 10 percent increase in growth. Difference in difference has come up a lot in various contexts.
And so it's important to be able to reason about those as well. And again, be clear both in writing and understanding.
So we don't want we don't want to. Visual comparison bar charts emphasized relative difference because the height of the bar is right there.
And the eye very naturally compares the difference between bars to the height of the bar itself.
Point plots emphasize absolute difference because you don't have the reference point of the size of the bar.
They're both of them. Make it pretty clear to see the also compare the differences.
See how different the differences are. Those are of evident both in bar charts and point plots.
So to wrap up, there are three primary ways to compute statistics, absolute relative and ratio.
You need to be very clear and unambiguous when you're writing the results of a
comparison and also when you're trying to understand what others have written.
Seek to accurately understand it. And if you're providing feeB,
if you're in a context where you're providing feedback and it's not clear that clarity is something you want to ask for revision.