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Hello, in this video,

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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.

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In the previous video or an earlier video, I talked about how bar charts emphasized relative differences.

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So in this one, I'm going to talk just a little bit about what that means.

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So are learning outcomes for this video to review a little bit of the statistics or the metrics that we've been talking about,

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to talk for you to be able to compute absolute and relative differences and to interpret a relative difference between two quantities.

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So as we've talked about, we can compute various statistics over our data means median mode success rates.

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We can compute percentiles, counts many.

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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.

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And this often serves as the metric for analysis or evaluation. Try to evaluate a program or tried to evaluate a technology.

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We have some metric that is measuring its effectiveness.

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And we want to see whether it's improved or changed somehow.

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So when we compare to values, though, with a few different ways to do it.

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So let's take a couple the population estimate in 2018 of Boise in Salt Lake City.

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And there's two ways that we few different ways that we can compare it.

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Two of them are the absolute difference. Boise has twenty eight thousand more people than Salt Lake City.

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The other is the relative difference. Boise has fourteen point five percent or fourteen percent more people than Salt Lake City.

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So the absolute value is the difference between two values is actually the absolute value of the difference between two values.

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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.

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That becomes useful. But what we're talking about here is the actual difference in the underlying units.

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So in our example case, number of people. And but the another way we can do it is to talk about the relative difference.

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So this is the it's the difference normalized by.

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The reference quantity, and we have to be clear on which ones,

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the reference quantity and the reference quantity is the one we're starting from whom we're computing the relative difference.

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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.

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But 40 is 20 percent is only 20 percent less than 50 because you take 50.

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10 is 20 percent a 50, whereas it's 25 percent of 40.

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You subtract it. And you get and you get 40.

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So this different this order difference is really, really important.

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So for the 50, what we've got is we have 50 minus 40, over 40.

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That's this one. And we have for the minus 50, over 50, negative 10, over 50.

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That's 20 percent. Ten over 40 is 25 percent.

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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.

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So this is when we say slike this year's sales of 20 million are twice as much as last year's 10 million.

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This is an apt. It's an absolute change of one of 10 million and it's a relative change of one hundred percent.

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Twenty million is twice as much as one is 10 million.

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And it is one hundred percent higher than 10 million.

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Now, one thing to think about, if I say this year's returns are two times larger than last year's.

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What does that mean? Does it mean it's two times?

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Does it mean it's 200 percent more, which would be three times?

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Is it clear? I would submit that this way of framing it is ambiguous.

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And so we should avoid it. The appropriate comparison really depends on context and problem.

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There's not a hard and fast rule when you need one or another.

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Relative comparisons are quite common because they they can be compared across a variety of contexts.

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But we still also need to pay attention to the underlying absolute difference in what

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the act what this what the change being made in this relative change actually is.

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One example of a high profile relative change.

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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,

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their internal movie recommender on the metric that they chose by 10 percent.

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They wanted a 10 percent improvement. And this metric it was. Lower is better, so they wanted you to.

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They wanted to decrease in the metric by 10 percent.

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We can also talk about a difference between differences, because if we compute a difference, that difference itself is just another value.

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So we could say ten sales grew 10 percent more this year than last year.

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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.

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And the growth of last year and we can compute the difference and difference.

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And so we can have a 10 percent increase in growth. Difference in difference has come up a lot in various contexts.

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And so it's important to be able to reason about those as well. And again, be clear both in writing and understanding.

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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.

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And the eye very naturally compares the difference between bars to the height of the bar itself.

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Point plots emphasize absolute difference because you don't have the reference point of the size of the bar.

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They're both of them. Make it pretty clear to see the also compare the differences.

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See how different the differences are. Those are of evident both in bar charts and point plots.

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So to wrap up, there are three primary ways to compute statistics, absolute relative and ratio.

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You need to be very clear and unambiguous when you're writing the results of a

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comparison and also when you're trying to understand what others have written.

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Seek to accurately understand it. And if you're providing feeB,

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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.

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