1 00:00:04,650 --> 00:00:05,470 Hello, in this video,
2 00:00:05,470 --> 00:00:14,610 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.
3 00:00:14,610 --> 00:00:21,220 In the previous video or an earlier video, I talked about how bar charts emphasized relative differences.
4 00:00:21,220 --> 00:00:24,450 So in this one, I'm going to talk just a little bit about what that means.
5 00:00:24,450 --> 00:00:30,040 So are learning outcomes for this video to review a little bit of the statistics or the metrics that we've been talking about,
6 00:00:30,040 --> 00:00:37,990 to talk for you to be able to compute absolute and relative differences and to interpret a relative difference between two quantities.
7 00:00:37,990 --> 00:00:43,870 So as we've talked about, we can compute various statistics over our data means median mode success rates.
8 00:00:43,870 --> 00:00:46,720 We can compute percentiles, counts many.
9 00:00:46,720 --> 00:00:57,530 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.
10 00:00:57,530 --> 00:01:04,210 And this often serves as the metric for analysis or evaluation. Try to evaluate a program or tried to evaluate a technology.
11 00:01:04,210 --> 00:01:08,920 We have some metric that is measuring its effectiveness.
12 00:01:08,920 --> 00:01:15,310 And we want to see whether it's improved or changed somehow.
13 00:01:15,310 --> 00:01:19,090 So when we compare to values, though, with a few different ways to do it.
14 00:01:19,090 --> 00:01:24,040 So let's take a couple the population estimate in 2018 of Boise in Salt Lake City.
15 00:01:24,040 --> 00:01:27,230 And there's two ways that we few different ways that we can compare it.
16 00:01:27,230 --> 00:01:33,460 Two of them are the absolute difference. Boise has twenty eight thousand more people than Salt Lake City.
17 00:01:33,460 --> 00:01:42,180 The other is the relative difference. Boise has fourteen point five percent or fourteen percent more people than Salt Lake City.
18 00:01:42,180 --> 00:01:49,020 So the absolute value is the difference between two values is actually the absolute value of the difference between two values.
19 00:01:49,020 --> 00:01:54,750 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.
20 00:01:54,750 --> 00:02:01,440 That becomes useful. But what we're talking about here is the actual difference in the underlying units.
21 00:02:01,440 --> 00:02:11,940 So in our example case, number of people. And but the another way we can do it is to talk about the relative difference.
22 00:02:11,940 --> 00:02:18,960 So this is the it's the difference normalized by.
23 00:02:18,960 --> 00:02:22,440 The reference quantity, and we have to be clear on which ones,
24 00:02:22,440 --> 00:02:29,700 the reference quantity and the reference quantity is the one we're starting from whom we're computing the relative difference.
25 00:02:29,700 --> 00:02:39,990 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.
26 00:02:39,990 --> 00:02:46,410 But 40 is 20 percent is only 20 percent less than 50 because you take 50.
27 00:02:46,410 --> 00:02:50,670 10 is 20 percent a 50, whereas it's 25 percent of 40.
28 00:02:50,670 --> 00:02:56,750 You subtract it. And you get and you get 40.
29 00:02:56,750 --> 00:03:01,010 So this different this order difference is really, really important.
30 00:03:01,010 --> 00:03:09,480 So for the 50, what we've got is we have 50 minus 40, over 40.
31 00:03:09,480 --> 00:03:20,010 That's this one. And we have for the minus 50, over 50, negative 10, over 50.
32 00:03:20,010 --> 00:03:25,080 That's 20 percent. Ten over 40 is 25 percent.
33 00:03:25,080 --> 00:03:33,330 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.
34 00:03:33,330 --> 00:03:40,470 So this is when we say slike this year's sales of 20 million are twice as much as last year's 10 million.
35 00:03:40,470 --> 00:03:47,010 This is an apt. It's an absolute change of one of 10 million and it's a relative change of one hundred percent.
36 00:03:47,010 --> 00:03:51,030 Twenty million is twice as much as one is 10 million.
37 00:03:51,030 --> 00:03:54,090 And it is one hundred percent higher than 10 million.
38 00:03:54,090 --> 00:03:59,940 Now, one thing to think about, if I say this year's returns are two times larger than last year's.
39 00:03:59,940 --> 00:04:03,750 What does that mean? Does it mean it's two times?
40 00:04:03,750 --> 00:04:08,100 Does it mean it's 200 percent more, which would be three times?
41 00:04:08,100 --> 00:04:13,350 Is it clear? I would submit that this way of framing it is ambiguous.
42 00:04:13,350 --> 00:04:20,400 And so we should avoid it. The appropriate comparison really depends on context and problem.
43 00:04:20,400 --> 00:04:25,320 There's not a hard and fast rule when you need one or another.
44 00:04:25,320 --> 00:04:31,740 Relative comparisons are quite common because they they can be compared across a variety of contexts.
45 00:04:31,740 --> 00:04:36,570 But we still also need to pay attention to the underlying absolute difference in what
46 00:04:36,570 --> 00:04:41,190 the act what this what the change being made in this relative change actually is.
47 00:04:41,190 --> 00:04:43,850 One example of a high profile relative change.
48 00:04:43,850 --> 00:04:53,940 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,
49 00:04:53,940 --> 00:04:58,740 their internal movie recommender on the metric that they chose by 10 percent.
50 00:04:58,740 --> 00:05:06,120 They wanted a 10 percent improvement. And this metric it was. Lower is better, so they wanted you to.
51 00:05:06,120 --> 00:05:10,380 They wanted to decrease in the metric by 10 percent.
52 00:05:10,380 --> 00:05:17,340 We can also talk about a difference between differences, because if we compute a difference, that difference itself is just another value.
53 00:05:17,340 --> 00:05:22,290 So we could say ten sales grew 10 percent more this year than last year.
54 00:05:22,290 --> 00:05:32,200 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.
55 00:05:32,200 --> 00:05:37,000 And the growth of last year and we can compute the difference and difference.
56 00:05:37,000 --> 00:05:44,080 And so we can have a 10 percent increase in growth. Difference in difference has come up a lot in various contexts.
57 00:05:44,080 --> 00:05:50,020 And so it's important to be able to reason about those as well. And again, be clear both in writing and understanding.
58 00:05:50,020 --> 00:05:58,120 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.
59 00:05:58,120 --> 00:06:04,120 And the eye very naturally compares the difference between bars to the height of the bar itself.
60 00:06:04,120 --> 00:06:10,840 Point plots emphasize absolute difference because you don't have the reference point of the size of the bar.
61 00:06:10,840 --> 00:06:17,170 They're both of them. Make it pretty clear to see the also compare the differences.
62 00:06:17,170 --> 00:06:23,590 See how different the differences are. Those are of evident both in bar charts and point plots.
63 00:06:23,590 --> 00:06:28,690 So to wrap up, there are three primary ways to compute statistics, absolute relative and ratio.
64 00:06:28,690 --> 00:06:32,470 You need to be very clear and unambiguous when you're writing the results of a
65 00:06:32,470 --> 00:06:36,370 comparison and also when you're trying to understand what others have written.
66 00:06:36,370 --> 00:06:39,340 Seek to accurately understand it. And if you're providing feeB,
67 00:06:39,340 --> 00:06:50,900 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.