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Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,1\N00:00:04,650 --> 00:00:05,470\NHello, in this video,
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,2\N00:00:05,470 --> 00:00:14,610\NI 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.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,3\N00:00:14,610 --> 00:00:21,220\NIn the previous video or an earlier video, I talked about how bar charts emphasized relative differences.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,4\N00:00:21,220 --> 00:00:24,450\NSo in this one, I'm going to talk just a little bit about what that means.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,5\N00:00:24,450 --> 00:00:30,040\NSo are learning outcomes for this video to review a little bit of the statistics or the metrics that we've been talking about,
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,6\N00:00:30,040 --> 00:00:37,990\Nto talk for you to be able to compute absolute and relative differences and to interpret a relative difference between two quantities.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,7\N00:00:37,990 --> 00:00:43,870\NSo as we've talked about, we can compute various statistics over our data means median mode success rates.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,8\N00:00:43,870 --> 00:00:46,720\NWe can compute percentiles, counts many.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,9\N00:00:46,720 --> 00:00:57,530\NBasically, 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.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,10\N00:00:57,530 --> 00:01:04,210\NAnd this often serves as the metric for analysis or evaluation. Try to evaluate a program or tried to evaluate a technology.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,11\N00:01:04,210 --> 00:01:08,920\NWe have some metric that is measuring its effectiveness.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,12\N00:01:08,920 --> 00:01:15,310\NAnd we want to see whether it's improved or changed somehow.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,13\N00:01:15,310 --> 00:01:19,090\NSo when we compare to values, though, with a few different ways to do it.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,14\N00:01:19,090 --> 00:01:24,040\NSo let's take a couple the population estimate in 2018 of Boise in Salt Lake City.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,15\N00:01:24,040 --> 00:01:27,230\NAnd there's two ways that we few different ways that we can compare it.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,16\N00:01:27,230 --> 00:01:33,460\NTwo of them are the absolute difference. Boise has twenty eight thousand more people than Salt Lake City.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,17\N00:01:33,460 --> 00:01:42,180\NThe other is the relative difference. Boise has fourteen point five percent or fourteen percent more people than Salt Lake City.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,18\N00:01:42,180 --> 00:01:49,020\NSo the absolute value is the difference between two values is actually the absolute value of the difference between two values.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,19\N00:01:49,020 --> 00:01:54,750\NWe 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.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,20\N00:01:54,750 --> 00:02:01,440\NThat becomes useful. But what we're talking about here is the actual difference in the underlying units.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,21\N00:02:01,440 --> 00:02:11,940\NSo in our example case, number of people. And but the another way we can do it is to talk about the relative difference.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,22\N00:02:11,940 --> 00:02:18,960\NSo this is the it's the difference normalized by.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,23\N00:02:18,960 --> 00:02:22,440\NThe reference quantity, and we have to be clear on which ones,
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,24\N00:02:22,440 --> 00:02:29,700\Nthe reference quantity and the reference quantity is the one we're starting from whom we're computing the relative difference.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,25\N00:02:29,700 --> 00:02:39,990\NSo, for example, 50 is 25 percent, more than 40 because you take 25 percent of fortius 10 add add that and you get 50.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,26\N00:02:39,990 --> 00:02:46,410\NBut 40 is 20 percent is only 20 percent less than 50 because you take 50.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,27\N00:02:46,410 --> 00:02:50,670\N10 is 20 percent a 50, whereas it's 25 percent of 40.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,28\N00:02:50,670 --> 00:02:56,750\NYou subtract it. And you get and you get 40.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,29\N00:02:56,750 --> 00:03:01,010\NSo this different this order difference is really, really important.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,30\N00:03:01,010 --> 00:03:09,480\NSo for the 50, what we've got is we have 50 minus 40, over 40.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,31\N00:03:09,480 --> 00:03:20,010\NThat's this one. And we have for the minus 50, over 50, negative 10, over 50.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,32\N00:03:20,010 --> 00:03:25,080\NThat's 20 percent. Ten over 40 is 25 percent.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,33\N00:03:25,080 --> 00:03:33,330\NSo 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.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,34\N00:03:33,330 --> 00:03:40,470\NSo this is when we say slike this year's sales of 20 million are twice as much as last year's 10 million.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,35\N00:03:40,470 --> 00:03:47,010\NThis is an apt. It's an absolute change of one of 10 million and it's a relative change of one hundred percent.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,36\N00:03:47,010 --> 00:03:51,030\NTwenty million is twice as much as one is 10 million.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,37\N00:03:51,030 --> 00:03:54,090\NAnd it is one hundred percent higher than 10 million.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,38\N00:03:54,090 --> 00:03:59,940\NNow, one thing to think about, if I say this year's returns are two times larger than last year's.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,39\N00:03:59,940 --> 00:04:03,750\NWhat does that mean? Does it mean it's two times?
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,40\N00:04:03,750 --> 00:04:08,100\NDoes it mean it's 200 percent more, which would be three times?
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,41\N00:04:08,100 --> 00:04:13,350\NIs it clear? I would submit that this way of framing it is ambiguous.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,42\N00:04:13,350 --> 00:04:20,400\NAnd so we should avoid it. The appropriate comparison really depends on context and problem.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,43\N00:04:20,400 --> 00:04:25,320\NThere's not a hard and fast rule when you need one or another.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,44\N00:04:25,320 --> 00:04:31,740\NRelative comparisons are quite common because they they can be compared across a variety of contexts.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,45\N00:04:31,740 --> 00:04:36,570\NBut we still also need to pay attention to the underlying absolute difference in what
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,46\N00:04:36,570 --> 00:04:41,190\Nthe act what this what the change being made in this relative change actually is.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,47\N00:04:41,190 --> 00:04:43,850\NOne example of a high profile relative change.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,48\N00:04:43,850 --> 00:04:53,940\NIf 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,
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,49\N00:04:53,940 --> 00:04:58,740\Ntheir internal movie recommender on the metric that they chose by 10 percent.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,50\N00:04:58,740 --> 00:05:06,120\NThey wanted a 10 percent improvement. And this metric it was. Lower is better, so they wanted you to.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,51\N00:05:06,120 --> 00:05:10,380\NThey wanted to decrease in the metric by 10 percent.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,52\N00:05:10,380 --> 00:05:17,340\NWe can also talk about a difference between differences, because if we compute a difference, that difference itself is just another value.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,53\N00:05:17,340 --> 00:05:22,290\NSo we could say ten sales grew 10 percent more this year than last year.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,54\N00:05:22,290 --> 00:05:32,200\NSo if we define growth as the one year sales minus the other year sales, then we can look at the growth of this year.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,55\N00:05:32,200 --> 00:05:37,000\NAnd the growth of last year and we can compute the difference and difference.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,56\N00:05:37,000 --> 00:05:44,080\NAnd so we can have a 10 percent increase in growth. Difference in difference has come up a lot in various contexts.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,57\N00:05:44,080 --> 00:05:50,020\NAnd so it's important to be able to reason about those as well. And again, be clear both in writing and understanding.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,58\N00:05:50,020 --> 00:05:58,120\NSo 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.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,59\N00:05:58,120 --> 00:06:04,120\NAnd the eye very naturally compares the difference between bars to the height of the bar itself.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,60\N00:06:04,120 --> 00:06:10,840\NPoint plots emphasize absolute difference because you don't have the reference point of the size of the bar.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,61\N00:06:10,840 --> 00:06:17,170\NThey're both of them. Make it pretty clear to see the also compare the differences.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,62\N00:06:17,170 --> 00:06:23,590\NSee how different the differences are. Those are of evident both in bar charts and point plots.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,63\N00:06:23,590 --> 00:06:28,690\NSo to wrap up, there are three primary ways to compute statistics, absolute relative and ratio.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,64\N00:06:28,690 --> 00:06:32,470\NYou need to be very clear and unambiguous when you're writing the results of a
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,65\N00:06:32,470 --> 00:06:36,370\Ncomparison and also when you're trying to understand what others have written.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,66\N00:06:36,370 --> 00:06:39,340\NSeek to accurately understand it. And if you're providing feeB,
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,67\N00:06:39,340 --> 00:06:50,900\Nif 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.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,