tag:blogger.com,1999:blog-32636283.post5292549576463335990..comments2023-03-26T03:50:25.501-04:00Comments on David's Secret Blog: Statistics IIUnknownnoreply@blogger.comBlogger13125tag:blogger.com,1999:blog-32636283.post-51349424295834396862010-04-18T01:26:31.973-04:002010-04-18T01:26:31.973-04:00If you tell me the mean and standard deviation of ...If you tell me the mean and standard deviation of a set of random numbers then there's no information because the numbers are random.<br /><br />If you give me the mean and standard deviation of the heights of people in a room, it's information (at least by the definition of information that I use) because it's descriptive. When I walk into that room, I'd have a better idea of what I'd expect to see than if I didn't have that information. No theory is involved, it's just a description of something.<br /><br />Just like saying, "Joe's eyes are blue". That's a single datum, no mean, no std, no theory, but still information. Having being told that, I'd expect that when I saw Joe's eyes, they'd be blue.Brethttps://www.blogger.com/profile/15063508651955739056noreply@blogger.comtag:blogger.com,1999:blog-32636283.post-44661781621243120182010-04-17T02:54:42.591-04:002010-04-17T02:54:42.591-04:00Bret:
Yes, I might be making a semantic argument....Bret:<br /><br />Yes, I might be making a semantic argument. I hope not, though.<br /><br />If I am not, it lies in my use of the concept of dependency.<br /><br />All sets of data have a mean. But the mean has no more meaning than any individual measure.<br /><br />I have a set of values ranging from 61 to 119. The mean is 79.<br /><br />What's the information?Hey Skipperhttps://www.blogger.com/profile/10798930502187234974noreply@blogger.comtag:blogger.com,1999:blog-32636283.post-60451067612269354802010-04-17T00:41:13.686-04:002010-04-17T00:41:13.686-04:00"Information" is not a formal statistica..."Information" is not a formal statistical term.Brethttps://www.blogger.com/profile/15063508651955739056noreply@blogger.comtag:blogger.com,1999:blog-32636283.post-10535793001464436572010-04-16T17:51:11.476-04:002010-04-16T17:51:11.476-04:00Bret, I was reluctant to drag semantics into this ...Bret, I was reluctant to drag semantics into this discussion, but a definition of terms would be useful.<br /><br />Information, data, theory, observation, patterns, etc. must have precise meanings vis a vis statistics that they don't have in casual conversation.erphttps://www.blogger.com/profile/09826044412670324694noreply@blogger.comtag:blogger.com,1999:blog-32636283.post-84439086356024452102010-04-16T17:15:55.380-04:002010-04-16T17:15:55.380-04:00This is a semantic argument. In my opinion, y'...This is a semantic argument. In my opinion, y'all are using an unusual and particularly definition for "information".Brethttps://www.blogger.com/profile/15063508651955739056noreply@blogger.comtag:blogger.com,1999:blog-32636283.post-13597399006736943042010-04-16T16:57:55.915-04:002010-04-16T16:57:55.915-04:00Bret:
The median height is just more data.
For a...Bret:<br /><br />The median height is just more data.<br /><br />For all populations greater than two, there exists a median height; that is just a brute fact. A median height, in and of itself, has no more information than an individual height.<br /><br />Add a theory: the distribution of height is correlated with sex. That imposes a dependency between two variables which allows deriving information.<br /><br />Given a median, it would be possible to calculate from that alone how many women are in a group with some degree of confidence that the calculation produces a result that has some likelihood of being within some amount of the actual number.<br /><br />Or, given how many women are in a group, it calculate a median.<br /><br />Both results are information extracted from data.<br /><br />The difference is very clear to me.<br /><br />I think.Hey Skipperhttps://www.blogger.com/profile/10798930502187234974noreply@blogger.comtag:blogger.com,1999:blog-32636283.post-12233054276202387802010-04-16T16:55:24.733-04:002010-04-16T16:55:24.733-04:00Right. In effect, statistics tells you nothing ab...Right. In effect, statistics tells you nothing about causes. Only theory tells you about causes. Statistics tells you whether your data is consistent with your theory, which more or less will be the subject of Statistics III.Davidhttps://www.blogger.com/profile/16902329503560660425noreply@blogger.comtag:blogger.com,1999:blog-32636283.post-27446280640379142952010-04-16T15:52:44.332-04:002010-04-16T15:52:44.332-04:00You don't need theory to have information from...You don't need theory to have information from data.<br /><br />If I have the heights of people in the room, that's data but there's also information. I can calculate a median height and then know that half the people are taller and half are shorter.<br /><br />You only need theory when trying to find relationships between data or when trying to extrapolate data to larger populations.Brethttps://www.blogger.com/profile/15063508651955739056noreply@blogger.comtag:blogger.com,1999:blog-32636283.post-7444975589621754802010-04-16T14:57:43.467-04:002010-04-16T14:57:43.467-04:00This is where I fear being pedantic.
Data, in and...This is where I fear being pedantic.<br /><br />Data, in and of itself, is theory and information free, so I think you should have said <i>Data without some theory conveys no information. There is lots of unstructured data available about the world.</i><br /><br />Data doesn't require theory, information does.Hey Skipperhttps://www.blogger.com/profile/10798930502187234974noreply@blogger.comtag:blogger.com,1999:blog-32636283.post-78222914135318842742010-04-16T13:26:17.736-04:002010-04-16T13:26:17.736-04:00Bret: No apologies necessary.
Skipper: I'm ...Bret: No apologies necessary.<br /><br />Skipper: I'm confused by your confusion, since you explain it quite nicely. In the absence of theory, statistics provide no information.Davidhttps://www.blogger.com/profile/16902329503560660425noreply@blogger.comtag:blogger.com,1999:blog-32636283.post-5082230063207810352010-04-16T12:55:50.937-04:002010-04-16T12:55:50.937-04:00… you can't collect data without some theory t...<i>… you can't collect data without some theory that tells you which data is relevant. There is lots of unstructured information available about the world.</i><br /><br />Yes, you can collect data absent theory. We can collect data on the number of fatal car crashes in a year simply as a matter of counting, because for us violent death matters even if we have absolutely no theory about those deaths. Similarly, we can count imported lemons for any number of theory-free reasons.<br /><br />Which means there is a lot of unstructured <i>data</i> -- first order knowledge -- available about the world. <br /><br />Obtaining information from data is where theory steps in. <br /><br />Noting that both Mexican lemon imports and US Highway fatalities varied over time is itself data: the chart itself is just data, not information. Mexican lemons do not "explain" 97% of US highway fatalities until someone asserts there is a dependency between the two.<br /><br />In other words, because there is no theory, those three data (lemons, deaths, and their trends over time) together provide no information.<br /><br />Which is why I'm lost when you say statistics don't work backwards. Data doesn't necessarily require theory, nor does data about data. <br /><br />Asserting dependencies, which are second order knowledge, does.Eric Guinnhttps://www.blogger.com/profile/01996553818848130748noreply@blogger.comtag:blogger.com,1999:blog-32636283.post-23966739672923391192010-04-16T11:54:32.333-04:002010-04-16T11:54:32.333-04:00Actually a nice post, but I couldn't help the ...Actually a nice post, but I couldn't help the snark. Sorry.Brethttps://www.blogger.com/profile/15063508651955739056noreply@blogger.comtag:blogger.com,1999:blog-32636283.post-50630408444804838562010-04-16T11:36:21.424-04:002010-04-16T11:36:21.424-04:00Clearly, eating Mexican lemons makes us better dri...Clearly, eating Mexican lemons makes us better drivers, no?Brethttps://www.blogger.com/profile/15063508651955739056noreply@blogger.com