<p>If (and it's a big if) your sample is unbiased, that is, random, and if the population sampled is large, then the percentage sampled is completely irrelevant - only the absolute number of samples matters.</p>
<p>100 drawn out of 1 000 000 is almost exactly the same statistically as 100 drawn out of 100 000 000 - or 100 drawn out of infinity for that matter!</p>
<p>How many samples is &quot;enough&quot; will depend both on the confidence you want, and the actual true distribution. It doesn't depend on the size of the population (as long as it's large).</p>

CC BY-SA 4.0
2021-01-01T06:22:23.533Z
2021-01-01T06:22:23.533Z
Kristoffer Sjöö
<p>What they have at present is best described as a theory based on data that is not precise enough to make a definitive statement.  They are telling people they think something is out there and roughly what they think it might be, but they really don't have accurate enough data to make any statements beyond that.</p>

<p>The fact that the possible range of distances they suggest is so large tells you all you need to know about the accuracy of the data being insufficient to draw reliable conclusions.</p>

<p>My biggest problem with this claim is that we have a historical lesson that suggests caution : Pluto.  Pluto was found when looking for an entirely different object ( coincidentally about the same mass as the new planet X, if memory serves me ).  It transpired that the orbital anomalies that led to predicting a Planet X 1.0 were later evaporated by more accurate measurements and theory.  </p>

<p>Are we now seeing the same sort of error ?  Could be, might not be.  All we can hope is that the quest for an explanation generates either the result claimed or, if not that, better data, more data and perhaps more accurate simulations and theory.</p>

<p>I am reminded that, in the past, quite eminent and respectable scientists have claimed any number of things, which would later prove incorrect.  Cold fusion leaps to mind.  The problem with humans looking at data is that, sometimes, they see what they want.  I think this planet X 2.0 claim needs a colder and more objective, perhaps even cynical, examination, away from the media.</p>

CC BY-SA 3.0
2016-01-26T11:57:23.883Z
*I think this planet X 2.0 claim needs a [cynical] examination*.  It's called *peer review*.
gerrit
CC BY-SA 3.0
2016-01-26T12:03:59.360Z
A peer review is supposed to be *objective* and I think cynical might be a little bit more than that.  YMMV.  :-)
StephenG - Help Ukraine
CC BY-SA 3.0
2016-01-26T21:35:06.017Z
@StephenG "skeptical" also works. I suspect that was the original idea, which then got transformed with more and more colorful synonyms until something much more emphatic came out. At least, that's what happens to me a lot.
DrZ214
CC BY-SA 3.0
2016-01-26T21:35:13.113Z
@gerrit see above comment.
DrZ214
CC BY-SA 3.0
2016-02-02T17:50:29.087Z
they must have a pretty good feeling that this is real (peers also) because there is going to be a lot of Subaru telescope time spent looking for it
Jack R. Woods
CC BY-SA 3.0
2016-02-06T16:20:13.007Z
The actual peer-reviewed paper is rather measured and low-key. That should be read, and not press releases. The range of distances is due to the eccentricity of the proposed orbit. Aside from your skepticism (which is fair enough), you don't actually address what is being asked in the question.
ProfRob
CC BY-SA 3.0
2016-01-25T22:09:01.400Z
2016-01-25T22:09:01.400Z
StephenG - Help Ukraine
<p>I'm sure Caltech has answered this in some way, but I think it's a good question have on this site.</p>
<p><strong>What good evidence exists</strong> for the 9th planet as spoken of by Caltech?</p>
<p>As I see it, Caltech has apparently looked at the orbital parameters of many Trans-Neptunian-Objects (TNOs) and noticed that the lines between their perihilion and aphelion (I don't know what the technical term might be) all run more or less in the same direction. This is evidence that some large body has gravitationally &quot;synced&quot; these planets over millions of years.</p>
<p>Except <strong>that alone isn't good evidence.</strong> Here are two stats first:</p>
<ol>
<li><p>Known TNOs: about 1,750 according to <a href="http://www.minorplanetcenter.org/iau/lists/TNOs.html" rel="nofollow noreferrer">the Minor Planet Center's list</a>.</p>
</li>
<li><p>Estimated existing Kuiper-Belt Objects: 120,000+ according to <a href="http://www.britannica.com/place/Kuiper-belt" rel="nofollow noreferrer">Britannica</a>. (That number is only estimating objects of 100-km diameter or more, but that's fine for our purposes.) Note: 120,000 is only for KBOs. There are other TNO sets such as the oort cloud (and the scattered disc if you define it separately), so I expect the number to be much much bigger than 120,000.</p>
</li>
</ol>
<p>Given that we've only measured about 1% or less of TNO orbits, how can we be sure we have a good random sample to say that a massive body must have aligned these orbits? In other words, all the other orbits might be randomly distributed, which would be compelling evidence that some giant body is <strong>not</strong> &quot;syncing&quot; orbits or else way more than 1% of them would be &quot;synced&quot;.</p>
<p>If I recall my statistics class correctly, 1% is not good enough for a random sample. The border-line good enough area starts at 3%, but there's still a catch: <strong>It has to be a random sample.</strong> There are still observation-bias questions here because obviously we've only mostly discovered the &quot;nearby&quot; TNOs, because they are easier to discover when they're &quot;nearby&quot;. That certainly would not be a random sample even if we had 3% of them.</p>
<p><strong>TLDR:</strong> There are at least 100,000 distant objects, of which less than 1% of them have some kind of aligned orbit as far as we know today. Is this actually good evidence that something has aligned them?</p>
<p><strong>EDIT:</strong> Another analogy that might help. You have a bag of 100 marbles. You reach in and pull out 5 from the top of the bag (notice I didn't say any random 5!). They turn out to be 4 red ones and 1 black one. Is this actually good evidence that about 80% <strong>of the whole bag</strong> is red?</p>

CC BY-SA 3.0
2016-01-25T19:40:56.557Z
Maybe I'll turn this into an answer, but Batygin & Brown address observational bias early in the paper, writing, "While observational bias does preferentially select objects with perihelia (where they are closest and brightest) at the heavily observed ecliptic, no possible bias could select only for objects moving from south to north."
HDE 226868
CC BY-SA 3.0
2016-01-25T19:44:53.580Z
@HDE226868 If you can turn that into an answer, I'd love to read it. But as it stands now, your comment doesn't address the "less than 1% of TNOs" problem. Is a sample of < 1% really enough good evidence? For all we know the other 99% will have totally differently aligned orbits, making that 1% look just like a random variation.
DrZ214
CC BY-SA 3.0
2016-01-25T19:45:38.670Z
Yeah, that still needs to be addressed.
HDE 226868
CC BY-SA 3.0
2016-01-26T11:55:59.123Z
I don't understand how a fixed % makes much sense.  Surely if we pull 5000 marbles from a bag containing 100000, we have a much better sample than if we take 5 marbles from a bag containing 100?
gerrit
CC BY-SA 3.0
2016-01-26T21:37:29.993Z
@gerrit I'm struggling to recall my stochastic models class all those years ago. You might be on to something there, but I'm very used to looking at things as a "per capita rate" in order to get the true rate. I don't see how leaving 99% unsampled is "safe".
DrZ214
CC BY-SA 3.0
2016-02-06T16:25:59.993Z
What is meant by "good" evidence? The peer reviewed paper is entitled "Evidence for a distant giant planet in the solar system".  To use your analogy at the end, your sample *is* evidence that the bag contains predominantly red balls. Whether it is good evidence, is often a matter of opinion. The idea of estimating the parameters of a population based on a subsample is what statistics is all about - and yes, opinion polls are often wrong.
ProfRob
<solar-system><planet><observational-astronomy><9th-planet>
What good evidence exists for the 9th planet as spoken of by Caltech?
DrZ214
# What good evidence exists for the 9th planet as spoken of by Caltech?

(Asked by: username_0 on 2016-01-25)

I'm sure Caltech has answered this in some way, but I think it's a good question have on this site.

**What good evidence exists** for the 9th planet as spoken of by Caltech?

As I see it, Caltech has apparently looked at the orbital parameters of many Trans-Neptunian-Objects (TNOs) and noticed that the lines between their perihilion and aphelion (I don't know what the technical term might be) all run more or less in the same direction. This is evidence that some large body has gravitationally "synced" these planets over millions of years.

Except **that alone isn't good evidence.** Here are two stats first:

1. Known TNOs: about 1,750 according to [the Minor Planet Center's list](http://www.minorplanetcenter.org/iau/lists/TNOs.html).
2. Estimated existing Kuiper-Belt Objects: 120,000+ according to [Britannica](http://www.britannica.com/place/Kuiper-belt). (That number is only estimating objects of 100-km diameter or more, but that's fine for our purposes.) Note: 120,000 is only for KBOs. There are other TNO sets such as the oort cloud (and the scattered disc if you define it separately), so I expect the number to be much much bigger than 120,000.

Given that we've only measured about 1% or less of TNO orbits, how can we be sure we have a good random sample to say that a massive body must have aligned these orbits? In other words, all the other orbits might be randomly distributed, which would be compelling evidence that some giant body is **not** "syncing" orbits or else way more than 1% of them would be "synced".

If I recall my statistics class correctly, 1% is not good enough for a random sample. The border-line good enough area starts at 3%, but there's still a catch: **It has to be a random sample.** There are still observation-bias questions here because obviously we've only mostly discovered the "nearby" TNOs, because they are easier to discover when they're "nearby". That certainly would not be a random sample even if we had 3% of them.

**TLDR:** There are at least 100,000 distant objects, of which less than 1% of them have some kind of aligned orbit as far as we know today. Is this actually good evidence that something has aligned them?

**EDIT:** Another analogy that might help. You have a bag of 100 marbles. You reach in and pull out 5 from the top of the bag (notice I didn't say any random 5!). They turn out to be 4 red ones and 1 black one. Is this actually good evidence that about 80% **of the whole bag** is red?

**Tags:** solar-system, planet, observational-astronomy, 9th-planet
> **Comments:**
> **username_1**: Maybe I'll turn this into an answer, but Batygin & Brown address observational bias early in the paper, writing, "While observational bias does preferentially select objects with perihelia (where they are closest and brightest) at the heavily observed ecliptic, no possible bias could select only for objects moving from south to north."  
> **username_0**: @HDE226868 If you can turn that into an answer, I'd love to read it. But as it stands now, your comment doesn't address the "less than 1% of TNOs" problem. Is a sample of < 1% really enough good evidence? For all we know the other 99% will have totally differently aligned orbits, making that 1% look just like a random variation.  
> **username_1**: Yeah, that still needs to be addressed.  
> **username_2**: I don't understand how a fixed % makes much sense.  Surely if we pull 5000 marbles from a bag containing 100000, we have a much better sample than if we take 5 marbles from a bag containing 100?  
> **username_0**: @gerrit I'm struggling to recall my stochastic models class all those years ago. You might be on to something there, but I'm very used to looking at things as a "per capita rate" in order to get the true rate. I don't see how leaving 99% unsampled is "safe".  
> **username_3**: What is meant by "good" evidence? The peer reviewed paper is entitled "Evidence for a distant giant planet in the solar system".  To use your analogy at the end, your sample *is* evidence that the bag contains predominantly red balls. Whether it is good evidence, is often a matter of opinion. The idea of estimating the parameters of a population based on a subsample is what statistics is all about - and yes, opinion polls are often wrong.  

---

## 2 answers

### Answer by username_4 on 2021-01-01. Score: 2

If (and it's a big if) your sample is unbiased, that is, random, and if the population sampled is large, then the percentage sampled is completely irrelevant - only the absolute number of samples matters.

100 drawn out of 1 000 000 is almost exactly the same statistically as 100 drawn out of 100 000 000 - or 100 drawn out of infinity for that matter!

How many samples is "enough" will depend both on the confidence you want, and the actual true distribution. It doesn't depend on the size of the population (as long as it's large).


---

### Answer by username_5 on 2016-01-25. Score: 2

What they have at present is best described as a theory based on data that is not precise enough to make a definitive statement. They are telling people they think something is out there and roughly what they think it might be, but they really don't have accurate enough data to make any statements beyond that.

The fact that the possible range of distances they suggest is so large tells you all you need to know about the accuracy of the data being insufficient to draw reliable conclusions.

My biggest problem with this claim is that we have a historical lesson that suggests caution : Pluto. Pluto was found when looking for an entirely different object ( coincidentally about the same mass as the new planet X, if memory serves me ). It transpired that the orbital anomalies that led to predicting a Planet X 1.0 were later evaporated by more accurate measurements and theory.

Are we now seeing the same sort of error ? Could be, might not be. All we can hope is that the quest for an explanation generates either the result claimed or, if not that, better data, more data and perhaps more accurate simulations and theory.

I am reminded that, in the past, quite eminent and respectable scientists have claimed any number of things, which would later prove incorrect. Cold fusion leaps to mind. The problem with humans looking at data is that, sometimes, they see what they want. I think this planet X 2.0 claim needs a colder and more objective, perhaps even cynical, examination, away from the media.

> **Comments:**
> **username_2**: *I think this planet X 2.0 claim needs a [cynical] examination*.  It's called *peer review*.  
> **username_5**: A peer review is supposed to be *objective* and I think cynical might be a little bit more than that.  YMMV.  :-)  
> **username_0**: @StephenG "skeptical" also works. I suspect that was the original idea, which then got transformed with more and more colorful synonyms until something much more emphatic came out. At least, that's what happens to me a lot.  
> **username_0**: @gerrit see above comment.  
> **username_6**: they must have a pretty good feeling that this is real (peers also) because there is going to be a lot of Subaru telescope time spent looking for it  
> **username_3**: The actual peer-reviewed paper is rather measured and low-key. That should be read, and not press releases. The range of distances is due to the eccentricity of the proposed orbit. Aside from your skepticism (which is fair enough), you don't actually address what is being asked in the question.  

---

