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mark999
mark999
09:50
@Glen_b I hope you won't mind answering a couple of questions following on from what you wrote about Antoni's answer.

1. The accepted answer to http://stats.stackexchange.com/questions/9573/t-test-for-non-normal-when-n50 says "The t-test assumes that the means of the different samples are normally distributed; it does not assume that the population is normally distributed." Is that incorrect?

2. Does your comment about the ratio converging to a normal distribution by Slutsky's theorem imply that if we have non-normal data and are relying on CLT and Slutsky's theorem then it would make mor…
 
5 hours later…
user777
user777
15:17
Do robots issue temporary suspensions?
StrongBad
StrongBad
15:51
@user777 sort of. There is a bot that can put you in a question ban: meta.stackexchange.com/questions/86997/…
As the answer says, it is not a suspension.
Suspensions are always handled by a human: meta.stackexchange.com/a/277551/209097
 
1 hour later…
daOnlyBG
daOnlyBG
17:04
Hello everyone. Can I get some help on a probability question?
Glen_b
Glen_b
17:18
@mark999 It's not correct. Try to derive the distribution of the test statistic, without actually assuming the population is normally distributed. If you can show it has a t-distribution, post it as a question and answer; if you do it correctly, I'll give it a 500 point bounty, and I'll suggest some possible journals to submit the result to.
@daOnlyBG Is it a question you can post to the main site?
daOnlyBG
daOnlyBG
@Glen_b Thank you for responding. I already have posted it, and user Xi'an has tried helping me in the comments section. However, I don't seem to be understanding what he's getting at with his comments. I normally would leave a question up for other users to chime in, but to be completely frank and honest with you, I've been stuck on this problem for several days now
Glen_b
Glen_b
@mark999 on point 2. Well, at least we have a justification for an asymptotic normal distribution from CLT + Slutsky; we have no corresponding small sample result for the t. That's not to say that the t will necessarily be terrible as an approximation (often it's not), but in some easy-to-get cases its actually worse than the asymptotic approximation.
daOnlyBG
daOnlyBG
(and for what it's worth, the question I have in mind is this one: stats.stackexchange.com/q/204759/67220 )
Glen_b
Glen_b
17:50
@daOnlyBG Xi'an's advice in that last comment there seems to the point.
daOnlyBG
daOnlyBG
Alright
maybe I'm just inept at this
thanks anyway
Glen_b
Glen_b
@daOnlyBG Is there a particular difficulty you're running into with it?
daOnlyBG
daOnlyBG
Sure. Xi'an says to find the distribution of $$N=∑^{100}_{i=1}T_i=n$$
sorry-
of $T_1$ conditional on $$N=∑^{100}_{i=1}T_i=n$$
I'm honestly not quite sure I understand him
(or her)
am I trying to find the probability of getting the first fax given that I already know how many milliseconds it would take to get 100 faxes?
Glen_b
Glen_b
18:15
@daOnlyBG He (rather than she; he's a well-known academic statistician) moved the last comment to an answer; that answer is how to do the last part of your question (you did the first part and the second part is simple, the last part's a little harder but still quite amenable to straight calculation along the lines he suggests)
daOnlyBG
daOnlyBG
Pardon me, I didn't know his exact identity.
alright, I'll try banging my head a little more
(well, figuratively speaking...for now)
Also, xi'an's hint doesn't directly help me get the joint PMF, but rather the conditional PMF, correct?
Glen_b
Glen_b
Correct, but what he begins with makes the joint obvious
daOnlyBG
daOnlyBG
Ah. I wish it was obvious to me
Anyway thanks for your help
maybe I'll figure it out
Glen_b
Glen_b
18:36
Must sleep now
mark999
mark999
19:24
@Glen_b Thanks for your replies. On the first point, I have no reason for thinking that the statement is correct. It's a claim I occasionally see here on CV but I've never understood the justification for the claim. What you wrote made me think that the claim was incorrect, and I just wanted to confirm that. Thank you for doing so.

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