Timeline for How to interpret confidence interval of the difference in means in one sample T-test?
Current License: CC BY-SA 3.0
14 events
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| Jun 15, 2011 at 22:05 | comment | added | whuber♦ | @Bogdan Interesting idea! I made the changes you suggest. I think it's great to visually distinguish parameters from random variables. I'm a little uneasy using the hat to do it, though, because neither $a$ nor $b$ is actually estimating anything. | |
| Jun 15, 2011 at 19:33 | comment | added | Bogdan Lataianu | I stress that $a$ and $b$ are random variables, so when @whuber writes Pr[$a\leq\mu\leq b$]=1-0.05, he means $a$ and $b$ are random, not fixed, and both are defined by him above. Perhaps adding hats Pr[$\hat{a}\leq\mu\leq \hat{b}$]=1-0.05 for them would make it clearer. | |
| Jun 14, 2011 at 13:20 | comment | added | whuber♦ | @ayush Consider how a 95% CI for the mean of a large sample of size $N$ from a population with mean $\mu$ is computed: one estimates the mean $\hat{m}$ and standard error $\widehat{se}$ from the sample and reports the interval $[\hat{a},\hat{b}]$ = $[\hat{m}-z_{0.05}\widehat{se}, \hat{m}+z_{0.05}\widehat{se}]$. Whence, by construction, $\hat{a} \le \hat{m} \le \hat{b}$. But you assert $\Pr[\hat{a} \le \hat{m} \lt \hat{b}] = 1 - 0.05$! The correct probability statement is $\Pr[\hat{a} \le \mu \le \hat{b}] = 1 - 0.05$. | |
| Jun 14, 2011 at 5:12 | comment | added | ayush biyani | @whuber -- if the confidence intervals are constructed such that the difference will lie there 100% of the time, what is 95% for then? Please make me clear. | |
| Jun 13, 2011 at 14:59 | comment | added | Anne | @Ayush, No I do not understand. The example I am thinking of is where you are looking a difference between a sample and population mean. In this case what exactly does the CI between sample and pop mean, mean. We have used the sample mean to estimate the pop standard deviation and thus from that we are estimating the CI around the mean estimate. But what then is the difference of means. It isn't the difference between the pop mean we have provided and the sample mean. So what is it? Is my question clear? | |
| Jun 13, 2011 at 14:55 | vote | accept | Anne | ||
| Jun 13, 2011 at 14:55 | |||||
| Jun 13, 2011 at 13:28 | comment | added | whuber♦ | @Ayush (-1) The characterization that currently appears in your reply can be interpreted in several ways, most of which (therefore) are incorrect. For example, confidence intervals $[a,b]$ are usually constructed so as to contain the "sample mean difference," implying that this difference will lie between the limits 100% of the time no matter what. | |
| Jun 13, 2011 at 6:33 | comment | added | ayush biyani | @anne -- are you clear with the meaning now ? Please keep subscripts in mind. | |
| Jun 13, 2011 at 6:33 | comment | added | ayush biyani | @probabilityislogic -- agree..the subscripts are necessary. | |
| Jun 13, 2011 at 6:06 | comment | added | probabilityislogic | @ayush - this is not the correct interpretation in your second last sentence. Or at least you should add subscripts to "a" and "b", which makes it clear that it is these quantities which are varying over the 100 times. Your current notation makes it seem like "a" and "b" are fixed quantities. | |
| Jun 13, 2011 at 5:33 | comment | added | ayush biyani | @anne -- Ok. What I mean is if you want to test the mean between two samples and lets say each sample has 1000 people, you can define infinite samples out of it ( of lets say 40 people from each)..I had wrote this to tell why do the different experiments differ from each other..The experiments where we are observing confidence interval. | |
| Jun 13, 2011 at 5:21 | comment | added | Anne | @ Ayush. thanks. That is helpful. Sorry I don't quite follow your final sentence. | |
| Jun 13, 2011 at 5:19 | vote | accept | Anne | ||
| Jun 13, 2011 at 14:55 | |||||
| Jun 13, 2011 at 5:16 | history | answered | ayush biyani | CC BY-SA 3.0 |