Timeline for Test of proportions when sample size is not known
Current License: CC BY-SA 3.0
17 events
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Oct 16, 2013 at 14:25 | vote | accept | prop | ||
Oct 6, 2013 at 9:33 | comment | added | Glen_b | prop in what sense does an average of different proportions represent any population value at all? Sampled in different ratios, you get a different average. | |
Oct 6, 2013 at 6:09 | history | tweeted | twitter.com/#!/StackStats/status/386735035820568576 | ||
Oct 6, 2013 at 5:03 | comment | added | probabilityislogic | Do you know how many components are in the average for $p_2$? If you do this number could be used as a lower bound for the sample size. | |
Oct 6, 2013 at 3:48 | comment | added | Glen_b | @gung for a proportions test to make sense any time, you have to assume homogeneity; if that's not reasonable, then even if you can justify the comparison (what's the population about which your inference is being made?), you have bigger issues - like computing a bound on your standard error. | |
Oct 6, 2013 at 3:47 | comment | added | prop | @gung Good question regarding equivalency. I do not think we can assume that the component proportions all have the same true proportion. So, in some sense, I want to test if the proportion I have is significantly different from the overall 'average' proportion. For example, think of $p_1$ as percentage of people who would vote Clinton in NH whereas $p_2$ is the 'average' percentage of people who would vote for Clinton in the remaining 49 states. This discussion with you and Glen has been very helpful. Thanks | |
Oct 6, 2013 at 3:45 | comment | added | Glen_b | prop, can you get even one of the component study values? | |
Oct 6, 2013 at 3:45 | comment | added | gung - Reinstate Monica | I agree w/ you there, @Glen_b. What I'm wondering is whether the whole endeavor makes sense. Imagine $p_2=.5$, but this is based on the averages from 2 studies where $p=.25$ & $p=.75$, respectively, w/ $N=1k$ in both cases. | |
Oct 6, 2013 at 3:41 | comment | added | Glen_b | @gung Actually, if they use weighted proportions (and don't round off prematurely), then we're actually back to a simple ratio of integers and my suggested bound on $n$. If they use an unweighted average, it's a bit trickier, since the smallest component $n_i$ may have a relatively big effect on the standard error of the average, but we may still be able to get some sort of usable bound on the s.e. of $p_2$. The more we know about how $p_2$ was obtained, the better the chances of making an argument about its size. | |
Oct 6, 2013 at 3:35 | comment | added | gung - Reinstate Monica | But you have good reason to believe that every one of those sample proportions is based on $N>1k$, & that all the proportions from the prior studies are sufficiently equivalent? | |
Oct 6, 2013 at 3:33 | comment | added | prop | Perhaps, it is weighted avg. I do not have access to that information. And, no I do not know the component proportions. | |
Oct 6, 2013 at 3:31 | comment | added | gung - Reinstate Monica | Do you know the component proportions (ie, from the individual studies) that went into $p_2$? Most likely, $p_2$ should be a weighted average of those proportions, where the individual study sample sizes are the weights, not the simple average. Note that this fact adds additional complexity to @Glen_b's otherwise good answer below. | |
Oct 6, 2013 at 3:29 | comment | added | prop | @gung It is a bit complex. $p_2$ is the overall average of several studies each one of which has its own sample size. All I know is that the sample size of each one of these individual studies is probably very high (maybe in the range of a 1000 to, not sure about this). $p_1$ is a vector of $1$s and $0$s. | |
Oct 6, 2013 at 3:16 | answer | added | Glen_b | timeline score: 5 | |
Oct 6, 2013 at 3:15 | comment | added | gung - Reinstate Monica | So, for $p_2$ someone just handed you a number, is that correct? What do you have for $p_1$, a vector of $1$s & $0$s? | |
Oct 6, 2013 at 2:52 | review | First posts | |||
Oct 6, 2013 at 3:15 | |||||
Oct 6, 2013 at 2:34 | history | asked | prop | CC BY-SA 3.0 |