standard deviation from frequency table
Dear friends: Does anyone know / remember how to obtain the standard deviation of a set of numbers given only a frequency table? e.g., xf(x) 00.2 10.3 20.2 30.2 40.1 Many thanks. Chris = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
Re: fla election stats
On 5 Jan 2001 17:32:16 -0800, [EMAIL PROTECTED] (dennis roberts) wrote: this is the perennial issue in national elections about ... if it looks like the election is sewn up from the east and south ... then what is to motivate those in the napa valley to leave their vinyards and head for the polls? i do think there are some data that roughly show that voter turnout is less out west ... compared to the east ... but, the difference is also confounded by many other factors The entire nation is not what I talked about in my post. I'm referring to voters in an individual state which is the same problem writ small. Voters in the panhandle region of Florida were confronted with electronic media calling the election before closing time. I think the annointing of a media "winner" based on exit poll data discourages "late" voting--period. In this instance a negative for both the V.P. and Bush. In close races, like the 2000 election, a few votes not cast might have changed the outcome. Is it too much to ask of the media not to call a state until the polls close? Does this infringe upon the First Amendment? These are indeed political and legal issues---not statistical ones. Statisticians should be above the fray and totally objective, right? I would be interested in research showing voter intentions in those western counties AFTER learning the election had been already called. It would be fascinating to find out what the exit pollsters revealed about those counties and if there were significant differences between the time zones factoring in prior election data, etc. What do voters think and then act on when confronted with the information that their vote will be meaningless? Or, at least the media says it would be meaningless? = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
Re: fla election stats
At 09:42 PM 1/5/01 -0800, Jake wrote: This is silly. Why inconvenience the voters when a news blackout until ALL the polls are closed will do the trick? The overzealousness of the press does not trump the people's right to vote. i totally agree ... but, in a democracy with a free press, how do you do this? i don't see any way ... unless all news organization agreed ... but how long would that last, eh (like a mideast peace agreement)? if you have a good and practical and doable solution to this ... this by FAR makes the most sense (by the way ... that was the first thing on my mind but, the thought of even suggesting it seemed silly in itself) == dennis roberts, penn state university educational psychology, 8148632401 http://roberts.ed.psu.edu/users/droberts/drober~1.htm = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
Re: standard deviation from frequency table
well, one way is to say ... i have n=10 ... so, there are 2 zeros, 3 ones, etc. and find it based on that data ... doesn't matter if there are 10 or 100 or 1000 ... now, if you had some n that did not divide exactly by these p values ... there might be another algebraic way to do it as long as the X values are fixed ... and the p values ... then you could do it that way ... of course, without the X values .. you are lost At 09:35 AM 1/6/01 -0500, Chris Chiu wrote: Dear friends: Does anyone know / remember how to obtain the standard deviation of a set of numbers given only a frequency table? e.g., xf(x) 00.2 10.3 20.2 30.2 40.1 Many thanks. Chris = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ = == dennis roberts, penn state university educational psychology, 8148632401 http://roberts.ed.psu.edu/users/droberts/drober~1.htm = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
Re: standard deviation from frequency table
Chris Chiu wrote:
Dear friends:
Does anyone know / remember how to obtain the standard deviation of a set
of numbers given only a frequency table?
e.g.,
xf(x)
00.2
10.3
20.2
30.2
40.1
Many thanks.
Chris
calculate average value "a"
change your "f(x)" into "f", which is number of observation in the given
row of the frequency table. Sum of "f" from all rows equals "n" (number
of observations).
s = sqr { [sum(f*(x-a)^2)] / [n-1] }
Have gave more brackets than necessary to make the formula more clear (i
hope :-)
Fowler J, Cohen L, Jarvis P 1998. Practical statistics for field
biology. Wiley, page 38.
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Re: fla election stats
At 02:34 PM 1/6/01 +, J. Williams wrote: The entire nation is not what I talked about in my post. I'm referring to voters in an individual state which is the same problem writ small. Voters in the panhandle region of Florida were confronted with electronic media calling the election before closing time. true ... but the principle is exactly the same this assumes of course that voters are really thinking about the electoral college ... if they are NOT thinking of the electoral college ... then why would they NOT go vote just because NBC said that al gore won the state? in the case that the person is thinking that my vote counts like any other vote ... then, to them, their vote would either make it more of a gore win or less of a gore win ... but that their vote would make some difference in the vote total ... and hence the country total ... this might actually suggest that they would increase their liklihood of going to vote IF they were really thinking about the us of a total for the popular vote and thinking that if NBC had said al gore won ... the voter thinks that if he/she goes and votes for bush ... that this will lessen the chance of al gore winning in the us of a if the person has clearly got the electoral college on his/her mind AND NBC said that al gore had won ... THEN those in the panhandle who were for bush might not make the effort ... why should they? their cause would have been lost ... the general fact is ... the PRESS hounds and hounds about it being the electoral college vote that counts and ... we all have emblazend in out minds that blue and red us of a map .. with blue STATES and red STATES ... and the electoral count totals ... and THAT is what is being pounded into the viewers and listeners' minds ... so, under that scenario ... the problem is more widespread that the panhandle voters in florida ... it will spread to anyplace where polls might still be open and, if the tallies look like one candiate will win over the other ... THAT is what can discourage any other potential voter from making the trip to the precinct voting booth ... and casthing their ballot it is not as much that networks project STATE victories ... prior to all polls being closed ... it is the overarching notion that media will report on the results of the election as fast as they can get their hands on them ... no matter if 1/2 the county has not voted already or not that is the fundamental problem that has to be addressed and as one other poster said ... a complete blackout of any reporting on results until all polls are closed is the ideal solution ... but, how that could be pulled off, i have no idea == dennis roberts, penn state university educational psychology, 8148632401 http://roberts.ed.psu.edu/users/droberts/drober~1.htm = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
Re: fla election stats
"J. Williams" [EMAIL PROTECTED] wrote in message [EMAIL PROTECTED]">news:[EMAIL PROTECTED]... I would be interested in research showing voter intentions in those western counties AFTER learning the election had been already called. It would be fascinating to find out what the exit pollsters revealed about those counties and if there were significant differences between the time zones factoring in prior election data, etc. What do voters think and then act on when confronted with the information that their vote will be meaningless? Or, at least the media says it would be meaningless? I've only seen two bits of research on this topic. Neither is particularly detailed, but both are referenced here http://www.bestbookmarks.com/election/#links Here is the direct link to one of these two analyses: http://www.be.wvu.edu/divecon/econ/sobel/election/centraltime.htm = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
standard deviation from frequency table
QUESTIONS Dear friends: Does anyone know / remember how to obtain the standard deviation of a set of numbers given only a frequency table? e.g., xf(x) 00.2 10.3 20.2 30.2 40.1 Many thanks. Chris ONE POSSIBLE ANSWER: Here is a worked solution. I used the Windows TextPad editor to cut your table out of your email messaage. Though not really needed here, I love TextPad for statistical work because you can cut out individual COLUMNS of data from a table to paste into stats. doftware. http://www.textpad.com/ Then I pasted the table into Minitab and ran a macro I wrote for this purpose. Your "frequencies" are actually relative frequencies and the macro treats them as probabilities. This is equivalent to dividing by n rather than n-1 in computing the variance and standard deviation. It's the best you can do if you don't know n and a good approximation if n is large. Worksheet size: 10 cells Welcome to Minitab!-) * NOTE * Standard Graphics are enabled. Professional Graphics are disabled. Use the GPRO command to enable Professional Graphics. MTB read into c1 c2 DATA 00.2 DATA 10.3 DATA 20.2 DATA 30.2 DATA 40.1 DATA end 5 rows read. MTB Execute "E:\STATS\MINITAB8\STATS1A\MACROS\VARPD.MTB" Executing from file: E:\STATS\MINITAB8\STATS1A\MACROS\VARPD.MTB This macro computes the mean, variance, and standard deviation of a probability distribution. The data values must be stored in c1 and their probabilities in c2. The results of all intermediate steps are printed out to aid students in learning to do these computations by hand. The macro will destroy any data stored in c2-c6, k1-k7, and any names given to c1-c6. Row x pxpresids. res.sq. res.sq.p 1 0 0.2 0.0 -1.7 2.89 0.578 2 1 0.3 0.3 -0.7 0.49 0.147 3 2 0.2 0.4 0.3 0.09 0.018 4 3 0.2 0.6 1.3 1.69 0.338 5 4 0.1 0.4 2.3 5.29 0.529 MTB print k1 mean = K11.7 MTB print k4 variance = K41.61000 MTB print k7 standard deviation = K71.26886 MTB end MTB If you do know n, multiply the variance above by n/(n-1) to get the variance with a divisor of n-1. Here is the macro if you want it. The "let" statements show you exactly what is being calculated at each step. notitle note noteThis macro computes the mean, variance, and standard notedeviation of a probability distribution. The data values notemust be stored in c1 and their probabilities in c2. noteThe results of all intermediate steps are printed out noteto aid students in learning to do these computations noteby hand. The macro will destroy any data stored in c2-c6, notek1-k7, and any names given to c1-c6. note noecho let c3=c1*c2 let k1=sum(c3) let c4=c1-k1 name c1 'x', c2 'p', c3 'xp', c4 'resids.' let c5=c4*c4 name c5 'res.sq.' let c6=c5*c2 name c6 'res.sq.p' let k4=sum(c6) let k7=sqrt(k4) note print c1-c6 note echo print k1 mean = print k4 variance = print k7 standard deviation = end -- _ | |Robert W. Hayden | | Work: Department of Mathematics / |Plymouth State College MSC#29 | |Plymouth, New Hampshire 03264 USA | * |fax (603) 535-2943 /| Home: 82 River Street (use this in the summer) | )Ashland, NH 03217 L_/(603) 968-9914 (use this year-round) Map of New[EMAIL PROTECTED] (works year-round) Hampshire http://mathpc04.plymouth.edu (works year-round) The State of New Hampshire takes no responsibility for what this map looks like if you are not using a fixed-width font such as Courier. "Opportunity is missed by most people because it is dressed in overalls and looks like work." --Thomas Edison = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
markov random field image segmentation
I need some information about MRF models for image analysis (segmentation) and in particular I need also software for image segmentation that based on this models. Thanks Andrea = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
Re: Effect size for heritability
I think I've resolved this question with a colleague. We likened the heritability of a given trait, for example, jump height, to the relationship between that trait and some other explanatory variable, such as leg length. The R^2 for leg length explaining jump height might be 0.36. Now, 0.36 is a gross underestimate of the effect of leg length on jump height. We should use root(0.36), i.e. 0.60, because, if you experimentally change leg length by one standard deviation with growth hormone during development, or if you move from one individual to another who differs by one standard deviation in leg length, you will find that jump height changes or differs on average by 0.60 of a standard deviation for jump height. Trust me, it's true. 0.60 is large on Cohen's scale, whereas 0.36 is moderate. Now let's bring in heritability. For the sake of simplicity, let's assume leg length is entirely inherited and is the only inherited factor explaining jump height. Therefore we would find that the H^2 for inheritance explaining jump height is 0.36. So we should interpret H, but not H^2, when we talk about magnitude of heritability, and we should do it in the following way: there is some variable, the values of which are determined by heredity, such that a change in one standard deviation of the variable results in a change of 0.6 standard deviations in jump height. Of course, there are lots of variables contributing to jump height, but you can combine them into one composite virtual variable for the sake of understanding what H means. I have been looking at Cleveland's "Visualising Data" and he introduces an "residual-fitted"/"r-f" spread plot that I'd like to see next time I read an article on hereditability. This is two graphs side by side on the same scale. One is a quantile plot of (fitted values - mean fitted values). The other is a quantile plot of residuals. Comparing these two plots gives you a very good idea of how predictive the fit is. It looks a bit like this: Fitted |-- Residuals -- * | * * |* * | * * |* * | * * |* * | * * |* --- Now if we had Y = X + E where Y is N(0, 1) and E is N(0, 1) we would be plotting fitted Y = X and the residual = E, so we would plot two identical graphs - as above, except that they wouldn't be straight lines, supporting an R^2 measure, which says 1/2, which does fit the symmetry of the situation. If you say there is really 1/sqrt(2) of relationship here when you know X but not E, then it looks a bit odd when you realise that there is another 1/sqrt(2) of relationship left if you know E but not X. -- A. G. McDowell = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
