Mistake in 2005 HSC? (1 Viewer)

[NightShadow]

i remember the stupid target charts with the accuracy..and it would hit the centre.. and reliabity.. and they would clump in some random place... [ i particularly liked the one with neither accuracy nor reliability hehe]

by improving the accuracy of the data set i meant.. improving the accuracy of the data values...for the experiment... accounting for experimental error...

thus if we go to our targets... the data set will be accurate more of the time... but the central point may not be at the centre... (due to experimental error) and the rest of the data values may be strewn around but largely based at that off centre point... which looking from a far off persective... would be counted as reliability...

..actually.. that was just plain confuzzling..

i'll stick with the standard deviation thing... OK... so high reliabity... means...a higher degree of yielding the same results... meaNING... that the standard deviation... is closer to zero... how do we get almost zero standard deviation.. a case in which the spread of the data..is close to zero.. we try to make the standard deviation denominator.. zero... which is acheivable only through repetition if we dont change anything else... and basically...let it all up to phenomena... or.. do quantum physics or something like that...

 

[NightShadow]

oh i think i can use the targets now...

OK.. i said repeating.. improves the accuracy of the measurement value...

suppose we take the case where the correct value of the experiment.. is 10
but doign it once.. we might yield the value.. 8... not as close as we would like it to be... so if i repeat... then i would get more values hitting the desired 10... thus a highly reliable experiment... would yield more accurate data values...

but accurate data values... only account of the degree in which the measurement values are the same... therfore... highly accurate data values... you can say the experiment was reliable...

ACCURACY RELATES ONLY TO THE EXPERIMENT PERFORMED... NOT THE DATA VALUE OUTPUT

 

[insert-username]

Accuracy is how close the results are to the 'bull's eye'. Reliability is the 'spread' of data.

As stated before, repetition does nothing to reduce the spread of data.

So according to you, repetition improves neither accuracy nor reliability. How close are the results to the bulls eye? The standard deviation, which "fluctuates both up and down around a horizontal midline", tells us, yes? Low deviation, mean value as the bulls eye equals high accuracy, no? What's the spread of data? According to you, it's standard deviation again. And since repetition does nothing to improve the standard deviation... neither reliability nor accuracy have any chance of being right!

I'll reiterate: if your equipment is calibrated incorrectly, or your measuring device consistently adds 0.2g to a mass, your results will not get more accurate through repetition. They will, however, be reliably inaccurate if you got the same result each time.


I_F

 

[pkc]

i'll stick with the standard deviation thing... OK... so high reliabity... means...a higher degree of yielding the same results... meaNING... that the standard deviation... is closer to zero... how do we get almost zero standard deviation.. a case in which the spread of the data..is close to zero.. we try to make the standard deviation denominator.. zero... which is acheivable only through repetition if we dont change anything else... and basically...let it all up to phenomena... or.. do quantum physics or something like that...

If you are meaning that standard deviation should approach zero with increasing sample size (N), because N is in the denominator of:
<DL><DD>

</DD></DL>Well unfortunately the numerator is a variable which goes up with increasing N, so this cancels out the effect of going toward zero.

I'll look for a reference on the web, but any decent 1st year maths book with stats in it will confirm that standard deviation does not decrease with increasing sample size.

 

[pkc]

So according to you, repetition improves neither accuracy nor reliability.


I_F

Well, thats half right.

What I've actually said is that repetition may improve accuracy (if calibration etc are correct), and repetition will never improve reliability (through decreasing spread of data anyways).

 

[helper]

Try looking at this page
http://sportsci.org/resource/stats/generalize.html#viacl

 

[NightShadow]

i know with the standard deviation thing and the numerator... i have done thest calculations with large data sets and believe me when i say its very annoying but simply saying that theres a numerator coefficient is simply not enough... because due to the nature of the equation... its hard to just spot out... try using the data set values 80, 79 and then go use 80, 79,80.. you will find that the later has a smaller deviation. go read on normal distribution : "as a sample from a population becomes larger, agreement between sample values and population values increases" quote unquote... the reason is just cause it does really... ts the whole bell curve thing.. if you want..go look it up in uni text books... and post grad stat uni courses... if you LIKE... its not a simple relationship as numerator.. and denominator... sorry for the misunderstanding presented in my other post...

but read my target entry... and insert username... wtf are you talking abouT?

whether a set of values has a low or large standard deviation depends upon the natural accuracy of the experiment... in this case..repetition does not change the natural accuracy of the experiment at all... thus we ask the question.. if my experiment is exactly the same.. why do my values fluctuate? instead of staying the same, thres probability involved and once again.. bell curves...

and i'm tired... >.<

 

[pkc]

Try this and see what happens to the standard deviation as you take more samples:

http://www.ruf.rice.edu/~lane/stat_sim/sampling_dist/index.html

 

[pkc]

"as a sample from a population becomes larger, agreement between sample values and population values increases" quote unquote... quote]

Exactly.
The agreement between the sample standard deviation and the "population" or "parent population" standard deviation (for the bell curve drawn around millions of results that would have come from the experiment if you did it so many times) definitely increases.

This agreement explains the convergence of the sample standard deviation values to a midline (whose value is the standard deviation of the "parent population") as sample number is increased.

Its all to do with the calculated sample standard deviation being an estimator (as all statistics are) of the parameters of the parent population. And this estimation has an increased accuracy as sample size increases.

But this has nothing to do with the value of the standard deviation getting smaller as more samples are take.

 

[pkc]

Here's data that Excel randomly generated (Tools-analysis-random number generation) from a population whose mean is 7.00 and standard deviation 0.02 - typical of a school pH measurement experiment.
The right hand column tracks the standard deviation of the samples as more results are added.

<TABLE borderColor=#000000 cellSpacing=0 cellPadding=2 width=134 border=1><TBODY><TR><TD width="50%" height=16>

Result​

​

​

</TD><TD width="50%" height=16>

SD​

​

​

</TD></TR><TR><TD width="50%" height=16>

6.99​

​

​

</TD><TD width="50%" height=16>
</TD></TR><TR><TD width="50%" height=16>

7.02​

​

​

</TD><TD width="50%" height=16>

0.017​

​

​

</TD></TR><TR><TD width="50%" height=16>

7.02​

​

​

</TD><TD width="50%" height=16>

0.013​

​

​

</TD></TR><TR><TD width="50%" height=16>

7.01​

​

​

</TD><TD width="50%" height=16>

0.011​

​

​

</TD></TR><TR><TD width="50%" height=16>

7.02​

​

​

</TD><TD width="50%" height=16>

0.011​

​

​

</TD></TR><TR><TD width="50%" height=16>

7.00​

​

​

</TD><TD width="50%" height=16>

0.010​

​

​

</TD></TR><TR><TD width="50%" height=16>

7.03​

​

​

</TD><TD width="50%" height=16>

0.011​

​

​

</TD></TR><TR><TD width="50%" height=16>

7.01​

​

​

</TD><TD width="50%" height=16>

0.011​

​

​

</TD></TR><TR><TD width="50%" height=16>

7.03​

​

​

</TD><TD width="50%" height=16>

0.012​

​

​

</TD></TR><TR><TD width="50%" height=16>

6.99​

​

​

</TD><TD width="50%" height=16>

0.012​

​

​

</TD></TR><TR><TD width="50%" height=16>

7.02​

​

​

</TD><TD width="50%" height=16>

0.012​

​

​

</TD></TR><TR><TD width="50%" height=16>

6.99​

​

​

</TD><TD width="50%" height=16>

0.014​

​

​

</TD></TR><TR><TD width="50%" height=16>

7.00​

​

​

</TD><TD width="50%" height=16>

0.013​

​

​

</TD></TR><TR><TD width="50%" height=16>

7.00​

​

​

</TD><TD width="50%" height=16>

0.013​

​

​

</TD></TR><TR><TD width="50%" height=16>

7.00​

​

​

</TD><TD width="50%" height=16>

0.013​

​

​

</TD></TR><TR><TD width="50%" height=16>

6.99​

​

​

</TD><TD width="50%" height=16>

0.013​

​

​

</TD></TR><TR><TD width="50%" height=16>

6.98​

​

​

</TD><TD width="50%" height=16>

0.014​

​

​

</TD></TR><TR><TD width="50%" height=16>

7.04​

​

​

</TD><TD width="50%" height=16>

0.016​

​

​

</TD></TR><TR><TD width="50%" height=16>

7.01​

​

​

</TD><TD width="50%" height=16>

0.016​

​

​

</TD></TR><TR><TD width="50%" height=16>

7.03​

​

​

</TD><TD width="50%" height=16>

0.016​

​

​

</TD></TR><TR><TD width="50%" height=16>

7.01​

​

​

</TD><TD width="50%" height=16>

0.016​

​

​

</TD></TR><TR><TD width="50%" height=16>

6.99​

​

​

</TD><TD width="50%" height=16>

0.016​

​

​

</TD></TR><TR><TD width="50%" height=16>

6.97​

​

​

</TD><TD width="50%" height=16>

0.017​

​

​

</TD></TR><TR><TD width="50%" height=16>

6.98​

​

​

</TD><TD width="50%" height=16>

0.017​

​

​

</TD></TR><TR><TD width="50%" height=16>

7.00​

​

​

</TD><TD width="50%" height=16>

0.017​

​

​

</TD></TR></TBODY></TABLE>

Can anyone please explain how the spread of results (reliability) has decreased by taking more samples ??

 

[NightShadow]

that certainly is interesting that the SD deviates away from zero as the sample size increases with the results fluctuating random around the general mean...

well try this time accounting for random outlyers as well... which i suppose is what repetition is designed to eliminate...

i remember with sciences, you plot these data... and then you draw a line of best fit... i suppose SD wasn't the best way to do it...

I'm guessing that with the line of best fit, if we have outlyers... we ignore them, and draw a line that passes through as many points as possible, which would only be possible if we had more data points to be sure of the position of that 'line of best fit' -- thats getting back down to the BOS standard of education...

 

[NightShadow]

and with your SD table... lets take the case of your second data result, the 6.99 + 7.02

...

actually when i calculated it.. i get a standard deviation of .0212... how did you get your values? and at the end my SD is 0.018

 

[pkc]

I'm guessing that with the line of best fit, if we have outlyers... we ignore them, and draw a line that passes through as many points as possible, which would only be possible if we had more data points to be sure of the position of that 'line of best fit' -- thats getting back down to the BOS standard of education...

Sure, but that's not reducing the spread of data (which the BOS definition calls for).

 

[NightShadow]

you're reducing the spread of data by visually eliminating the outlyers and by drawing the line of best fit... it eliminates all variance, since now that you have the line of best fit... its king

and i think theres something wrong with you SD values? read my last post

 

[pkc]

Here's 100 results:
(Sampling from normal distribution, mean =7.00, sd=0.02)
sorry its so big
pH SD
<TABLE borderColor=#000000 cellSpacing=0 cellPadding=2 width=134 border=1><TBODY><TR><TD width="50%" height=16>

7.04​

</TD><TD width="50%" height=16>
</TD></TR><TR><TD width="50%" height=16>

7.01​

</TD><TD width="50%" height=16>

0.021​

</TD></TR><TR><TD width="50%" height=16>

7.01​

</TD><TD width="50%" height=16>

0.018​

</TD></TR><TR><TD width="50%" height=16>

6.99​

</TD><TD width="50%" height=16>

0.021​

</TD></TR><TR><TD width="50%" height=16>

6.99​

</TD><TD width="50%" height=16>

0.021​

</TD></TR><TR><TD width="50%" height=16>

7.01​

</TD><TD width="50%" height=16>

0.019​

</TD></TR><TR><TD width="50%" height=16>

7.04​

</TD><TD width="50%" height=16>

0.022​

</TD></TR><TR><TD width="50%" height=16>

6.98​

</TD><TD width="50%" height=16>

0.022​

</TD></TR><TR><TD width="50%" height=16>

7.01​

</TD><TD width="50%" height=16>

0.021​

</TD></TR><TR><TD width="50%" height=16>

6.98​

</TD><TD width="50%" height=16>

0.021​

</TD></TR><TR><TD width="50%" height=16>

6.99​

</TD><TD width="50%" height=16>

0.020​

</TD></TR><TR><TD width="50%" height=16>

7.01​

</TD><TD width="50%" height=16>

0.020​

</TD></TR><TR><TD width="50%" height=16>

7.01​

</TD><TD width="50%" height=16>

0.019​

</TD></TR><TR><TD width="50%" height=16>

6.99​

</TD><TD width="50%" height=16>

0.018​

</TD></TR><TR><TD width="50%" height=16>

6.98​

</TD><TD width="50%" height=16>

0.019​

</TD></TR><TR><TD width="50%" height=16>

7.04​

</TD><TD width="50%" height=16>

0.020​

</TD></TR><TR><TD width="50%" height=16>

6.99​

</TD><TD width="50%" height=16>

0.020​

</TD></TR><TR><TD width="50%" height=16>

6.99​

</TD><TD width="50%" height=16>

0.020​

</TD></TR><TR><TD width="50%" height=16>

7.04​

</TD><TD width="50%" height=16>

0.021​

</TD></TR><TR><TD width="50%" height=16>

7.00​

</TD><TD width="50%" height=16>

0.020​

</TD></TR><TR><TD width="50%" height=16>

6.96​

</TD><TD width="50%" height=16>

0.021​

</TD></TR><TR><TD width="50%" height=16>

6.98​

</TD><TD width="50%" height=16>

0.022​

</TD></TR><TR><TD width="50%" height=16>

7.01​

</TD><TD width="50%" height=16>

0.021​

</TD></TR><TR><TD width="50%" height=16>

6.98​

</TD><TD width="50%" height=16>

0.021​

</TD></TR><TR><TD width="50%" height=16>

7.03​

</TD><TD width="50%" height=16>

0.022​

</TD></TR><TR><TD width="50%" height=16>

7.00​

</TD><TD width="50%" height=16>

0.021​

</TD></TR><TR><TD width="50%" height=16>

6.99​

</TD><TD width="50%" height=16>

0.021​

</TD></TR><TR><TD width="50%" height=16>

6.99​

</TD><TD width="50%" height=16>

0.021​

</TD></TR><TR><TD width="50%" height=16>

7.01​

</TD><TD width="50%" height=16>

0.020​

</TD></TR><TR><TD width="50%" height=16>

7.00​

</TD><TD width="50%" height=16>

0.020​

</TD></TR><TR><TD width="50%" height=16>

6.98​

</TD><TD width="50%" height=16>

0.020​

</TD></TR><TR><TD width="50%" height=16>

6.98​

</TD><TD width="50%" height=16>

0.020​

</TD></TR><TR><TD width="50%" height=16>

7.02​

</TD><TD width="50%" height=16>

0.020​

</TD></TR><TR><TD width="50%" height=16>

7.03​

</TD><TD width="50%" height=16>

0.020​

</TD></TR><TR><TD width="50%" height=16>

7.00​

</TD><TD width="50%" height=16>

0.020​

</TD></TR><TR><TD width="50%" height=16>

7.03​

</TD><TD width="50%" height=16>

0.020​

</TD></TR><TR><TD width="50%" height=16>

7.01​

</TD><TD width="50%" height=16>

0.020​

</TD></TR><TR><TD width="50%" height=16>

6.97​

</TD><TD width="50%" height=16>

0.021​

</TD></TR><TR><TD width="50%" height=16>

7.00​

</TD><TD width="50%" height=16>

0.020​

</TD></TR><TR><TD width="50%" height=16>

6.96​

</TD><TD width="50%" height=16>

0.021​

</TD></TR><TR><TD width="50%" height=16>

7.00​

</TD><TD width="50%" height=16>

0.021​

</TD></TR><TR><TD width="50%" height=16>

6.95​

</TD><TD width="50%" height=16>

0.022​

</TD></TR><TR><TD width="50%" height=16>

6.99​

</TD><TD width="50%" height=16>

0.022​

</TD></TR><TR><TD width="50%" height=16>

7.04​

</TD><TD width="50%" height=16>

0.022​

</TD></TR><TR><TD width="50%" height=16>

6.97​

</TD><TD width="50%" height=16>

0.022​

</TD></TR><TR><TD width="50%" height=16>

7.00​

</TD><TD width="50%" height=16>

0.022​

</TD></TR><TR><TD width="50%" height=16>

7.00​

</TD><TD width="50%" height=16>

0.022​

</TD></TR><TR><TD width="50%" height=16>

7.03​

</TD><TD width="50%" height=16>

0.022​

</TD></TR><TR><TD width="50%" height=16>

7.01​

</TD><TD width="50%" height=16>

0.022​

</TD></TR><TR><TD width="50%" height=16>

6.96​

</TD><TD width="50%" height=16>

0.022​

</TD></TR><TR><TD width="50%" height=16>

7.00​

</TD><TD width="50%" height=16>

0.022​

</TD></TR><TR><TD width="50%" height=16>

7.01​

</TD><TD width="50%" height=16>

0.022​

</TD></TR><TR><TD width="50%" height=16>

6.98​

</TD><TD width="50%" height=16>

0.022​

</TD></TR><TR><TD width="50%" height=16>

6.98​

</TD><TD width="50%" height=16>

0.022​

</TD></TR><TR><TD width="50%" height=16>

7.03​

</TD><TD width="50%" height=16>

0.022​

</TD></TR><TR><TD width="50%" height=16>

7.01​

</TD><TD width="50%" height=16>

0.022​

</TD></TR><TR><TD width="50%" height=16>

7.00​

</TD><TD width="50%" height=16>

0.022​

</TD></TR><TR><TD width="50%" height=16>

7.03​

</TD><TD width="50%" height=16>

0.022​

</TD></TR><TR><TD width="50%" height=16>

6.98​

</TD><TD width="50%" height=16>

0.022​

</TD></TR><TR><TD width="50%" height=16>

7.01​

</TD><TD width="50%" height=16>

0.022​

</TD></TR><TR><TD width="50%" height=16>

6.98​

</TD><TD width="50%" height=16>

0.022​

</TD></TR><TR><TD width="50%" height=16>

7.00​

</TD><TD width="50%" height=16>

0.021​

</TD></TR><TR><TD width="50%" height=16>

6.99​

</TD><TD width="50%" height=16>

0.021​

</TD></TR><TR><TD width="50%" height=16>

6.97​

</TD><TD width="50%" height=16>

0.021​

</TD></TR><TR><TD width="50%" height=16>

7.00​

</TD><TD width="50%" height=16>

0.021​

</TD></TR><TR><TD width="50%" height=16>

7.01​

</TD><TD width="50%" height=16>

0.021​

</TD></TR><TR><TD width="50%" height=16>

7.01​

</TD><TD width="50%" height=16>

0.021​

</TD></TR><TR><TD width="50%" height=16>

7.04​

</TD><TD width="50%" height=16>

0.021​

</TD></TR><TR><TD width="50%" height=16>

7.01​

</TD><TD width="50%" height=16>

0.021​

</TD></TR><TR><TD width="50%" height=16>

7.02​

</TD><TD width="50%" height=16>

0.021​

</TD></TR><TR><TD width="50%" height=16>

6.99​

</TD><TD width="50%" height=16>

0.021​

</TD></TR><TR><TD width="50%" height=16>

6.99​

</TD><TD width="50%" height=16>

0.021​

</TD></TR><TR><TD width="50%" height=16>

6.98​

</TD><TD width="50%" height=16>

0.021​

</TD></TR><TR><TD width="50%" height=16>

6.97​

</TD><TD width="50%" height=16>

0.021​

</TD></TR><TR><TD width="50%" height=16>

7.02​

</TD><TD width="50%" height=16>

0.021​

</TD></TR><TR><TD width="50%" height=16>

7.01​

</TD><TD width="50%" height=16>

0.021​

</TD></TR><TR><TD width="50%" height=16>

7.00​

</TD><TD width="50%" height=16>

0.021​

</TD></TR><TR><TD width="50%" height=16>

6.99​

</TD><TD width="50%" height=16>

0.021​

</TD></TR><TR><TD width="50%" height=16>

6.98​

</TD><TD width="50%" height=16>

0.021​

</TD></TR><TR><TD width="50%" height=16>

7.06​

</TD><TD width="50%" height=16>

0.022​

</TD></TR><TR><TD width="50%" height=16>

7.03​

</TD><TD width="50%" height=16>

0.022​

</TD></TR><TR><TD width="50%" height=16>

6.99​

</TD><TD width="50%" height=16>

0.022​

</TD></TR><TR><TD width="50%" height=16>

7.02​

</TD><TD width="50%" height=16>

0.022​

</TD></TR><TR><TD width="50%" height=16>

6.99​

</TD><TD width="50%" height=16>

0.022​

</TD></TR><TR><TD width="50%" height=16>

7.01​

</TD><TD width="50%" height=16>

0.022​

</TD></TR><TR><TD width="50%" height=16>

7.01​

</TD><TD width="50%" height=16>

0.021​

</TD></TR><TR><TD width="50%" height=16>

7.02​

</TD><TD width="50%" height=16>

0.021​

</TD></TR><TR><TD width="50%" height=16>

6.98​

</TD><TD width="50%" height=16>

0.021​

</TD></TR><TR><TD width="50%" height=16>

7.02​

</TD><TD width="50%" height=16>

0.021​

</TD></TR><TR><TD width="50%" height=16>

7.03​

</TD><TD width="50%" height=16>

0.021​

</TD></TR><TR><TD width="50%" height=16>

7.03​

</TD><TD width="50%" height=16>

0.021​

</TD></TR><TR><TD width="50%" height=16>

6.98​

</TD><TD width="50%" height=16>

0.021​

</TD></TR><TR><TD width="50%" height=16>

6.96​

</TD><TD width="50%" height=16>

0.022​

</TD></TR><TR><TD width="50%" height=16>

7.00​

</TD><TD width="50%" height=16>

0.022​

</TD></TR><TR><TD width="50%" height=16>

6.98​

</TD><TD width="50%" height=16>

0.022​

</TD></TR><TR><TD width="50%" height=16>

6.99​

</TD><TD width="50%" height=16>

0.022​

</TD></TR><TR><TD width="50%" height=16>

7.01​

</TD><TD width="50%" height=16>

0.021​

</TD></TR><TR><TD width="50%" height=16>

7.00​

</TD><TD width="50%" height=16>

0.021​

</TD></TR><TR><TD width="50%" height=16>

6.98​

</TD><TD width="50%" height=16>

0.021​

</TD></TR><TR><TD width="50%" height=16>

7.00​

</TD><TD width="50%" height=16>

0.021​

</TD></TR></TBODY></TABLE>

 

[NightShadow]

sorry..theres some discrepancy with mine and your Sd values... try using your calculator? thats what i did, and ieven used the formula, i dont get quite those values... but if we use the values you had before... instead of these new ones? cause this is just too big for my calc.. and my botheredness

and you do have alot of time on your hands dont you? unless you're a uni stats student...

 

[pkc]

you're reducing the spread of data by visually eliminating the outlyers and by drawing the line of best fit... it eliminates all variance, since now that you have the line of best fit... its king

Sure, but the BOS definition of reliability is about the spread of the results produced by the experiment - not the results after removing the ones that suit.

By the way there are no outliers which can be legitimately removed from this data, they are all within reasonable limits of possibility. They are all taken from an ideal bell-curve.

 

[pkc]

sorry..theres some discrepancy with mine and your Sd values... try using your calculator? thats what i did, and ieven used the formula, i dont get quite those values... but if we use the values you had before... instead of these new ones? cause this is just too big for my calc.. and my botheredness

and you do have alot of time on your hands dont you? unless you're a uni stats student...

The average of the sd values gets closer to 0.02 as you take more samples. Thats the converging of the estimator (sample sd) on the true population sd as sample number increases.

 

[helper]

The average of the sd values gets closer to 0.02 as you take more samples. Thats the converging of the estimator (sample sd) on the true population sd as sample number increases.

So your now saying the data is converging to a normal distribution but that isn't more reliable?

Or are you saying BOS definition doesn't mean this?

 

[pkc]

So your now saying the data is converging to a normal distribution but that isn't more reliable?

Or are you saying BOS definition doesn't mean this?

Correct, the BOS definition does not mention reliability as anything to do with how closely the data resembles a bell-curve.