Flashcards
binomial or poisson (when given experimental dist)
Cards in this deck (14)
- 1The question will often start by representing collected data as a table of frequencies.we need to compare two frequency tables
(1) the first table will have frequencies using collected data (since the frequencies come from an 'experiment', we call this an experimental distribution). This table will be part of the question
(2) The second table you will have to create. The frequencies in this table are made from your calculator (this is a theoretical dist)
and yes, a table of frequencies (or probabilities) is a type of distribution - 2heres an example. In the experimental distribution (the first one) the frequencies or probabilities are arrived at using COLLECTED DATA (which can be thought of as an 'experiment') the theoretical results (the second one) is where the frequencies or probabilities are created using a computer or CALCULATOR. no data collection whatsoever. all theoreticalTo make theoretical dist:
use Ppd/Bpd to find probabilities for each X.
then multiply each answer by the total freq in the experimental table. This will find the theoretical frequencies (called expected numbers)
- 3comment on fit (we would expect some difference, but not vast difference)for eg on the left: seem to be close enough except the theoretical is a bit low for X=0 (0 seeds germinating)
- 4if given a graph, add red lines to show theoretical frequencies/probabilities (theoretical because you never collected data, so no EXPERIMENT, you just used your calculator)
- 5given a graph what can I comment oncomment on FIT (we would expect some difference, but not a vast difference. when is the red line too high, too low and just right).
Eg. the theoretical values are too low for X=0,4,5. they are too high for X=1,2. they are a good fit for X=3
- 6given a graph what nextcomment on SHAPE
both experimental and theoretical dist are skewed to the left, but the experimental is more strongly skewed. They are both unimodal - 7given a graph what nextcompare MODE:
the experimental dist has a mode at X=3 and so does the theoretical, so a good fit based on this
- 8given a graph what else?ENDPOINTS (this is not visual, just think about it logically):
for binomial distribution, the experimental data should all fit between 0 and n, everything else should be impossible.
for poisson distribution, it should be impossible to collect data for X (whatever we are studying) less than 0, and as you get to the other end (getting more and more positive) it should be possible but exceedingly unlikely - 9—even if I took another sample of 50 years, the data has to be between 0 and 12. it is impossible for less than 0 months in a year, or more than 13 months in a year to have 600 mm rain.
this is another argument for good fit for binomial distribution
- 10—even if I took another sample, the data cannot be less than 0, its impossible for there to be a negative number of flaws in a piece of cloth. Also, if I took another sample, it is possible that I would find more than 6 flaws in a metre squared of cloth, BUT it would be super unlikely (the frequency would be really low)
so, from this point of view, Poisson is a good fit
- 11finallydiscrete data ONLY
impossible for these distributions to work for continuous data - 12table only recapmake two tables of frequencies.
(1) the first table will have frequencies using data that is given (experimental dist)
(2) another table with frequencies made from your calculator (theoretical dist)
(3) discuss fit (when is the difference acceptable, when is it vast)
and yes, a table of frequencies/probabilities is a type of distribution - 13graph recap(1) draw lines next to each bar to signify the frequency/probability found from your calculator
(2) discuss fit (when is the difference acceptable, when is it vast)
(3) discuss shape (skewed to left/skewed to right/symetrical/unimodal/bimodal)
(4)discuss mode
(5) endpoints
(6) is data discrete - 14overall recap. tables graphs everythingThe Fit Lad Feared Sea Monsters Eating Drugs
T F L F S M E D
Table, Fit, Lines, Fit, Shape, Modes, Endpoints, Discrete vs continuous
make a table, comment on fit, add red lines, comment on fit, compare shapes, compare modes, think logically about endpoints, is data discrete?
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- Flashcards on binomial or poisson (when given experimental dist), created by Anzar Chida on 10/10/2019.
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- Anzar Chida
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