L4 Dealing with uncertanity Flashcards
what was it believed about probability until the 17th century?
to be Fortuna / fate
until the 17th century, it probability was seen as something which could not be…
analysed systematically nor scientifically
however in the 21st century what do we now know we can do when it comes to probability?
make surprisingly precise predictions about how ‘chance’ will turn out
what does the ability to make precise predictions lead betting companies to do?
hire statisticians
imprecisions are often referred to as =
uncertainty
thing can go wrong in the …….. sometimes
…media…
what does things going wrong in the media lead to with numbers?
uncertainty
why can we predict coin tosses?
the law of large numbers
individual events when it comes to probability such as a coin toss =
unpredictable
however if we repeat a coin toss several times…what will we get?
we will get the average
(i.e. 50% heads / 50% tails)
eventually, a large number of events becomes…
predictable
when does a large number of events become predictable?
around the 100 times range
for a random coin toss n =
6
for a random coin toss p =
0.5
the more coin tosses done means that the distribution is what?
smoother
when the distribution is smoother for coin tosses it means that there is what?
a more equal split of heads and tails
how can we visualise this coin toss?
a histogram
CLT =
Central Limit Theorem
what is the law of large numbers basically?
if we repeat an experiment many times, we can work out the average from the repetitions
what does the Central Limit Theorem (CLT) say?
that the sampling distribution of the mean will always follow a normal distribution - if the sample size is big enough
what do histograms look similar to?
bar charts
what does a histogram do?
summaries the distribution of data over a time period
how does a histogram capture the information?
it uses bins to capture the numbers of things that fall within each range of values
bar chart is interested in -
the height of the bars
histogram is interested in -
the area of bins
binomial distributions =
the discrete probability distribution
what does enough tosses =
normal distribution
what does a normal distribution spread allow for?
features to be predicted
………….. is at the core of statistics
probability
what does probability also concern (+ an example)
our future (i.e. if its going to rain)
measuring something is like doing what?
taking an educated guess
- it would be exactly right but will be an informed decision
MoSE =
margin of sampling error
logic =
single measurement from a sample reflects one set of possible outcomes
a different sample would have what?
different results
what will repetition when it comes to different samples do?
show us where the true value is
statistics set out to measure the …….. - but there are …………..
world
imperfections
random error =
the difference between the true value and the observed value
do all samples come with random errors?
yes
random errors is a ………… ……. of sampling process
normal part
the coin tossing example can be what?
modelled
MoE =
margin of error
what is typically polls sample size?
N=1000
we account for random error by…
reporting results with a ‘margin of error’
enough measurements or sample draws will -
resemble a normal distribution
however, there are many sources of error that are not random such as -
- sampling error
- coverage error
- non response bias
diminishing returns =
the trade off between cost and uncertainty or the size of the MoE
at large numbers, random variables follow what?
very predictable patterns
the reason for measuring things if everything is uncertain
imagine next time going to get a blood test doctor takes all of it out…
what is this blood test / soup analogy an example of?
sample representativness
subsampling =
dividing the data into smaller groups
when it comes to subsampling, we must be…
extra careful
what does subsampling drastically change?
the MoSE
- margins of error = larger
what can patterns be used to make?
predictions + calculations
