understanding the p-value one of the
most important concepts and statistics
is the meaning of the p-value whenever
we use Excel or other computer packages
to analyze data one of the key outputs
is the p value or sig in formal terms
the p value is the probability that if
the null hypothesis were true sampling
variation would produce an estimate that
is further away from the hypothesized
value than our data estimate in less
formal terms the p-value tells us how
likely it is to get a result like this
if the null hypothesis is true we will
now go through the step by step with an
example
Hellen cells choconutties recently she
has received complaints that the
choconutties had fewer peanuts in them
than they are supposed to the packet
says that each 200 gram packet of
choconutties contains 70 grams of
peanuts or more Helen can't open up all
the packets to check as then she
wouldn't be able to sell any so she
decides to use a statistical test on a
sample of the Packers the null
hypothesis often called H naught is the
thing we are trying to provide evidence
against for Helen the null hypothesis is
that the choconutties are as they should
be the mean or average weight of peanuts
and the packet of 70 grams the
alternative hypothesis called H 1 or H a
is what we're trying to prove the
customers have complained that the
weight of peanuts is less than what it
should be so the alternative hypothesis
is that the average weight of peanuts is
less than 70 grams
Helen decides to use a significance
level of point zero five if the p-value
is lower than this she will reject the
null hypothesis having decided on her
hypotheses and on a significance level
Helen takes a random sample of 20
packets of choconutties from her current
stock of 400 packets
she melts down the choconutties and
weighs the peanuts from each packet if
all of the values were lower than 70
grams was a mean of 30 grams for
instance it would be quite obvious that
the bars did not have the required
number of peanuts it is really unlikely
that you will get 20 packets or the mean
of 30 grams if the overall mean of all
our packets and the population
70 grams conversely of all the values of
the 20 packets are much higher than 70
grams it would be obvious that there
were enough peanuts and that there was
nothing to complain about
however in this case the 20 packets
contained the following weights of
peanuts in the mean is sixty eight point
seven grams
this caused Helen to ask herself does
this provide enough evidence that the
bars are short of peanuts or could this
result just be from lack she asks your
brother to use excel to find the p-value
for this data comparing with a mean of
70 grams the p-value is 0.18 judging
from the data that we have there is an
18% chance of getting a mean as low as
this or lower if there is nothing wrong
with the bars that is if the null
hypothesis is true in the mean weight of
naps is 70 grams or more this p-value of
0.18 does not provide enough evidence to
reject the null hypothesis in this case
Helen does not have evidence to say that
the bars are short of peanuts
this is a relief the smaller the p-value
is the less likely it is that the result
we got was simply a result of lack if
the p-value had turned out to be very
small we then would say that the result
was significantly different from 70
grams in general we start by saying that
the null hypothesis is true we take a
sample and get a statistic we work out
how likely it is to get a statistic like
this if the null hypothesis is true this
is the p-value if the p-value is really
really small then our original idea must
have been wrong so we reject the null
hypothesis P is low now must go a small
p-value indicates a significant result
the smaller the p-value is the more
evidence we have that the null
hypothesis is probably wrong if the
p-value is large then our original idea
is probably correct we do not reject the
null hypothesis this is called a non
significant result the p-value tells us
whether we have evidence from the sample
that there is an effect in the
population a p-value less than point
zero five means that we have evidence of
an effect a p-value of more than point
zero five means that there is no
evidence of nfe
sometimes the significance level
different from point zero five is used
but point zero five is the most common
one disclaimer this video uses plain
language to get difficult ideas across
some terminology might be viewed as
incorrect by a rigorous statistician