One of the most important concepts in statistics is the meaning of the P-value. Whenever we use Excel or other computer packages to analyse 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 hypothesised 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 this step-by-step with an example. Helen sells Choconutties. Recently she has received complaints that the choconutties have fewer peanuts in them. than they are supposed to. The packet says that each 200g
packet of choconutties contains 70g 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 packets. The null hypothesis, often called H "nought" is the thing
we're 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 in the packet is 70 grams. The alternative hypothesis called H1 or HA is what we're trying to prove. The customers had complained that the weight of peanuts is less than what it should be. So the alternative hypothesis is that
the average rate of peanuts is less than 70 grams. Helen decides to use a significance
level of 0.05 if the P-value is lower than this, she will reject the null hypothesis Having decided on her hypotheses and on the significance level Helen takes
a random sample of 20 packets of Choco-nutties from her current
stock of 400 packets.
She melts down the Choco-nutties and weighs the peanuts from each packet. If all of the values were lower than 70
grams with a mean of 30 grams for instance,
it will be quite obvious that the bars did not have the required number of
peanuts. It is very unlikely that you'll get 20
packets with a mean of 30 grams if the overall mean of all the packets in the
population is 70 grams Conversely, if all the values of the 20
packets were 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
contain the following weights of peanuts and the mean is 68.7 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 luck?" She
asks her brother to use Excel to find the p-value for this data, comparing with the mean of 70 grams. The P value is 0.18 Judging from the data that we have,
there is an 18 percent 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 and the mean weight of nuts 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 luck. 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
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, Null 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 nonsignificant 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 0.05 means that
we have evidence of an effect. A P-value of more than 0.05 means that there is no evidence of an
effect. Sometimes a significance level different from 0.05 is used, but 0.05 is the most common one. This video uses plain language to get
difficult ideas across. Some terminology might be viewed as
incorrect by a rigorous statistician..