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,

In less formal terms,

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 H0

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 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, 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.