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• 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,

• 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.

One of the most important concepts in statistics

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B1 null hypothesis hypothesis helen evidence packet reject

# Understanding the p-value - Statistics Help

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羅紹桀 posted on 2016/11/19
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