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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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