Understanding the p-value – Statistics Help

Understanding the p-value – Statistics Help


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
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.

100 comments

  1. Please see the 2016 American Statistical Association statement on "Statistical Significance and P-Values." The world's foremost experts address the problem of common misinterpretations of the P-value. The P-value does not tell you whether the data are due to random chance or whether the null hypothesis is true or false. It is a measure of the goodness of fit between the observed data and the statistical model.

  2. I loved this lesson. Not only was it super educational and valuable in that aspect, but it was clever and it made me laugh really hard. You had my attention the entire time. Thanks XD

  3. This is really good, and funny, which helps. I'm new to statistics – how come they just don't call it the "hypothesis"? What's with "Null" adjective?

  4. YOu screwed up this explanation by confusing the issue with Null Hypothesis and which side of the argument you are on, without explaining it.

  5. This wasn’t a clear explanation. What about t-score? You’re confusing p-value with t-score.
    The p-value is used to calculate the t- score number on the table. A two tail hypothesis requires t-alpha/2.
    What about the degrees of freedom?
    You have totally confused the issue of hypothesis testing.
    Good night!!!

  6. You gave an a statistical example as definition. What is the definition of p- value?
    P-value is the level of significance.
    This is the definition of p-value:
    The p-value is the level of marginal significance within a statistical hypothesis test representing the probability of the occurrence of a given event. The p-value is used as an alternative to rejection points to provide the smallest level of significance at which the null hypothesis would be rejected.

  7. level of significance…
    The null hypothesis is rejected if the p-value is less than a predetermined level, α. α is called the significance level, and is the probability of rejecting the null hypothesis given that it is true (a type I error). It is usually set at or below 5%.

  8. Great explanation. Just for clarification, the p-value came from using the statistical rules of a one-sample t-test? I've been a little mystified as to where the actual p-value comes from. I understand a low p-value means reject null. I've used the software to get a p-value. We must set up our problem appropriately and select the right statistical test which then yields a p-value?

  9. The perfect video! I don't understand why college makes it sound like a concept of god; it's simple: if p is low, the null must go!
    Thank you!

  10. Null hypothesis means that you are testing your variables at 0.05 (%95 level) significance level your variables if they are correct to estimate your model or sample then youe variables is not equal to zero,they are affecting your sample which null hypothesis was Ho:B1=B2=0 this implies if you have right variables to solve your model then you reject null hypothesis because b1 and b2 has an effect on your model.p value determines your null hypothesis is really true or wrong.So if mean average of your variables more than 0.05 in p value than you have to accept that your variables are wrong and has no effect or your null is true.

  11. I little bit confused when it said we want to proof the alternative hypotheses however all of the video is saying that we will be happy if the null hypothesis is true

  12. The p-value is used to determine if the outcome of an experiment is statistically significant. A low p-value means that, assuming the null hypothesis is true, there is a very low likelihood that this outcome was a result of luck. A high p-value means that, assuming the null hypothesis is true, this outcome was very likely.

  13. I just dont understand why Helen is allowed to define the significant level (=0.05) and the amount of chocolates she wants to test (=20) by herself to proof her chocolates are alright. She could have decided to take a random sample of 5 chocolates and win the case anyway. It would make so much more sense when the judge decided the parameters.

    Either I dont understand it, or your example has some flaws.

  14. I disagree. This is why studies are often wrong. Raise the arbitrary significance level to 18% and you get a different conclusion. The truth is too many bars have too little peanuts and even the average is too low. Most should have more than 70 grams or they should put a different number on the package. No amount of statistical juggling with numbers is going to change the truth that there are too few peanuts.

  15. Wonderful explained!! Those wonderful people who take from their time in order to help others..
    God bless you!

  16. Wow. TY. I only need to know this 1/8th of test and I WILL NEVER need again. TY for explaining simply. It made the more complex explanation understandable,

  17. If I read an article that gives a statistic then in parenthesis gives a p value of <0.05 does that mean the information before the p value is wrong or that the information is correct ?

    example: The CHHIPS (Controlling HTN and Hypotension Immediately Post-Stroke) trial compared the effects of lisinopril, labetalol, and placebo on the 2-week death or dependency rate when administered between 5 and 36 hours from the onset of ischemic or hemorrhagic stroke. The decrease in SBP was significantly greater in the combined active treatment group than in the placebo group during the first 24 hours [difference: mean=10 mm Hg, 95% confidence interval (CI)=3-17 mm Hg; p=0.004]. However, there was no difference in the primary end point of the 2-week death or dependency rate within treatment groups or between the treatment and placebo groups.12

    In the example above does that mean that there is a 95% confidence that the information about the difference in mean blood pressures in the two groups is likely wrong and that there is a difference in blood pressures that is different than 10mmHg either higher or lower?

  18. The video is wrong… for Helen's choconutties case, the null hypothesis should be that "they are short of peanuts" (the video says it is they are as they should be) !!!!

  19. Fair of you to throw in the disclaimer but that was really well explained. "If you can't explain it simply, you don't understand it well enough" – Einstein.

  20. isn't it – the 0.18 is the probability of the mean being close to 70. so being higher than the 5%, the Hypothesis of 70 is not being rejected?

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