 # Pvalue

An analyst suspects that the average PE ratio for an index is at the most 15. She finds that the average PE and standard deviation of a sample of 40 is 16.5 and 7 respectively. At an alpha of 0.02 what is the p value of this test?

.98

getterdone Wrote: ------------------------------------------------------- > .98 nope

getterdone Wrote: ------------------------------------------------------- > .98 formula ?

the p value is the one thing on stats I can NEVER remember for som stupid reason! daj I used 1- alpha

I am confused as well… so waiting for other people. However the result is 0.0869.

you usually find it by trial and eror, or use some excel sheet, etc. Unless there is a trick to this, don’t expect a question like that.

for your convenience. standard error = 7/ sqrt(40) = 1.1068 strangedays Wrote: ------------------------------------------------------- > An analyst suspects that the average PE ratio for > an index is at the most 15. She finds that the > average PE and standard deviation of a sample of > 40 is 16.5 and 7 respectively. At an alpha of 0.02 > what is the p value of this test?

ahhh then you minus 1 and minus alpha I take it? that gives you the correct value. please verify

THis the result I have: The p value of a test is the lowest level of significance for which the null hypothesis may be rejected. The z statistic is calculated as 1.36 The probability remaining in a one-tailed test 1.36 standard errors below the mean is 0.0869. However to me its still not clear

P-value was not give a lot of explanations in the curriculum, whoever can explain it, please help. strangedays Wrote: ------------------------------------------------------- > THis the result I have: > > The p value of a test is the lowest level of > significance for which the null hypothesis may be > rejected. The z statistic is calculated as 1.36 > The probability remaining in a one-tailed test > 1.36 standard errors below the mean is 0.0869. > > However to me its still not clear

getterdone Wrote: ------------------------------------------------------- > ahhh then you minus 1 and minus alpha I take it? > that gives you the correct value. > > > please verify OK, I SAW IT IN BOOK, PP 465-66, BUT IT DOES NOT GIVE A FORMULA, AND THIS CRAP IS NOT IN SECRET SAUCE EITHER

lets hope it aint on the exam boys and girls!

LOUD NOISES!!! getterdone Wrote: ------------------------------------------------------- > ahhh then you minus 1 and minus alpha I take it? > that gives you the correct value. > > > please verify OK, I SAW IT IN BOOK, PP 465-66, BUT IT DOES NOT GIVE A FORMULA, AND THIS CRAP IS NOT IN SECRET SAUCE EITHER

I dont how to start to solve this exercise… if I get this one on the exam day if is one point less for me! WTF!!!

SO ARE WE SAYING P VALUE = STANDARD ERROR - 1 - ALPHA???

I LOVE LAMP!

From WIKIPEDIA: In statistical hypothesis testing, the p-value is the probability of obtaining a value of the test statistic at least as extreme as the one that was actually observed, given that the null hypothesis is true. The fact that p-values are based on this assumption is crucial to their correct interpretation. More technically, a p-value of an experiment is a random variable defined over the sample space of the experiment such that its distribution under the null hypothesis is uniform on the interval [0,1]. Many p-values can be defined for the same experiment.  Coin flipping example For example, say an experiment is performed to determine if a coin flip is fair (50% chance of landing heads or tails), or unfairly biased, either toward heads (> 50% chance of landing heads) or toward tails (< 50% chance of landing heads). Since we consider both biased alternatives, a two-tailed test is performed. The null hypothesis is that the coin is fair, and that any deviations from the 50% rate can be ascribed to chance alone. Suppose that the experimental results show the coin turning up heads 14 times out of 20 total flips. The p-value of this result would be the chance of a fair coin landing on heads at least 14 times out of 20 flips plus the chance of a fair coin landing on heads 6 or fewer times out of 20 flips. In this case the random variable T has a binomial distribution. The probability that 20 flips of a fair coin would result in 14 or more heads is 0.0577. By symmetry, the probability that 20 flips of the coin would result in 14 or more heads or 6 or fewer heads is 0.0577 ¡Á 2 = 0.115. Interpretation Generally, one rejects the null hypothesis if the p-value is smaller than or equal to the significance level, often represented by the Greek letter ¦Á (alpha). If the level is 0.05, then the results are only 5% likely to be as extraordinary as just seen, given that the null hypothesis is true. In the above example we have: null hypothesis (H0) ¡ª fair coin; observation (O) ¡ª 14 heads out of 20 flips; and probability (p-value) of observation (O) given H0 ¡ª p(O|H0) = 0.0577x2 (two-tailed) = 0.1154 = 11.54%. The calculated p-value exceeds 0.05, so the observation is consistent with the null hypothesis ¡ª that the observed result of 14 heads out of 20 flips can be ascribed to chance alone ¡ª as it falls within the range of what would happen 95% of the time were this in fact the case. In our example, we fail to reject the null hypothesis at the 5% level. Although the coin did not fall evenly, the deviation from expected outcome is just small enough to be reported as being “not statistically significant at the 5% level”. However, had a single extra head been obtained, the resulting p-value (two-tailed) would be 0.0414 (4.14%). This time the null hypothesis - that the observed result of 15 heads out of 20 flips can be ascribed to chance alone - is rejected. Such a finding would be described as being “statistically significant at the 5% level”. Critics of p-values point out that the criterion used to decide “statistical significance” is based on the somewhat arbitrary choice of level (often set at 0.05). A proposed replacement for the p-value is p-rep. It is necessary to use a reasonable null hypothesis to assess the result fairly. The choice of null hypothesis entails assumptions. Frequent misunderstandings The conclusion obtained from comparing the p-value to a significance level yields two results: either the null hypothesis is rejected, or the null hypothesis cannot be rejected at that significance level. You cannot accept the null hypothesis simply by the comparison just made (11% > 5%); there are alternate tests that have to be performed such as some “goodness of fit” tests. It would be very irresponsible to conclude that the null hypothesis needs to be accepted based on the simple fact that the p-value is larger than the significance level chosen. The use of p-values is widespread; however, such use has come under heavy criticism due both to its inherent shortcomings and the potential for misinterpretation. There are several common misunderstandings about p-values. The p-value is not the probability that the null hypothesis is true (claimed to justify the “rule” of considering as significant p-values closer to 0 (zero)). In fact, frequentist statistics does not, and cannot, attach probabilities to hypotheses. Comparison of Bayesian and classical approaches shows that a p-value can be very close to zero while the posterior probability of the null is very close to unity. This is the Jeffreys-Lindley paradox. The p-value is not the probability that a finding is “merely a fluke” (again, justifying the “rule” of considering small p-values as “significant”). As the calculation of a p-value is based on the assumption that a finding is the product of chance alone, it patently cannot simultaneously be used to gauge the probability of that assumption being true. This is subtly different from the real meaning which is that the p-value is the chance that null hypothesis explains the result: the result might not be “merely a fluke,” and be explicable by the null hypothesis with confidence equal to the p-value. The p-value is not the probability of falsely rejecting the null hypothesis. This error is a version of the so-called prosecutor’s fallacy. The p-value is not the probability that a replicating experiment would not yield the same conclusion. 1 − (p-value) is not the probability of the alternative hypothesis being true (see (1)). The significance level of the test is not determined by the p-value. The significance level of a test is a value that should be decided upon by the agent interpreting the data before the data are viewed, and is compared against the p-value or any other statistic calculated after the test has been performed. The p-value does not indicate the size or importance of the observed effect (compare with effect size).

actually this one isnt that complicated. x-m/(s/n^.5) is your z value. (16.5-15) / (7 / 40^.5) = 1.36. Check the cumulative distribution table, z < 1.36 = .9131. 1-.9131 = .0869

What a pedantic piece from Wiki… Indeed, the P-value is the smallest alpha could be and allow you to reject the null hypothesis. That defn doesn’t usually help anybody. The P-value is the probability of observing a test statistic as contrary to the null hypothesis as the one you observed if H0 was true. Here H0: “population P/E” <= 15 (there are some real issues with that) and HA: P/E > 15. Then we gather our sample and find X-bar = 16.5, etc. calculate our Z-statistic and find Z = 1.36. The trick - P-value always “looks like” HA. So in this case P-value = P(Z > 1.36) = 0.0869. If HA was P/E <15 our P-value would be P(Z < 1.36) and if HA: P/E <> 15 our P-value would be P(Z > 1.36) + P(Z < -1.36) In this case, our P-value > alpha so we don’t reject H0. However, alpha is not involved in our calculation of the P-value.