Hypothesis Testing and P-values
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That was amazing, I was watching random statistics videos on YouTube, then I remembered about you and I asked myself if you had created a video designed for medical students, p value was <0.001 for the null hypothesis (was it?! XD)
+Aditya Chauhan Thanks, so I'm basically confusing the std dev of the sample with that of the std dev of sample means?
And we can take the population and sample std devs to be the same thing, since in reality we wouldn't know the population std dev?
+Colin Java okay, so for the formula you need the std dev of the distribution of sample means, but in the ques 0.5 is the std dev of the sample taken for the experiment itself. It's like when 100 rats' reaction time was measured, he found 0.5sec was the std dev of that sample.
Now we need to calculate what would be the std dev of the distribution made by the means of such infinite samples, we have central limit theorem for that.
In that theorem, we need population std dev which was approximated as sample std dev.
I hope this helps.
I don't get it though, with central limit theorem, you take the std dev of the distribution of sample means to be sigma/sqrt(n), where sigma is the population std dev, then when you look at the bell curve, you have z = [x- mu] / [sigma/sqrt(n)].
But... in the question, it explicitly tells you the std dev of the sample times is 0.5 seconds, so why not just use that when you get to the bell curve and use z =
[x - mu] / 0.5?
I don't think I'm the only one who thinks something is wrong here.
Easy way to remember:
P = Probability of null hypothesis is true, which is => u = 1.2 being true.
Since P value calculated is small = only 0.03 (0.3 %) of samples taken from population will actually have u =1.2.
This means u is not equal to 1.2 in 99.7% of samples taken from population. Therefore we reject null hypothesis since it's only true in 0.3% of samples taken from population.
I think that the null hypothesis should be "There is no difference between the response time of rats injected with the drug (1.05 seconds), and the response time of rats without the drug (1.2 seconds)" rather than saying that mu is equal 1.2 s (even w/ drug) since obviously, it's not (it's 1.05 s).
Khan Academy, regarding determining the z-score, should it rather be the t-score because the population SD is unknown. That is t = (1.05 - 1.2)/(0.05) = -3. The area from the left of t = -3 is 0.0017. This means the P-value is 0.0017 because probability is area under a normal distribution. This is a normal distribution b/c the data sample amount is 100 > 30; thus, this is in accord to the Central Limit Theorem. If I compare this P-value= 0.0017 to a low alpha value, alpha = 0.01, then, yes, reject H null. That is, the drug has no effect. My point is t-distribution should have been used and not z-score distribution. Please advise.
For those of you who are confused, P value is the probability that the data from a given sample is not due to the changes made or external influences. In other words, if the null hypothesis was correct, we would end up with a large probability that the sample mean would still be possible without any external influences i.e. injecting rats in this case. A smaller P value means greater confidence that the results were due to the external factors.
Why are we estimating the standard deviation of the sampling distribution when we already have the sample standard deviation?
Why are we dividing the "population" standard deviation with square root of the "sample" size?
so puzzling part about sd (6:40). the instruction says "with a sample sd of 0,5", then he says "best estimation of sampling distribution standard deviation" - does it mean population distribution or what?
It means that the null hypothesis is unlikely to be the true population mean. The nearer the null hypothesis is from the sample mean, the greater will be it's probability to be the true population mean. But the result showed it was far away, so, as the result showed, you can reject it with a probability of 0.3% to be mistaken. There's 0.3% chance that the true population mean will be greater or equal to 1.05+3*0.05=1.2s or less or equal to 1.05-3*0.05=0.9s. As a result, there's a 99.7% chance to be 0.9<True pop. mean<1.2.
Look at it this way, the null is saying that "there is no way on earth that the average is any value but 1.2 seconds." Then, assuming that is true, we do some math and figure out that if the drug indeed did have no effect, and we randomly sampled mice 100 times, it there would be a 0.3% chance that some of those mice had response times of 1.05 seconds. So it would be super improbable to get a value of 1.05 seconds. Now....rewind back to the problem. We were told that the scientist not only had mice with a response time of 1.05, but even better, that was his average response time! This means that it is crazy to think that the drug had no effect, because if it didn't there would only be a 0.3% chance we got a value of 1.05 seconds.
Okay, I don't get why you'd choose to reject the null hypothesis if the probability of getting the extreme result of the alternative hypothesis is only 0.3%.For me, if something has 99.7% chance of happening, then it is almost certain. I feel like I'm stupid here.
why isn't the sample standard deviation what the video calls the standard deviation of our sampling distribution?
I understand that s = 0.5 and that std dev of x bar = 0.05 but i just wanna understand the difference so i know how to clock it on the exam
can somebody tell me what is the reason why a author would not add a p value or confidence interval in his randomised controlled trial? the author already stated there is no significant difference but is there any literature I can use to back the reason of why he didn't add a p values or confidence interval in his randomised controlled trial???
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