I am studying this lecture. It looks like that it is for undergraduate, but I find it is useful.
At the same time, I am reading Intuitive biostatistics to solve the problem that Dr.Thoma gave.
The mean temperature of 130 people is 36.82 and the 95% CI ranges from 36.75 to 36.89. The 95% CI does not include 37, which is from most of the books. In other words, our data are inconsistent (with 95% confidence) with the hypothesis that values were drawn from a population whose mean is 37.
If p values=0.000000018, which is reported by many programs that p<0.0001. This small p value tells us that if the population mean truly is 37 (hypothesis is correct), there is a very small chance of obtaining the data we observed, which also means the discrepancy is very unlikely to be the result of chance.
if with a smaller sample( n=12), we find p value is 0.0687, which is greater than 0.05, that is not statistically significant. That means, if the hypo were ture, the data we observed would not seem surprising.
with smaller sample(n=12 vs n=130), the population mean is defined with less precision, so the 95% CI is wider.
rule: to interpret the p value, the Ho should be defined
Example 4:
the null is that the risk of death, or heart failure is the same in both populations of patients, so that any discrepancy observed in the particular patients in the study is the result of chance
p values answers question like this: if the null hypo were true, what is the chance that random sampling would lead to the situation in this study.
one or two tail p values
to compute one tail p value, we must specify the direction of the alternative hypo
it is half of the two-tail p value(assume gaussian distribution)
an example to use one tail p value. according common sense, the case can only go in one direction. According to the rules, the drug can either not change the antibiotics level of the population, or it will increase the anti level in the population. Accordingly, it makes sense to calculate a one tail p value. If the antibiotics level goes down, no matter how much, you’d attribute the decrease to chance.
p values summary
the hypo tested Ho is usually opposite to the hypo the experimenter expects to be true.
P GOOD SUMMARY
you observe a sample and want to make inferences about the population. calculations of the p values start with an assumption about the population(Ho) and determine the probability of randomly selecting samples with as large a difference as you observed.
p=0.03. you can explain, if the null hypo were true, then 97% of experiments would result in a difference smaller than the one you observed, and 3% of experiments would lead to a difference as large as , or larger than, the one you observed.
questions
high p value prove the null hypo is true?------no. high p value means that if the null hypo were true, it would not be surprising to observe the difference or effect seen in the experiment. But that does not prove the null is true.
can p values be negative?--no, always ranges from 0 to 1
one tail value always equal to half the two-tail p value?------no. a lot of restrictions need to implement to get half. The first and easiest restriction is symmetrical.
null hypo ever true?---whenever you compare two groups, it is very unlikely that the two population means will be exactly the same. when you apply a treatment, it is very unlikely that the treatment has zero effect. The scientific question is whether the difference between the groups are large enough to matter. In some situations, the groups might be very similar or the treatment may have only a trivial effect. But even in those cases, the null hypo is not quite true.
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