FAQs on the exercise Assumptions of Numerical Hypothesis Tests
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In hypothesis testing it says if the ratio of two standard deviation is staying within 10 percent then it should suffice .What i don’t understand is with respect to what should the ratio be 10 percent.what are we comparing ratio with when we say 10 percent ,for example we get the ratio between dist_2/dist_3 as 58 % what does the percentage imply?
I might not have understood what you mean, but 58% means one is almost double the other, and so the two samples are too different in shape to compare reliably, as the tests assume distributions are normal and similar. Up to 10% difference ie within a range of 90% to 110% (depending which sample you divide by) means they are roughly (enough) the same shape.
I don’t know why they have to be the same shape, though!
I think I am wrong when I say 90% to 110%.
I got 0.58 for dist_2/dist_3, but 1.71992083922 for dist_3/dist_2.
But what I take from the explanation is: check the stds before you test, and if they are way different then think again, and if they are close, divide one by the other (smaller divided by larger) to see if the ratio is closer than 90%.
According the 3 assumptions given in this exercise, it mentions that the samples being compared should be independent. However, I found this a little confusing as in a previous exercise 2 Sample T- tests, we compared the the average visit time for the same website in 2 weeks (consecutive). According the the assumption given, this, in my opinion does not really qualify as independent samples.
Am i missing something ? This still isn’t clear to me. Would be great if someone can help me figure this out.
How are dependent and independent samples different?
Dependent samples are paired measurements for one set of items. Independent samples are measurements made on two different sets of items.
When you conduct a hypothesis test using two random samples, you must choose the type of test based on whether the samples are dependent or independent. Therefore, it’s important to know whether your samples are dependent or independent:
If the values in one sample affect the values in the other sample, then the samples are dependent.
If the values in one sample reveal no information about those of the other sample, then the samples are independent.
Example of collecting dependent samples and independent samples
Consider a drug company that wants to test the effectiveness of a new drug in reducing blood pressure. They could collect data in two ways:
Sample the blood pressures of the same people before and after they receive a dose. The two samples are dependent because they are taken from the same people. The people with the highest blood pressure in the first sample will likely have the highest blood pressure in the second sample.
Give one group of people an active drug and give a different group of people an inactive placebo, then compare the blood pressures between the groups. These two samples would likely be independent because the measurements are from different people. Knowing something about the distribution of values in the first sample doesn’t inform you about the distribution of values in the second.
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