# Hypothesis testing clarification

Recently I was debating with someone about the theory and the ideas behind what does this procedure really test. In simple terms, is it testing the hypothesized (expected) data or the sample (actual) data? I believe that we are testing the validity of the hypothesized data so that inferences can de derived from it to conclude the rationale behind the sample data. And we are not testing the sample data itself. For example, if a coin toss results in 60 heads out of 100 flips and a hypothesis statement says a coin toss averages 50 heads - then a hypothesis test can be formulated to test whether a coin toss will equal 50 heads, i.e.: (i) reject if the test statistic is outside the boundaries of critical values - we conclude that the coin toss does not equal 50 b/c the sample value is significantly different from the hpothesized value. (ii) fail to reject if the test statistic is within the confidence intervals - we conclude that there is not enough evidence to suggest that the coin toss does not equal 50 We have completed the test on the validity of the hypothesized value. Based on one of these results and the given sample information we can then make decisions to take action. Is this your understanding? Appreciate your thoughts.

Anyone have an opinion? Cheers.

> In simple terms, is it testing the hypothesized (expected) data or the sample (actual) data? It is testing the Sample Data to give you a decision (within specified significance level) on how Close or Far away is your Sample Data from your Population Data, in terms of the point estimates (mean or standard deviation) your Sample is generating. In the coin example above, 100 flips of the coin is Sample Data with your sample mean as 60%. Whereas your population mean is 50%. Now, you are trying to see that at given significance level, is your sample of 100 flips with the mean of 60% representative enough for the Population Mean of 50%. The idea is, since you dont have time and money to gather all of Population Data to get your statistics, you are doing it on its subset (a Sample). And with Hypothesis Testing, you are deciding, if results obtained from your Sample are representative enough of the results that would have come from the Population. This is how I look at this whole thing. Comments?

Thanks rus1bus, Agree with some of your points, but a couple of clarifications on your response would help. May be I am confused with the wordings, but it seems to me that when you say: >It is testing the Sample Data to give you a decision the tests are performed on the ONE Sample Data (60%), which is obviously not true. If you meant the tests are holistically conducted on the sample data as a whole (as opposed to the population) then it makes sense, however this does not answer the question I was seeking. >Whereas your population mean is 50%. The 50% is not factual - it is a statement/opinion yet to be proven, so concluding the population mean to be 50% without completing the tests first is probably not correct. In literal terms when I think of hypothesis testing I think of a test as a means to validate the hypothesized (expected) data before drawing a conclusion about the Sample Data. The completioin of the validation will then allow me to draw inferences to conclude “…(within specified significance level) on how Close or Far away is your Sample Data from your Population Data, in terms of the point estimates …”. Not that I am nit picking or anything, but the first step in conducting a hypothesis test is to ‘State the hypthesis’ - this is where you set up your null and alternative hypothesis with the use of expected data to be tested. This is what I meant by the question above. Doesn’t the conclusion of the test validate this hypothesized value, the ‘expected data’. Also, I think the interpretation of the following paragraph from Schweser (SS#3, page 290) supports the statements above: “Hypothesis testing is the statistical statement of a statement or idea regarding a population. For instance, a statement could be as follows: ‘The mean return for the US equity market is greater than zero.’ Given the relevant returns data, hypothesis testing procedures can be employed to test the validity of this statement at a given significance level.” The last sentence really hits it home for me. Or am I really confused??

Sujan, I think what you are saying is correct. But to get something conceptually more accurate and precise on this, I will have to get back to books. In the meantime, I will summarize my understanding on hypothesis testing as: 1. You have some hypothesized value or belief 2. You compare this value to a Standard given value (this standard given value could be from Population or it could be from a Sample, if former is not available) 3. You calculate your test statistics based on your comparison in 2. 4. If test statistics falls within critical value, you accept your belief (or fail to reject to be more technically correct) 5. If not then you reject your belief. Sorry to chicken out for now, with what you probably already know. Cheers :).

Appreciate your time with this rus1bus. Let me know if you ever get around to the conceptual precision. Cheers