FIREchief wrote: ↑Sun Jun 24, 2018 8:32 am

jalbert wrote: ↑Sat Jun 23, 2018 10:09 pm

Well, an introductory text on mathematical statistics might have one or more chapters on the estimation of parameters of probability distributions, such as mean or variance, from sample statistics. If you repeatedly sample a distribution, and compute sample statistics such as sample means or sample variances for each sample, the computed values will vary from sample to sample. The sample statistic such as the sample mean or sample variance then becomes a random variable with its own probability distribution referred to as the sampling distribution....

The theory of the t-test, F-test, and chi-squared test depend on the sampling distribution to be well approximated by the limit distribution in the limit theorem, which means that to interpret the statistic of the test, you have to meet the conditions of the relevant limit theorem.

I can’t see any reason to believe that a sample of 3 consecutive years of return data would be a sufficiently large random sample of independent trials for appropriate limit theorems to apply. They certainly are not random or independent data points.

Thank you!!! I think you've just written six paragraphs that invalidate a whole bunch of guidance provided by "academic research by Nobel prize winning authors." Best post of the thread since Rick's OP.

Actually, I think this is worth pursuing a bit, because there is indeed something weird in the Fama-French paper, 1992,

The Cross-Section of Expected Stock Returns.

In Table III, page 439, they do indeed present a table of values together with "t statistics."

As jalbert notes, the use of t statistics to show statistical significance is only valid if you have some good reason to believe that you are looking at a) independent values of b) normally distributed data. There are other statistical techniques,

**well**-known in 1992 but for some reason (yes, I'm cynical) rarely used by financial economists, that do not depend on the assumption of normality. That might not be a big deal compared to a far more serious problem: the assumption of independence. And there is potentially a third problem, because that table does not show a single t-test, it shows

**twenty-six of them**, all being computed

**simultaneously**.

Now, let's be clear. As nearly as I can tell, Fama and French are

**not** trying to prove that the t-statistics for "Size, Book-to-Market Equity, Leverage, and E/P"

**are** significant. They seem to be mostly concerned with proving that β has no explanatory power.

**They do not mention a significance level anywhere. **In fact, it is not clear to me why they are even presenting them. They do mention a few of them a few times within the paper, but never with any significance level assigned to them, just as qualitative comparisons. For example, p. 441

The average slope from the monthly regressions of returns on ln(BE/ME) alone is 0.50%, with a t-statistic of 5.71. This book-to-market relation is stronger than the size effect, which produces a t-statistic of - 2.58 in the regressions of returns on ln(ME) alone.

You can't argue with that, they are just presenting values of a number and saying that one indicates a "stronger" relationship to another.

But I have to ask: why are they presenting all of those t-statistics

**most of which are never used in the paper?**
Yeah, I think this is a little weird. And I don't think it's unreasonable to raise questions about it.

And in general I think the endless citation of "t-statistics," sometimes by the nickname "t-stats," in financial economics,

**without any explanation or defense** as to why this would be a valid number to test and why they think the assumptions behind the test are close to being met, is also weird.

Vineviz and others: under what specific situations in financial economics do you think that the use of a T-test is appropriate, and under what situations is it inappropriate?

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