I meant the extreme case (to illustrate the problem) in which one of the five data columns A,B,C,D, or E happens to contain only 1's. Using criteria based on "shared values of 1" as the basis for determining the clustering, this column would be deemed most similar to, and should cluster with, all others, even though it is independent of all of them. Correlation is not as susceptible to this problem.

Using correlation would handle 0 and 1 equally, so that a column of all 1's is not treated as being the item most similar to everything else. There are only 13 nontrivial partitions of five objects, so it is feasible and probably desirable to do some of the analysis by hand taking other criteria into account.

Excel can compute inter-column correlations but I don't know if there is any clustering functionality. The usual method to do anything complicated with a spreadsheet is to export it to a CSV file that can be processed by statistical software such as R.

@whuber: I made no such assumptions. As your own example illustrates, it is not true that "large differences in the variance of sampling distributions" can explain a high SD/mean ratio (without having even higher unexplained ratios in the observations for the high variance components). In that example of two regressions, an overall SD/mean ratio of 10 was derived from a ratio of 22000 for the higher-variance regression. This phenomenon and its generalizations are calculations and theorems, not "assumptions".

@whuber: Notice, as in your example, that in order for such things to occur, a conspiracy (that is, an actual phenomenon in the data generation) has to occur to suppress the high-variance terms from contributing to the mean. So one still can say something, and it will likely be interesting in relation to the problem of interest. It will not be as simple as the canonical case of i.i.d or nearly iid gradients. But you still have to explain how a mean that "could" have been larger is ten times smaller than the SD. Numerical accidents can be ruled out by taking subsamples.

@whuber: re "that might or might not be consistent with the true mean being zero" -- how could it be inconsistent with the mean being zero? It is consistent with the mean being zero, and also consistent with the mean being nonzero but the observations of the mean having SD higher than the value of the mean. As was pointed out in the answer. Are you saying there are relevant classes of models where a small observed ratio (mean/SD) disfavors the hypothesis that the true mean is zero?

The OP called 1/10000 "small" and knows what units and meaning it has in his problem. Here the mean and SD have the same units and their ratio is dimensionless. It is not necessary to assume a single common sampling distribution, only similar variances (and if that is not the case, a small ratio of mean to SD still imposes strong constraints). More information is needed but as e.g. the Chebyshev calculation indicates one can say something, just a lot less than with full information.

@Andy W, why should it be clear a priori that the hypothesis tests for the individual parameters do not say anything about significance of the overall model? (It is not assumed in OP's question or my comments, by the way, that the model significance can be quantified only by F-tests, and even in that case there are examples where F is equivalent to a t-test, so why not contemplate the possibility of a more complicated F being computable or estimable from a suite of t-tests?).

@Andy, it seems to me that link #2 does not address the question in any apparent way. Having high p-values for the regressors and low p-value for the overall model, does not indicate whether the former "can ... be combined into a p-value for the whole model". Maybe under some strong assumptions on what "combine" can mean, such as using a formula that extends continuously to the limit where some regressor p-values are zero, or something more than that, plus the ability to produce unboundedly extreme examples of the type seen in link #2. But all this is well beyond link #2 contents.

@Andy W: none of the F-test links pertain to item 3 of the question, which was whether one can determine the model p-value from coefficient p-values (or, interpreted more broadly, whether there is some other relation between the two types of p-value).