Changes

P in the last column is the t-test probability for a one-side test of women being shorter than men. (Formally, it’s the probability of getting a value of t greater than that calculated from the data if women are in fact taller than men on average.)

P in the last column is the t-test probability for a one-side test of women being shorter than men. (Formally, it’s the probability of getting a value of t greater than that calculated from the data if women are in fact taller than men on average.)

Should the fact that, in the fourth sample, the average height of the women is taller than the men make us doubt that men are in fact taller on average? Should we be concerned about the last sample, in which the difference in height of the two sexes is rather small, though in the expected direction? No, in both cases. When we combine the data on all 10 men and all 10 women, we get this:

Should the fact that, in the fourth sample, the average height of the women is taller than that of the men make us doubt that men are in fact taller on average? Should we be concerned about the last sample, in which the difference in height of the two sexes is rather small, though in the expected direction? No, in both cases. When we combine the data on all 10 men and all 10 women, we get this:

{| class="wikitable"

{| class="wikitable"

Clearly, combining the data from several similar experiments strengthens the conclusions considerably, as shown by the fact that ''P'' is much smaller for the combined data than for any individual sample.

Clearly, combining the data from several similar experiments strengthens the conclusions considerably, as shown by the fact that ''P'' is much smaller for the combined data than for any individual sample.

The combination of data from several experiments is a specialised and sometimes difficult area of statistical theory but I see nothing particularly incorrect about the approach used by Lenski and his colleagues. The general point is that it is valid to combine the results of different experiments if it is scientifically meaningful to do so. (For example: A. Combining the results of five samples of the heights of men and women is clearly valid. B. Combining three samples of heights of men and women with two samples of lengths of male and female squid clearly isn’t.)

Although the combination of data from several experiments is a specialised area of statistics, I see nothing particularly incorrect about the approach used by Lenski and his colleagues. The general point is that it is valid to combine the results of different experiments if it is scientifically meaningful to do so. (For example: A. Combining the results of five samples of the heights of men and women is clearly valid. B. Combining three samples of heights of men and women with two samples of lengths of male and female squid clearly isn’t.) Generally speaking, the outcome of a combined analysis of several small experiments which all point in the same direction (or at least in a similar direction) will be more significant than that of any one of those experiments, as is shown in the larger table above.

I hope this clarifies the extensive discussion on this point and puts Aschafly’s mind at rest on this subject. [[User:KennyMac|KennyMac]] 08:20, 18 September 2008 (EDT)

I hope this clarifies the extensive discussion on this point and puts Aschafly’s mind at rest on this subject. [[User:KennyMac|KennyMac]] 08:20, 18 September 2008 (EDT)