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Talk:PNAS Response to Letter (view source)
Revision as of 12:20, September 18, 2008
, 12:20, September 18, 2008→Data from several experiments: new section
If I combine the 2 experiments, I get a total of 56 "pro" and 54 "con", so more than 50% "pro" (in a large total sample size!),
If I combine the 2 experiments, I get a total of 56 "pro" and 54 "con", so more than 50% "pro" (in a large total sample size!),
appearing to support the hypothesis, even though that's obviously not the case! --[[User:DRamon|DRamon]] 14:33, 17 September 2008 (EDT)
appearing to support the hypothesis, even though that's obviously not the case! --[[User:DRamon|DRamon]] 14:33, 17 September 2008 (EDT)
== Data from several experiments ==
I would like to contribute to this discussion because I have taught statistics to graduate biology students for 16 years.
The combination of data from several experiments is a specialist and sometimes difficult area of statistical theory but a simple example shows why Aschafly’s concern about combining the results of three different experiments is not justified and why his criticism of Lenski’s recent paper in PNAS is not valid.
Suppose we want to conduct a test of whether or not men are taller than women on average. For the sake of the example, I generated random heights of people from a population in which men had an average height of 175cm (5’10’) and women of 165cm (5’6”). The standard deviations of height in both sexes were 7cm. I think these numbers are approximately correct for people in the UK but the details aren’t important.
Suppose we take 5 samples of 2 men and 2 women. Here are the numbers I generated:
{| class="wikitable"
|-
! Man1 !! Man2 !! Woman1 !! Woman2 !! Men mean !! Women mean !! Mean difference !! t !! P
|-
| 176 || 179 || 157 || 148 || 177.5 || 152.5 || 25 || 5.27 || 0.017
|-
| 180 || 176 || 160 || 164 || 178 || 162 || 16 || 5.66 || 0.015
|-
| 176 || 175 || 167 || 165 || 175.5 || 166 || 9.5 || 8.50 || 0.0068
|-
| 169 || 171 || 168 || 173 || 170 || 170.5 || -0.5 || -0.19 || 0.57
|-
| 179 || 175 || 166 || 178 || 177 || 172 || 5 || 0.79 || 0.26
|-
|}
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:
{| class="wikitable"
|-
! Men mean !! Women mean !! Mean difference !! t !! P
|-
| 175.6 || 164.6 || 11 || 3.85 || 0.00058
|-
|}
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.)
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)