A multi-strain versus an outbred stock experiment. The data below has been made up to illustrate a multi-strain experiment comparing a treated and control group using either sixteen rats of eight inbred strains or sixteen outbred rats.
1. Using eight inbred strains
In this hypothetical experiment it is assumed that the two rats of each strain are assigned at random either to the treated or control group, and that after a suitable period some outcome is measured. The table shows the resulting data in “units”.
It seems clear that strains differ, with WKY, BDIX and MNR giving relatively low values both in the treated and control groups. A paired t-test is used looks at the column of differences and tests whether the mean is significantly different from zero (i.e. it looks at the probability that a mean difference as large as -2.625 could have arisen by chance sampling variation in the absence of a true difference between the treated and control groups).
The statistical analysis was done using the MINITAB computer program. The output from the computer shows N, the mean difference, its standard deviation and standard error, gives a 95% confidence interval for the difference, and a p-value of 0.025. Thus there is only a 2.5% chance of getting such a difference simply by chance. Accordingly, the null hypothesis that there is no difference between the two groups will be rejected at p=0.05..
| Table 1. Data for a paired t-test | |||
| Strain | Control | Treated | Difference |
| DA | 12 | 16 | -4 |
| F344 | 15 | 17 | -2 |
| LEW | 18 | 15 | 3 |
| WKY | 9 | 15 | -6 |
| BDIX | 7 | 9 | -2 |
| BUF | 16 | 19 | -3 |
| ACI | 15 | 18 | -3 |
| MNR | 10 | 14 | -4 |
| Mean | 12.75 | 15.38 | -2.625 |
Computer output
One-Sample T: Difference
Test of mu = 0 vs mu not = 0
Variable N Mean StDev SE Mean
Difference 8 -2.625 2.615 0.925
Variable 95.0% CI T P
Difference ( -4.813, -0.437) -2.84 0.025
2. Using an outbred stock
Exactly the same data are shown in Table 2 except that each column has been randomised to simulate the use of an outbred stock where it is not possible to match genotypes. The treatment means and the difference between the treated and control groups is exactly the same as in Table 1. No pairing is possible (pairing must always be done before starting the experiment), so a two-sample t-test is used to compare the two groups.
| Table 2. Data for a two-sample t-test | |
| Control | Treated |
| 15 | 16 |
| 12 | 15 |
| 7 | 19 |
| 9 | 17 |
| 10 | 14 |
| 16 | 18 |
| 15 | 15 |
| 18 | 9 |
| Mean 12.75 | 15.38 |
Computer output
Two-sample T for Control vs Treated
N Mean StDev SE Mean
Control 8 12.75 3.85 1.4
Treated 8 15.38 3.07 1.1
Difference = mu Control – mu Treated
Estimate for difference: -2.63
95% CI for difference: (-6.36, 1.11)
T-Test of difference = 0 (vs not =): T-Value = -1.51 P-Value = 0.153 DF = 14
Both use Pooled StDev = 3.48
Conclusion
Uncontrolled genetic variation (or variation due to any other cause) reduces the power of an experiment, leading to more false negative results or the need to increase sample size.