BuiltWithNOF
Example 1

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.