Analysis of some real data from a multi-strain experiment
The aim of this experiment was to see whether the anti-oxidant BHA altered the activity of the liver enzyme EROD when administered in the diet, and also to see whether any response was genetically determined (i.e. strain-dependent). A randomised block experimental design was used. Each block consisted of one treated and one control mouse of each of four inbred strains. The resulting data are shown in Table 1.
Block 2 was done approximately three months after block 1. Blocking was used for convenience because only eight mice needed to be on the experiment at a time, and also to ensure that the results were repeatable over time. Brief details of the experiment are given elsewhere.
The analysis of these data was done using the MINITAB statistical package. Like most statistical software, the data are entered one row per experimental subject, with the strain of mouse, the observed EROD activity, a code to indicate the treatment (1=Treated, 2=Control) and a code to indicate the block.
The analysis of variance (ANOVA) command was then invoked and the command table was filled in to indicate the type of analysis wanted. In this case a three-way ANOVA with strain and treatment being fixed effects (determined by the experimentalist) and the block being a random factor (i.e. not a specific treatment). The resulting ANOVA is given below.
| Table 1. EROD activity following treatment | |||
| Strain | EROD activity | Treatment | Block |
| A/J | 18.7 | 1 | 1 |
| 129/Ola | 17.9 | 1 | 1 |
| NIH | 19.2 | 1 | 1 |
| BALB/c | 26.3 | 1 | 1 |
| A/J | 7.7 | 2 | 1 |
| 129/Ola | 8.4 | 2 | 1 |
| NIH | 9.8 | 2 | 1 |
| BALB/c | 9.7 | 2 | 1 |
| A/J | 16.7 | 1 | 2 |
| 129/Ola | 14.4 | 1 | 2 |
| NIH | 12.0 | 1 | 2 |
| BALB/c | 19.8 | 1 | 2 |
| A/J | 6.4 | 2 | 2 |
| 129/Ola | 6.7 | 2 | 2 |
| NIH | 8.1 | 2 | 2 |
| BALB/c | 6.0 | 2 | 2 |
This shows the three factors (block, strain and treatment, abbreviated Trt), their type (random or fixed), the number of levels and the designation in the table of the individual levels. Below that is given the ANOVA table showing the source of variation, degrees of freedom (DF) sums of squares (SS), mean square (MS), the F value (F is a test statistic) and the p-values. At the 0.05 level of significance the treatment effect was highly significant (p=0.000 to three decimal places), and the strain * treatment interaction was significant at p=0.034. This implies that there were strain differences in response, although further tests are needed to clarify what these are (not shown here). Although the strains do appear to respond differently, these differences are not all that great and may not be biologically of great importance.
Analysis of Variance for EROD
Source DF SS MS F P
Block 1 47.610 47.610 18.37 0.004
Strain 3 32.962 10.988 4.24 0.053
Trt 1 422.303 422.303 162.96 0.000
Strain*Trt 3 40.343 13.448 5.19 0.034
Error 7 18.140 2.591
Total 15 561.358
It is clear that the treatment induced the enzyme levels (p<0.001). The statistical analysis also shows that the strains respond slightly differently, largely because BALB/c responds more than the other strains. Had the experiment been done with sixteen outbred mice it is highly likely that a significant treatment effect would also have been observed. However, there would have been no indication whether there was any genetic variation in response, and if the stock was genetically quite variable, the power of the experiment would have been reduced.