# analysis for different kinds of in vivo experiments with multiple groups (ANOVA vs. t-test)

Many in vivo experiments with mice involve four groups. For example, in oncology models often there are two treatments (one experimental and one standard of care) that are given alone, jointly, and then compared to a vehicle control. The standard analysis for this type of experiment appears to be a two-way ANOVA test.

However, in my case the experimental design is quite different and with it the hypothesis to be tested. I also have four groups of mice with two independent factors. Here, one is a treatment that induces a disease state while the other is the mutational status of a gene. My hypothesis, based on a variety of additional data points, is that the mutation in the gene will suppresses the disease.

It was suggested to me that, as above, I should perform a two-way ANOVA to analyze the data. However, I believe that in this case the untreated animals are merely a control to show that my disease-causing intervention is working as expected. In fact, the only comparison I am interested in is between the wild type and mutation group of mice that were treated to induce the disease. Furthermore, my hypothesis is that the gene will suppress the disease (and not merely affect it in an unknown direction).

So my contention is that the 'correct' test in this case would be a simple one-tailed student's t-test between the wild type and mutant group of mice on the disease-inducing treatment.

If I understand correctly, you have two groups (control and treatment) and they are independent. So this makes a two-samples independent t-test appropriate.

Note that if your dependent variable is:

• quantitative: you can indeed compare the two groups with:
• a Student t-test if normality is respected in both groups and variances are equal between groups,
• a Welch t-test if normality is respected in both groups but variances are unequal or
• a Wilcoxon test if normality is not respected, no matter if variances are equal or not. See more details about the different versions of the t-test.
• binary: you would need to perform a Chi-square test for independence, since you have two qualitative variables. See how to do so in R or by hand.

Regarding the direction of the test when your dependent variable is quantitative, if you want to test whether the mean in the treatment group is lower than in the control group, you can indeed test:

• $$H_0: \mu_c = \mu_t$$
• $$H_1: \mu_c > \mu_t$$

When your dependent variable is qualitative, in order to test for the "direction" you could compute the odds ratio. The odds ratio, in addition to testing if there is a significant association between the two variables (which can be found thanks to the Chi-square test for independence), allows you to quantify this association.

Hope this helps.

Regards, Antoine

• Thank you, Antoine. I believe this answers my question. However, just to clarify: I have in total four groups coming from two independent variables (disease-inducing intervention and genetic background). But the two groups without the disease-inducing) are merely there as a baseline to show that the experimental intervention is working well to induce the disease. My hypothesis is exclusively focused on whether or not the genetic background affects the disease--hence the proposed two-group approach for analysis. Feb 1 at 14:04