My biologist friend is having a bad time with her experiment. It's suspected that changing the temperature and organic content in water may affect the growth of crustaceans. In her experiment, two formulations of different organic content combined with four different temperatures (plus control) were combined. 10 tiny crustaceans were put to grow in each combination and weighed weeks later. However, the crustaceans are too small to be weighed individually, so they were all weighed together and the result divided by 10. The experiment generated the following table:
Formulation 1 Formulation 2 Temp A 0.132 0.155 Temp B 0.136 0.143 Temp C 0.141 0.139 Temp D 0.128 0.132 Control 0.123 0.138
Now she'd like to find out whether any combination of Temperature x Formulation affects the crustaceans' weight considerably compared to the control groups. In my opinion, the best way to detect whether the Temperatures or Fractions affect the group's weight is via two-way ANOVA without replication, which gives the following:
Analysis of Variance Table Response: weight Df Sum Sq Mean Sq F value Pr(>F) temperature 4 0.0002966 7.415e-05 1.5561 0.33940 formulation 1 0.0002209 2.209e-04 4.6359 0.09764 . Residuals 4 0.0001906 4.765e-05
But I have a few questions: how reliable such statistic would be? Is this really the correct way to detect the effect of each combination in each group (in this case, that there's no effect whatsoever)?
Or would it be necessary to re-run the experiment with replication for a proper result? In this case, it's gonna be difficult since these crustaceans are quite expensive.