Analysis recommendation

Based on the diagram, this analysis should make a comparison between measurements at different time points within a single group, or a comparison between at least two related groups. For example, multiple treatments may be tested (in the same order) within each animal or a single treatment is administered to all animals and the animals are then assessed at multiple time points. This analysis includes a single continuous outcome measure, at least one covariate, five or more blocking factors and a single categorical factor of interest: the repeated factor.

If this description is not accurate, please check your diagram and verify that all nodes are connected properly, all variable categories are indicated and tagged to the relevant interventions or measurements and the information provided in the properties of each node is accurate; then critique it again.

The number of blocking factors is very high. The decision to include blocking factors in the randomisation and the analysis depends on previous experience and/or literature evidence that nuisance variables (e.g. practical constraints on the experiment) may influence the outcome and potentially increase the variability. Blocking involves dividing the experiment into a series of mini-experiments; each mini-experiment should ideally contain all the treatments but have fewer animals per treatment group than the full design. If all treatments are present in each of the mini-experiments, then five blocking factors imply dividing the experiment into a minimum of 32 mini-experiments (5 factors with at least 2 categories each: 25) and it seems unlikely to run an experiment with such a large number of animals. The best course of action would be to consult a statistician to estimate the effect of these blocking factors, and screen them to only include those that are influential.

Statistical analysis methods compatible with this design include a one-way repeated measures mixed model with blocking factor(s). This test assumes that the data satisfies these assumptions: residuals are normally distributed, homogeneity of variance and the outcome is measured on a continuous scale (read more about parametric and non-parametric tests).

Alternatively, a repeated measures one-way ANCOVA with blocking factor(s) could be used but note that the mixed model approach includes two benefits over the ANCOVA approach:

  1. If a data point is missing for an animal the rest of the data from that animal can still be used.
  2. The mixed model approach can be applied when the assumption of sphericity does not hold (condition where the variances of the estimates of the differences between all possible pairs of groups are equal).

Note that the data cannot be analysed using a standard one-way ANCOVA — a repeated measures approach should be applied because the levels of the repeated factor are not randomised within each animal and the independence of the errors assumption will probably not hold. It is also important to consider if the covariate should be used in your analysis.

Only include a covariate in your analysis if:

  • The covariate is independent of the treatment.
  • There is a strong relationship between the covariate and the outcome measure (i.e. either they both increase together or one increases while the other decreases).
  • The relationship between the outcome measure and the covariate is similar for all treatments (i.e. there is no significant treatment by covariate interaction).

The above assumptions can be tested by plotting your data, details of what to look for and example graphs can be found on the independent variables page of the EDA website. If there are multiple covariates you are considering including in your analysis, ensure that the assumptions hold for each of them.

In many cases you will not know if including a particular covariate in your analysis is appropriate when planning your experiment. You should measure the covariate during your study, but only include it in your statistical analysis if the assumptions for covariate inclusion are met.

If you have reasons to think the data are normally distributed, and/or the variability of the responses is related to their numeric size, you should first consider transforming the data to normalise it (read more about data transformation) and assess if the transformed data fits the parametric assumptions. Most data can be normalised using transformations such as log or square root and using parametric tests is preferable as they have more statistical power than non-parametric tests, as long as the assumptions of normality are met.

When normality assumptions do not hold, even after a mathematical data transformation, a rank transformation can be applied to the data and parametric tests (in this case a repeated measures one-way ANCOVA with blocking factor(s)) can be performed on the ranked data. Note that there are assumptions associated with non-parametric tests also. For example, to perform a rank transformation the data must be able to be ranked, with only a few ties (e.g. identical values that will end up with the same rank), the observations must be independent and the covariate must have a linear relationship with the rank. Another option is categorical data analysis (e.g. categorising data as ordinal or binary outcomes and using generalized estimating equations or a generalized linear mixed effects model for the analysis). Your local statistician can help advise on this. These approaches will lead to a loss in power due to the categorisation of continuous data.

Please note that an experiment with a single variable of interest, a covariate and a blocking factor might not make the most efficient use of the data. Consider using a factorial design.

Analysis software

Software such as InVivoStat can be used to run a one-way repeated measure mixed model with blocking factors, and apply data transformations. The test can be found in the following menu:

Statistics>Additional Analyses>Paired t-test/within subject Analysis