In growth response studies anova is only relevant at a particular time point e.g. end-point size. Otherwise there is a multitude of growth functions to model growth profiles. Parameters and meaningful functions (e.g. half-life) can be analysed in anova too. you need to model the growth pattern first. I attach a file that explains growth functions.

Duncan’s new multiple rang test may be a good test to separate significant differences among treatment means.

Another option is:

>> Parallel curve analysis

In parallel curve analysis we compare shape and size parameters. This consists of the following steps: NB: Information below with respect to y = A + B exp(-k{Time}), B=A exp(k {lag}) and ‘k’ is the Relative rate.

1. Fit overall curve for all factor levels assuming no Group differences

2. Make Constant Parameter separate (separate asymptotes)

3. Make all linear parameters separate (separate both A & B parameters)

4. Make all Linear & Nonlinear Parameters separate (fit curve to each group separately)

Interpretation (if assumption in (1) above is not true)

(a) Extended model in (2) should explain some of the ‘residual ss’ from (1). So we test the difference “residual from (1) – residual from (2)” using F-test. If this is significant (at p ≤ 0.05) then we retain separate asymptotes.

(b) Now do the same between (2) & (3). If significant keep ‘B’ separate too.

(c) Do the same between (3) & (4). If significant then separate curve for each of the factor Group is indicated.

(d) If shape parameter is different, you must fit curves to groups individually. Thus in this example your grouping Factor has made a significant change.

as the variable is quantitative I think that: you can use the distribution of F (ANOVA) mostly; if you use a placebo sample, while calculating the variances of the two samples then you calculate the formula: f = (variance E1 / variance E2); ddn = n1 -1 and ddd = n2-1;

Then go on the table to compare the calculated value F with the value F of the table....

In feeding trials, when treatments have equal replicates and experimental unit the ANOVA is fair to be used. Otherwise GLM procedure must be used. Comparison between treatment means is done by Duncan or LSD.

Hi Guys,

thanks for the responses, it appears that ANOVA has the dominant fans but as the number of replicates increases and as the variance tends to decrease, as an example sometimes a value of 2.04 is significantly better than 2.01. If growth is a compared between the testaments and the economics associated with this difference and after analysis there is still a question that remains is it really significant???? The effect size statistics offers a concrete definition of the quantitative difference between the treatments but still the question is is this a better statistic than ANOVA??? or is this a complement or a support to ANOVA???

Linear analysis comparison is only good in continuous variable but if the treatments are independent and not continuous (discrete variable) then ANOVA or Effect size is the choice?? but which is better and why it is better are common question that confuses a student and a researcher of animal nutrition. Sometimes if selection of a statistical tool is incorrect this could led to a bias and jeopardizes the conclusion.

Maybe Duncan's multiple domain testing can help you.

Dear Dr. Traifalgar,

If I understand your question, we may could be talking about a misinterpretation of the noun "significant"; and yes, that is a common issue. In your question, I find two different uses of the noun "significant":

1) "a value of 2.04 is SIGNIFICANTLY better than 2.01", and

2) "after analysis (economics) there is still a question that remains is it really SIGNIFICANT???

In both cases the noun "significant" has different connotations:

In the first case you may refer to the output of a hypothesis test by statistical analysis, and for me the easiest way to explain the meaning is to equal "significant" with "attributable to", meaning that the difference of 0.03 between the two treatments is "attributable to the treaments relying on the statistical analysis". In this case, the noun "significant" is often confused with "relevant" an that is not correct.

In the second case, the noun "significant" does refer to "relevant".

So, the P value obtained from an ANOVA does not inform about how important or relevant the effect is, but only about how probable that difference is attributable to the treatments.