2nd Nov, 2018

Drexel University

Question

Asked 28th Sep, 2017

Hello,

I've got measurements of water quality parameters over time in fish tanks (3 tanks per treatment) and I want to see where in time they, if at all, become significantly different between groups (control vs. treatment).

I think my setup is like this: my dependent variable is concentration, my independent variable is time, for which I have 3 or more measured time points (three or more related groups). Note: the fish are NOT subjected to both treatments in time.

And how do I set up my xcel file used for importing data? Do I use all measurements done per group over the time points, or do I use the means per treatment (3 groups in each treatment) as input?

The results I find by doing Repeated Measures Analysis don't make much sense so I'm not sure about my approach?

Thank you so much in advance :)

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Thijs,

The t-test and ANOVA require independence among observations. Since your design includes time, it creates temporal correlations. So, these two options are too much simple. The Repeated Measures ANOVA has an assumption called "Sphericity", which is rarely met. I suggest you an alternative approach. Use Nested ANOVA, with factors nested in this way: Treatment < Tank < Time.

Your excel table would be organized with the columns (from left to right):

Treatment - Tank - Time - Concentration,

Using this design, you will be able to identify if the Treatment differs (which I think is your main objective) and if there was a time at which the treatments become different.

This analysis can be done in R using function aov in the following form:

aov(Concentration ~ Treatment + Treatment:Tank + Tank:Time, data = ___)

6 Recommendations

This seems to be a 2 x 3, between x within (repeated measures design); correct me if I'm wrong. If it indeed is a between x within design, just run a two-way ANOVA: group x time. In Excel you would have 6 rows corresponding to 2 groups (control vs. treatment) x 3 tanks (observational units or 'subjects'); there would be 3 columns of concentration data for each of the 3 time points (more columns if more time points).

Thijs,

The t-test and ANOVA require independence among observations. Since your design includes time, it creates temporal correlations. So, these two options are too much simple. The Repeated Measures ANOVA has an assumption called "Sphericity", which is rarely met. I suggest you an alternative approach. Use Nested ANOVA, with factors nested in this way: Treatment < Tank < Time.

Your excel table would be organized with the columns (from left to right):

Treatment - Tank - Time - Concentration,

Using this design, you will be able to identify if the Treatment differs (which I think is your main objective) and if there was a time at which the treatments become different.

This analysis can be done in R using function aov in the following form:

aov(Concentration ~ Treatment + Treatment:Tank + Tank:Time, data = ___)

6 Recommendations

As I understand, the analysis suggested by Matheus is a repeated measures ANOVA on the data in *'long'* format. The analysis I proposed is the same, but on the data in *'wide*' format. With only 3 repeated measures, the 'sphericity' issue is not really a huge problem. With most common statistical software packages (SAS, SPSS, R, STRATA) one can model the covariance structure.

1 Recommendation

Thank you all for your answers. I think I was able to perform adequate analysis using your tips.

@Jos: it's indeed a 2 x 3, between x withing (repeated measures design).

I did my statistical analyses like this:

1.Mixed model ANOVA used to assess whether there were significant differences between and within treatments over time.

2. Separate one-way randomized ANOVA (as follow-up tests) for each time point to assess at what time point these mean values became significantly different between treatments.

3. Another follow up test, separate one way repeated measures ANOVA's for each treatment to get value for significance within treatments.

This would imply that you predicted and indeed found an interaction* group x time*. If not, you should consider *post hoc* tests. In SAS, this can be done on the data in *long* format using proc mixed, with the statement:

means time / LSD e= time*tank(group);

for the* least sign. post hoc* test for times.

See the attachment for an example.

- 2.42 KBrepmeasmixed.sas

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- Ganesh Ambigapathy

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I did real-time qPCR and have ct values. I calculated ∆Ct = Ct[Target]-Ct[Housekeeping] ... and ∆∆Ct = (∆Exp.)-(∆Control) and got the -∆∆Ct log-fold-change. It looks all the values are almost same and not much different between the groups.

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