For my studies it is not so much about avoiding pseudoreplication as it is about taking pseudoreplication into account. I, for instance, have a dataset with some real replicates, which are the kelp stations, and then I have several kelp plants at each station. These kelp plants are pseudoreplicates, and we include "station" as a random factor in the analyses i order to take the pseudoreplication into account. Regards, Trine 

Hello Azwandi

Pseudoreplicatoin is not so much about a minimum distance between plots. Minimum distance, as well as plot size, should be determined by the size of your animals, mobility, spatial distribution, and other biological factors.

Pseudoreplicatoin is more about how you report and interpret/extrapolate your sample size. For instance, if you are working in 3 geographically isolated lakes, and you have n = 15 replicates per lake, your sample size is not 45 (15*3). It is not 15. Its 3. You looked at 3 lakes.

It is sill important to have sufficient replication at your base unit of replication. Even if you only look at 1 lake you still want to have sufficient replication that your study accurately (as possible) represents the conditions in the area you study. However, the smaller you sample size the more caution you should utilize when extrapolating your findings. 

To avoid pseudoreplication all you need to do is clearly communicate your sample size. For instance: From 5 independent sites, we collected 10 samples per week, over a total of 4 weeks ( n = 10 per week, 40 per site, 200 total).

Hope this helps!

Travis 

I think Travis' answer is a really good one.  The only thing I would add is to make sure you use the proper analysis for your data. i.e. make sure you models the correct parameters as random effects.  Cheers, Dan

For my studies it is not so much about avoiding pseudoreplication as it is about taking pseudoreplication into account. I, for instance, have a dataset with some real replicates, which are the kelp stations, and then I have several kelp plants at each station. These kelp plants are pseudoreplicates, and we include "station" as a random factor in the analyses i order to take the pseudoreplication into account. Regards, Trine 

Azwandi also asked about distance between sites. I think there are two main drivers to help you on this. First: which species are you working with? Are they mobile ones or not? By knowing the biology of the "target" species you may be guided on how avoiding interference. Second, how big is the area you are interested in? If you want to have an idea of a phenomenon at a landscape scale, is then advisable to have distant sites in order to account for possible differences locally. Unlikewise, in a crop field this issue is less relevant. Hope this helps. 

Hi! interesting question. I work with soil invertebrates and is much easier for me to avoid pseudoreplication. But, even with invertebrates, it will depend of the size and mobility of the group that we are working with. It will also depend of the spatial scale that you are working. Please, go to this link: https://www.google.com/webhp?sourceid=chrome-instant&ion=1&espv=2&ie=UTF-8#q=biodiversidade%20e%20monitoramento%20ambiental%20integrado

It will show several examples using different group of organisms.

Semms to me, just use a hierarhical mix-effect models, and corectly choose the denominator in case look likes mix-eff nested ANOVA ;-)

If the goal is to optimize your budget and maximize the amount of information from a given number of samples, you should consider to complete a pilot study. Minimal between sample distance that avoid spatial autocorrelaion can be determined using Wagner's approach (implementd in vegan from R).

I would add to this discussion, that in a field study it is important to understand the level of spatial autocorrelation in your target organisms, and second to figure out how much distance-decay exists in community structure. Sometimes the goal of community studies is to directly measure these two factors, in which case replicates can be contiguous. But if your goal is to avoid collecting samples that are not independently distributed or to avoid sampling within the 'effect zone' of a treatment, your samples should be reasonably isolated from each other. The definition of 'reasonably isolated' depends on your study goals and organisms as others have said here already.

Azwandi,

If we take Travis’s example 3 lakes and 15 samples each. Actually each lake is a treatment. If the 15 samples are randomly distributed then you do have n=15. If however to get your 15 samples you decide that you can save time by going to 5 locations and take 3 samples at each location then those 3 samples are in effect sub-samples and need to be combined (as with Trine’s kelp) so n=5. By the same measure if you decide to get your 15 samples by taking 5 samples at the same place on 3 days then again n=5. If you decide for convenience sake to have 15 random samples but only on the side where there is road access, then you would need to be sure that the conditions on that side are representative of the lake as a whole.

For your animals the overlap question does get important particularly if your sampling methods are destructive (pit-fall etc). However, if they are not destructive and you want to either know presence/absence or trend then total independence may not be so important. A case would be ‘Five Minute Bird Counts” Bird territories (across species) are so variable as is behaviour that the most important thing is to be consistent with as many things that can be controlled as possible. You will double count some birds, equally on another day the more mobile birds may not be counted at all, not because they’re not there just because the 5 minute count didn’t coincide with their movements around a much bigger territory. Over time a population trend still emerges.

Hello Azwandi Ahmad,

Your query, lo these many years, highlights one of the confusions created by Hurlbert (1984). The publication conflates 2 problems: spatial autocorrelation of proximately located plots, and incorrectly formed F-ratios due to failure to distinguish random from fixed factors. Some of the replies address the first problem (potential autocorrelation of proximate plots) some address the second (forming the correct F-ratio).

As an entertaining sidelight my first encounter with "pseudoreplication" was back in 1992. A student came to my door with a rejected paper that was a latin square design, rejected as pseudoreplicated because all the plots were in only one field. Aargh!!!!

The most recent encounter was earlier this year. Again the F-ratios were correctly formed, but they were taken as pseudoreplicated by a reviewer. I showed the author how to write out the expected mean squares to obtain the correct F-ratio and the paper was then accepted.

The Hurlbert (1984) publication identifies a recurrent problem, that of incorrectly formed F-ratios , under the neologism of "pseudoreplicaton." The key to identifying this problem is the distinction between random and fixed factors. Neither term occurs in Hurlbert (1984) !!!!

So when considering "pseudoreplication" the first question to ask is what was the fixed factor and what was the random factor? Was a random term (plots) crossed with a fixed term? or was it nested ? Was the F-ratio for the fixed effect tested over the correct error term ?

The 2nd question to ask is that of autocorrelation of proximate experimental units. It is telling that Quinn and Keough (2002) explicitly choose to not use the term "pseudoreplication" in their text in experimental design.

~David S