# Comparing 3 countings of a phytoplankton sample

##### New Member
Dear coleagues,

A friend of mine is trying to "be sure" that her counting method for phytoplankton communities is solid and unbiassed. She makes 3 essays (repeating 3 times the counting of N species of the same sample -and transforming to percentage data-) and wants to be sure that there are not significant differences between the essays, so that the method is consistent and results (in terms of percentage abundance of the N species) are homogeneous.

Which would be the propper test/s to perform in this case?

Thank you very much,

Andrés

#### obh

##### Member

I never counted phytoplankton.
statistics common methods compare different samples with the same metric.
If you count the same sample, why do you get a different result? is this a random process? do you count the entire sample?

##### New Member
Thanks obh,

Yes, it's a random sub-sampling procedure. You take 3 "subsamples" (transects counting of species under the microscope) of the same sample (in this case the actual sample from a lake would be our "population", I guess). The entire sample is never counted, too much time-cost.

#### obh

##### Member

So the data you have is 3 proportions and 3 totals?

method1: p1=0.71, n1=100
method2: p2=0.76, n2=102
method3: p3=0.84, n3=97

Are n1=n2=n3?

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##### New Member
Hi obh,

In fact we have a 3 essays x 25 species matrix, all species summing 100% for each essay. Data are % abundance. So we have to probe that the 3 essays are equivalent or comparable.

hth,

Andrés.

#### obh

##### Member
Can you please give example data? (with 4 species...)

##### New Member
Ok, here we go!

Essay 1. Essay 2. Essay 3.
Sp 1 45 43 38
Sp 2 30 32 35
Sp 3 25 25 27
...
...

#### obh

##### Member
Is there any connection between sp1 and sp2 and ..?
Say if 3 essays (methods) give similar results in sp1 they will give similar results in sp2 and sp3 etc....

or do you need to run a statistic test for each sp separately?

##### New Member
I can't understad your question...it's just a sample (a bottle of water with N (millions of cells) organisms belonging to X species) so we extract 3 random samples (essays) and count the number of organisms of each species and express as percentage in the sample...

#### obh

##### Member
Using different method of counting in each essay?
What is the the difference in counting?

##### New Member
No diference we hope, it's just a quality control...imagine three people doing the same counting

#### obh

##### Member
So if understand you correctly, you don't compare 3 different methods, but count 3 times and expect to get the same results.
Since it is not an accurate method you won't get exactly the same results and you treat each count as a random variable.

You want to quality test any SP separately and If the results are not exactly the same you need to decide is it okay to use the results, or do you need to check again this specific SP count?

If this is the case you may use the chi-square test for goodness of fit.

SP1
Essay: Essay 1. Essay 2. Essay 3.
Expected: 1/3 1/3 1/3
Actual: 45/126 43/126 38/126

or with counts

Essay: Essay 1. Essay 2. Essay 3.
Expected: 42 42 42
Actual: 45 43 38

http://www.statskingdom.com/310GoodnessChi.html

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##### New Member
Thank you obh!
Do you think there is a posibility of doing a single chi-square test for the whole community (I mean considering all species)?

#### obh

##### Member
You can do one test if meet the test's assumptions.
But I can see 2 problems :
1. If you are interested in accuracy for each SP several SP mistakes won't be detected.
2. Also If SP sizes are not similar, problems with the small sizes won't be detected.

So for quality assurance I think it make sense to check each SP. Otherwise you may miss the point.

You may consider smaller p value for many tests.

But independent to statistics you need to decide what level of accuracy is required.?