# Comparing the size of fish exposed to a pesticide - Which test use?

#### Jonathan M

##### New Member
Hello everyone!

I did an experiment exposing my fish to 10 micrograms/liter of atrazine (environmentally relevant concentration). Now, i want to analise my data. I have measured the total length and body weight. The fish were kept in 4 aquariums (Control - Control - 10 ug/l - 10 ug/l) 6 fish per aquarium. I have 12 total length and 12 body weight measurements for the Control and the same for the treated group.

As the data proved to be nonparametric i choosed the Mann-Whitney test. So, my question is, can i consider the 2 controls aquariums as one group and compare with the other 2 10ug/l aquariums, the other group? (12 measurements column one vs 12 measurements column two - i use the graphpad prism) This is the concept of duplicate?

Thanks

#### obh

##### Active Member
Hi Jonathan,

Why not?
If you believe that the IV of the aquarium is not relevant, only the IV treat/not treat is relevant, you can compare the two groups of 12.

#### GretaGarbo

##### Human
As the data proved to be nonparametric
By that I guess that you mean that the data were not normally distributed. But there are many other parametric distribution, besides the normal distribution. Also, - as has been said a million times on this site - it is the residuals that are considered to be normal, not the variable it self. And, it might be possible to transform to normality (e.g. taking the log)

You could just show us the data of the 24 fishes and the aquariums.

The more important question is: did you randomize the 24 fishes to the 4 aquariums (i.e. by lottery choose that fish number 14 would go to aquarium 3, etc)?

You could have a model:

weight = a + b_1*treatment + dummy_aquarium + residual

#### Jonathan M

##### New Member
You could just show us the data of the 24 fishes and the aquariums. OK, i'm going to show the data.

The more important question is: did you randomize the 24 fishes to the 4 aquariums (i.e. by lottery choose that fish number 14 would go to aquarium 3, etc)? Yes!

#### GretaGarbo

##### Human
The more important question is: did you randomize the 24 fishes to the 4 aquariums (i.e. by lottery choose that fish number 14 would go to aquarium 3, etc)? Yes!
Good!

Now, good luck with showing the data.

#### Jonathan M

##### New Member
Control aquarium 1:
3717,41
3742,92
3646,11
3702,51
3655,61
3642,08

Control aquarium 2:
3694,08
3750,82
3713,06
3791,52
3690,23
3648,14

10 micrograms/liter aquarium 1:

3135,72
3210,48
3485,56
3443,72
3428,42
3610,35

10 micrograms/liter aquarium 2:

2317,76
1878,45
3594,26
2317,76
3565,86
2771,05

The total length of the larvae is in micrometers. Thanks

#### obh

##### Active Member
It would be nice to have headers and units for the data ...

To find the residuals you should know the predicted value of H1.
If you try to use the two-sample t-test the predicated value of each group is the average of the group.

I checked the left column ...

Only the treated data is probably skewed
The residuals don't distribute normally ...(SW p-value 0.002809)

If you use the Mann Whitney U test the difference is significant 0.00003644
I would use the Mann Whitney U test.

So generally maybe if both were skewed and a transformation would make the residuals normal then the t-test
over the transformed data would be a bit more powerful than the MannWU test.
But when only one is skewed most likely the residuals won't distribute normally.
Greta?

#### Jonathan M

##### New Member
So, while doing the Mann Whitney U test, i need to consider the 2 aquariums of each group as one right?(when putting the data into the program
the data)