Nonparametric test for a factorial desing (2 x 3)

[Vieira]

Dear,

First of all, thanks for this support!

Questions: We have an experimental two factors design (3 different substrates and 2 different fungi) and I'm struggling to find how to use a nonparametric test to compare in such way:

Substrate       Fungus 1     Fungus 2

    D5                    X                 X

    D10                  y                 y

    D15                  z                 z

I would like to compare Fungus 1 within different Substrates; Fungus 2 within different Substrates; Fungus 1 and Fungus 2 within the same substrate (e.g. D5..)... Any idea how to proceed with this analysis?

Thank you in advance.

Fabricio.

[sld]

Do you have replications? If so, what is your experimental design (e.g., completely randomized, split plot)?

What is your response variable, and what sort of values does it take?

Why do you think you need a nonparametric test?

[Vieira]

First of all, thank you for a quick reply.

Questions:
- Do you have replications? If so, what is your experimental design (e.g.,
completely randomized, split-plot)?

The experimental design is a completely randomized and each treatment have
10 replicates, ie., 3 different substrates * 2 different fungi = 6
treatments * 10 replicates = 60 experimental units.

- What is your response variable, and what sort of values does it take?

The response variable is the mushroom yield, i.e, the percentage of
mushroom (kg of mushroom/kg of the substrate * 100). The values are
presented in percentage.

- Why do you think you need a nonparametric test?

Because by using a Shapiro-Wilk test seems to be a not normal distribution
and I tried using the ANOVA and Tukey test. Since the Tukey test is used
for a parametric test I'm not sure how or which test can be used to verify
the data normality for 2 x 3 factorial design and if the dataset is not
normal what Post hoc test I can use for a factorial design and
nonparametric.

I would like to discuss the data in that way if it is possible:

*Substrate Fungus 1 Fungus 2*
D5 33 Aa 28 Ab
D10 29 Aa 27 Ba
D15 23 Ba 22 Ca

Uppercase letter in the column (*Fungus 1* by varying the substrate and *Fungus
2* by varying the substrate).
Lowercase letter in the rows (*Fungus 1* and *Fungus 2* in the same
substrate).

PS: Here is how the dataset looks like:

Substrates Fungus Mush. Yield
D5 F1 39.76
D5 F1 34.18
D5 F1 33.76
D5 F1 33.52
D5 F1 30.96
D5 F1
35.85
D5 F1
35.35
D5 F1
27.18
D5 F1
32.35
D5 F1
30.52
D5 F2 33.91
D5 F2
33.75
D5 F2
33.27
D5 F2
36.48
D5 F2
25.77
D5 F2
21.60
D5 F2
35.93
D5 F2
31.71
D5 F2
30.90
D5 F2
35.38
D10 F1
31.40
D10 F1
33.17
D10 F1
22.27
D10 F1
23.15
D10 F1
34.10
D10 F1
30.58
D10 F1
30.62
D10 F1
31.48
D10 F1
32.37
D10 F1
44.06
D10 F2 21.68
D10 F2
16.73
D10 F2
21.10
D10 F2
20.24
D10 F2
22.37
D10 F2
15.73
D10 F2
23.00
D10 F2
21.56
D10 F2
21.60
D10 F2
28.27
D15 F1 32.42
D15 F1
27.46
D15 F1
32.22
D15 F1
15.78
D15 F1
31.40
D15 F1
28.87
D15 F1
25.47
D15 F1
34.32
D15 F1
19.03
D15 F1
20.68
D15 F2 20.01
D15 F2
27.36
D15 F2
7.78
D15 F2
16.50
D15 F2
18.47
D15 F2
19.96
D15 F2
15.90
D15 F2
18.76
D15 F2
27.55
D15 F2
20.46

Thanks again!
Best,
Fabricio.

[PaigeMiller]

Because by using a Shapiro-Wilk test seems to be a not normal distribution

This sentence is extremely difficult to understand.

The distribution of your data's errors (not the distribution of the data itself) must be normal to do ANOVA. What do you think the distribution of the errors is? If you do an ANOVA and plot the residuals, do they have a normal distribution?

[Vieira]

Hi Miller,

"This sentence is extremely difficult to understand."

Sorry to not be clear enough and to make the mentioned sentence extremely difficult to understand. I don't know about the distribution of the errors but I can check that and I will. Should I use a factorial test (any specific?) and then run an ANOVA using a parametric test and check the distribution of the errors?

Fabricio.

[PaigeMiller]

Run the standard 2-way ANOVA and check the distribution of the residuals.

[Vieira]

Sorry about the mess in the previous post... here is how we would like to see the data:

Substrate     Fungus 1    Fungus 2
   D5                  33 Aa         28 Ab
   D10                29 Aa         27 Ba
   D15                23 Ba         22 Ca

Uppercase letter in the column (Fungus 1 by varying the substrate and Fungus 2 by varying the substrate).
Lowercase letter in the rows (Fungus 1 and Fungus 2 in the same substrate).

Thanks again!

Fabricio.