# Non-parametric statistical test with two nominal variables

#### yamaneko

##### New Member
Hello everyone,:wave:

I have the following data: feces density of a carnivore species subdivided according to sex. I am looking for appropriate test suggestions.

I have calculated the density according to main habitat types, topography, and road types. To determine if results are statistically significant, I would believe the Friedman`s test or Wilcoxon signed-rank test would apply in this case since there is one continuous variable (feces density) and two nominal variables (e.g., habitat type and sex; road type and sex; topography and sex), and both are non-parametric statistical tests.

Any help would be greatly appreciated.

Thank you in advance!
:tup:

#### rogojel

##### TS Contributor
Hi,
any reason not to chose ANOVA? This seems to be a clear case of applying ANOVA unless your data is really ugly.

regards
rogojel

#### yamaneko

##### New Member
Hi rogojel,

Thank you for your reply! But would it be recommendable to use ANOVA with results that have very high SD?

Another thing I have being doing recently (Do I need to start another thread?) is to combine the categorical data with the feces data. I have been using a generalized linear model (GLM) , assuming binomial error and a log-link function with the response variable as binary data (male: 1, female: 0).

So by using R software:
> fit<-glm(y1~factor(x1)+factor(x2)+factor(x3)+factor(x4)+factor(x5),data=waterpots, family="binomial")
x1= main habitat type; x2= road type; x3= topography x4= habitat edge; x5= region

> fit<-glm(y1~factor(x1)+factor(x2)+factor(x3)+factor(x4)+factor(x5),data=waterpots, family="binomial")
> print(summary(fit))

Call:
glm(formula = y1 ~ factor(x1) + factor(x2) + factor(x3) + factor(x4) +
factor(x5), family = "binomial", data = waterpots)

Deviance Residuals:
Min 1Q Median 3Q Max
-1.52474 -0.70017 0.00008 0.87627 1.85253

Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) 2.9589 2.0162 1.468 0.1422
factor(x1)CV -2.0651 1.0310 -2.003 0.0452 *
factor(x1)NF -5.6497 4326.6475 -0.001 0.9990
factor(x1)RM 15.5040 1751.7149 0.009 0.9929
factor(x1)SF -3.2241 1.3603 -2.370 0.0178 *
factor(x1)SF 33.0701 4326.6464 0.008 0.9939
factor(x2)B 0.2057 0.7263 0.283 0.7770
factor(x3)200m 0.4085 1.7143 0.238 0.8116
factor(x3)50m -1.7452 1.3750 -1.269 0.2044
factor(x4)FoR 1.1621 4326.6465 0.000 0.9998
factor(x5)Hokugan 0.8208 1.5572 0.527 0.5981
factor(x5)Komi -16.9234 1751.7156 -0.010 0.9923
factor(x5)Mihara -0.6663 1.4276 -0.467 0.6407
factor(x5)Otomi 1.9076 1.9800 0.963 0.3353
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

(Dispersion parameter for binomial family taken to be 1)

Null deviance: 83.178 on 59 degrees of freedom
Residual deviance: 60.822 on 46 degrees of freedom
AIC: 88.822

Number of Fisher Scoring iterations: 16

> stepAIC(fit)

After the stepAIC, I get the following results:

Call: glm(formula = y1 ~ factor(x1) + factor(x3), family = "binomial",
data = waterpots)

Coefficients:
(Intercept) factor(x1)CV factor(x1)NF factor(x1)RM
2.70646 -1.73086 -2.49296 -0.05688
factor(x1)SF factor(x1)SF factor(x3)200m factor(x3)50m
-2.15445 14.81604 0.63379 -1.95643

Degrees of Freedom: 59 Total (i.e. Null); 52 Residual
Null Deviance: 83.18
Residual Deviance: 66.28 AIC: 82.28

I have two questions: Does this statistical analysis make any sense?

And does my interpretation of the results make any sense? Since the feces and sex data is binary(male=1 so results are positive, female=0 so results are negative), the results tell me that females are significantly attracted to CV and SF (two main habitat types). factor(x1)SF -2.15445 and factor(x1)CV -1.73086

Thanks!

yamaneko