It sounds like your independent variable is ordered (categorical ordered), not just nominal categorical. You will probably want to take this into account in your analysis.

Thank you very much Dr. Salvatore for your suggestion. I am thinking of using Kruskal-wallis test but not sure if it is appropriate or not. Please let me know your view.

If your dependent variable is measured on a ratio scale, it means you can do almost any test. Kruskal-Wallis test is okay, only that it is not as robust as ANOVA. Remember that the Kruskal-Wallis test is a non-parametric test and is less rigorous compared to the parametric ANOVA test. If your dependent variable is categorical, it means you have both dependent and independent variables measured on an ordinal scale and for such a case you can measure strength of association using Goodman-Kruskals' Gamma coefficient.

Faruque As Sunny ,

The Kruskal-Wallis test is a possibility. I recommend using the Dunn test (1964) as a post-hoc test.

Since your groups are ordered, you might also be interested in seeing if there is trend. That is, if e.g. fertilizer use increases as typology increases (assuming this makes sense !). For this, you might use something like the Cuzick or Jonckheere–Terpstra tests. But something like Kendall correlation may be more familiar to your audience.

Thank you, Dr. Joseph, for your valuable suggestion. What concerns me is that the data are not normally distributed, and therefore I believe ANOVA or Goodman-Kruskals' Gamma test is not suitable. I request you to please correct me if I am mistaking.

I am also interested to know another issue on how to check the strength of association of these variables? For instance, Cramer's V (do not require normality of data) is used to check the strength of association between two categorical variables (dependent and independent).

Although point biserial correlation can measure the strength between a continuous and a categorical variable, it needs data normality. But as my data is not normally distributed hence, according to you, which test is appropriate to check the strength between a continuous dependent and a categorical independent variable?

Thank you very much.

Dr. Salvatore, thank you so much for sharing your view. As I am not familiar with those tests you have mentioned, I definitely will learn more about those. Thanks a lot again.

Hi, Faruque As Sunny . To some extent, the statistic you choose for the degree of association (effect size statistic), will depend on what statistical test or analysis you use. For example, if you use a traditional anova, you might use r-squared (or the equivalent eta-squared). But if you use Kruskal-Wallis, another statistic makes more sense with how you're approaching the data. Maybe maximum Cliff's delta or the epsilon-squared that is used with K-W.

Dr. Salvatore, thanks a lot for your valuable suggestions.

@Faruque Sunny, Goodman-Kruskals' Gamma does not require data normality. It is a robust test for association between ordinal data.

Dr. Joseph, thanks a lot again.

Dr. Salvatore, I cannot find any source stating how to conduct the Kruskal-Wallis epsilon-squared test in STATA. Could you please provide references that describe the STATA procedures? Thank you very much.

The variables of a research play a role (Role-Playing) in the target process .

Dependent role (strategic consideration of the researcher) and independent role (process stimulus).

Therefore, we can follow the cause and effect of target variables from different statistical methods. One of these methods: Causal research plan - comparative & ... Explore your own comparative world (Internal-system components strategy). &...

Faruque As Sunny ,

Some references that have the formula:

King, B.M., P.J. Rosopa, and E.W. Minium. 2018. Statistical Reasoning in the Behavioral Sciences, 7th ed. Wiley. Or 6th ed (2010).

Tomczak and Tomczak is an easily accessible source of the formula. http://tss.awf.poznan.pl/files/3_Trends_Vol21_2014__no1_20.pdf . "The need to report effect size estimates revisited. An overview of some recommended measures of effect size"

I attached the formula from Tomczak and Tomczak as an image.

I don't know about STATA specifically, but the formula is so simple, you should have no trouble calculating it by hand.

Note also that the formula reduces to H / (n-1) . I'm not sure why they also write it out in a longer form.

As an example, the following data:

A = (2,4,6,8,10,12)

B = (3,5,7,9,11,13)

C = (20,21,22,23,24,25)

H = 11.474

n = 18

epsilon-squared = 0.675

R code follows for this example.

_____________________________________

A = c(2,4,6,8,10,12)

B = c(3,5,7,9,11,13)

C = c(20,21,22,23,24,25)

Y = c(A,B,C)

Group = rep(c("A","B","C"), each=6)

Data =data.frame(Group, Y)

kruskal.test(Y~Group, data=Data)

# Kruskal-Wallis rank sum test

#

# Kruskal-Wallis chi-squared = 11.474, df = 2, p-value = 0.003225

library(rcompanion)

epsilonSquared(Y, Group)

# 0.675

H = 11.474

n = 18

H / ((n^2-1)/(n+1))

# 0.6749412

H / (n-1)

# 0.674941

Dear Seyyed Akbar Sadaty, thank you for your suggestion.

Dear Dr. Salvatore, thanks a lot for sharing the resources. After reading i felt we can not directly calculate through Stata and have to manually calculate after Swallis test. Thank you so much.

Check out a (Ecology, Environment and Conservation) Journal

Hi, Mateen Yilmaz Al-Bayati . I've read through all 123 issues of the Ecology, Environment, and Conservation Journal. It was only 2706 articles covering 21648 pages, so it didn't take too long. But I wasn't sure how what I was reading was relevant to this question. Would you be so kind as enlighten us as to what in this journal is relevant to the question OP asked ?

Sal Mangiafico please suggest how to interpret?

Faruque As Sunny , did you really have only one female observation? If so, there's not much use to trying a hypothesis test comparing males to females. You simply don't have enough information about the variability of the female group to make a comparison to the male group.

Dr. Salvatore, thanks a lot for the reply. I was also thinking to exclude this variable but was confused. Thank you again.