I have a slope data classified based on weather an area is vulnerable to erosion. Below is an example: vulnerability is a categorical variable (yes/no) and slope is a continuous variable ranging from 0 to 90.
I want to know if the slope of vulnerable areas is significantly different from that of non-vulnerable areas. At first, I performed unpaired two-samples t-test by classifying slope data into two groups based on vulnerability. Then, while I was looking into statistics for other dataset, I realized this dataset might be interpreted in a different way: one continuous variable (i.e., slope) and one categorical variable (i.e., vulnerable or non-vulnerable). If it is correct, ANOVA or logistic regression can be used? Also, I'm wondering which analysis (two continuous variables VS one categorical and one continuous variables) is more appropriate in my case. Thanks.
If I understand correctly, you are asking, if you have a continuous measure of vulnerability, should you dichotomize it. No. Lots of sources stating this, for example,
@article{MacCallumEA2002,
journal = {Psychological Methods},
year = {2002},
volume = {7},
pages = {19--40},
doi = {10.1037/1082-989x.7.1.19},
title = {On the Practice of Dichotomization of Quantitative Variables},
author = {Robert C. MacCallum and Shaobo Zhang and Kristopher J. Preacher and Derek D. Rucker},
}
Hello Jeongho,
I agree with Daniel Wright that collapsing a continuous variable into a categorical variable is generally not a good idea.
If what you wish to know is, do vulnerable and non-vulnerable sites have equal slopes, then the independent t-test you mention should probably be fine. If you have concerns about the distributional assumptions (normality, homogeneity), you can always turn to either an exact/permutation test, or the more commonly available bootstrap/resampling test option.
Good luck with your work.
If I understand the question, I think I'm going to disagree with some of the previous responses. I take the main point of the post to be,
"I want to know if the slope of vulnerable areas is significantly different from that of non-vulnerable areas."
In this case, yes, it makes sense to use something that compares the central tendency of slope for the two groups, like t-test, Wilcoxon-Mann-Whitney, a test for medians, and so on.
However, if the underlying idea is that the value of slope affects the vulnerability, it makes more sense to use logistic regression, with vulnerability as the dependent variable and slope as the independent variable.
Either approach makes sense for the research question.
I am going to offer another interpretation of the original question. Here is an excerpt:
At first, I performed unpaired two-samples t-test by classifying slope data into two groups based on vulnerability. Then, while I was looking into statistics for other dataset, I realized this dataset might be interpreted in a different way: one continuous variable (i.e., slope) and one categorical variable (i.e., vulnerable or non-vulnerable). If it is correct, ANOVA or logistic regression can be used?
I think that Jeongho Han may be describing the unpaired t-test as having two continuous variables--i.e., the DV for two different groups. Further, I think that ANOVA and logistic regression are being described as having one categorical variable and one continuous variable.
Jeongho Han, if that is what you meant, please note that the unpaired t-test also has one categorical variable (Group) and one quantitative variable (the DV). And t2 from an unpaired t-test = F from a one-way ANOVA on the same data--i.e., the two analyses are equivalent.
Re the choice between t-test (or equivalent ANOVA model) and logistic regression, use the former if the quantitative variable (slope) is the outcome variable, and the former if vulnerability (the dichotomous variable) is the outcome variable. What you've said suggests that slope is the outcome (or dependent) variable, so use the t-test (or equivalent ANOVA model).
Apologies if I have misinterpreted your question.
A t-test is sensible as the most simple statistic, but it feels odd. Mathematically, the t-test independent variable is erosion vulnerability and the dependent is slope. But the slope is the cause (i.e., independent variable) and erosion vulnerability is the effect (i.e., dependent variable). Mathematicians and scientists have slightly different definitions of "independent variable" and "dependent variable." Scientifically the intuitive model matching reality would be a regression; it's a sensible choice too. Regardless of what you choose, the result should be the same. To illustrate I've made up a simple data-set and analyzed it with a correlation, t-test, ANOVA, and regression (below). Notice the resulting p value is always the same because - at their essence - all of these statistical analyses are the same. Hope this helps, Jeongho! ~ Kevin
split biserial correlation: r=.505, p=.094
t-test: t(10)=1.852, p=.094
ANOVA: F(1,10)=3.429, p=.094
Regression (predict erosion from slope): r-squared=.255, p=.094
* In addition to the p value, notice other systematic relationships: the r from the correlation squared is the r-squared from the regression (.5052=.255) and the t-ratio squared is the F-ratio (1.8522=3.429).
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Thanks everyone for all answers and explanations. In particular, Bruce Weaver and Salvatore S. Mangiafico were helpful for me to understand the relevant knowledge and make it clear.
You have one continuous, independent variable and one dichotomous dependent variable, and an unpaired t-test is appropriate
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