I got aggregated patient data with patient numbers within different score ranges for males and females as the follow:
Score male (n) female (n)
1-10 17 15
11-20 21 13
21-30 24 26
31-40 17 19
41-50 16 15
51-64 6 14
How to statistically compare whether males have better scores than female?
If your scores are actually continuous, then a simple t-Test will do. Or, if the data were reported in ranges as you show, then recode each range to its mid-point (e.g., 1-10 would be 5.5) before doing the t-Test.
You may want to consider ordinal multinomial model which allows varying denominators and then a dummy to represent gender as the predictor variable. You are then modelling the (log-odds) of the proportion that gets that ordered score. This model deals quite naturally with what you call aggregated that is grouped data.
What I would recommend is to 1) Consider Score to be an ordinal variable. 2) Transform the data into long form, so that you have 203 observations (101 Male and 102 Female). 3) Use a test like Wilcoxon-Mann-Whitney test. 4) Calculate the probability of an observation in one group being larger than an observation in the other group.
The following is what I did in R.
p-value for the WMW test is 0.114.
Vargha and Delaney's A is 0.563. That can be interpreted as the probability that an observation in Female is greater than an observation in Male.
###
Data = read.table(header=TRUE, stringsAsFactors=TRUE, text="
ScoreGroup Gender Count
1 Male 17
2 Male 21
3 Male 24
4 Male 17
5 Male 16
6 Male 6
1 Female 15
2 Female 13
3 Female 26
4 Female 19
5 Female 15
6 Female 14
")
Long = Data[rep(row.names(Data), Data$Count), c("ScoreGroup", "Gender")]
rownames(Long) = seq(1:nrow(Long))
Long
wilcox.test(ScoreGroup ~ Gender, data=Long)
library(lattice)
Long$ScoreGroup.f = factor(Long$ScoreGroup)
histogram(~ ScoreGroup.f | Gender, data=Long, layout=c(1,2), col="darkgray")
library(rcompanion)
vda(ScoreGroup ~ Gender, data=Long, verbose=TRUE)
library(FSA)
Summarize(ScoreGroup ~ Gender, data=Long)
P. S.
I also ran a t-test on the midpoints of the groups and an ordinal regression. The R code below uses the data frame from my previous response.
Welch's t-test: p-value = 0.0984. Cohen's d = 0.233.
Ordinal regression: p-value = 0.113.
Upshot: any of these methods leads to similar conclusions. The mean or mean rank for Female is slightly higher than for Male. But the distributions of observations between these two groups is relatively similar. Both center on the 21 - 30 response category, with Female having higher proportions of the higher response categories than Male. Hypothesis tests do not support the conclusion that the responses between the two groups are statistically significantly different.
###
library(ordinal)
model = clm(ScoreGroup.f ~ Gender, data=Long)
anova(model)
### p = 0.113
Midpoint = c(mean(c(1,10)), mean(c(11,20)), mean(c(21,30)), mean(c(31,40)), mean(c(41,50)), mean(c(51,64)))
Long$Midpoint = Midpoint[Long$ScoreGroup]
## histogram(~ Midpoint | Gender, data=Long, layout=c(1,2), col="cornflowerblue")
t.test(Midpoint ~ Gender, data=Long)
### p = 0.984
library(FSA)
Summarize(Midpoint ~ Gender, data=Long)
library(lsr)
cohensD(Midpoint ~ Gender, data=Long)
Before suggesting a test I would want to know a little bit about the data. First, these are 100+ patients. Are they from different hospitals, different doctors, etc.? The previous responders are making some assumptions about this. Second, please say something about what the response variable is, and do you have access to the non-binned scores?
Thank you all very much for your expert inputs!
Dr. Wright: this data came from a database query. The patients were from different countries and I did not have access to the individual score.
Jianli Sun , sounds like more information is needed before thinking whether doing a significance test is justified. What other information do you have available for who these cases were sampled? The norm with much patient data is that they are nested within doctors/hospitals, etc. If you do not have this information, I would find it before doing any significance test (which many would argue is of limited value anyway).
- Badges
- Science topic
- Similar topics
- Mathematical Sciences
- Statistics
- Statistical Software
- SPSS