[FRIAM] statistics question

[Marcus Daniels]

You want a Wilconxon test. Here is an example for R.

# Load necessary libraries 
library(ggplot2) # For plotting 
library(stats) # For statistical tests (base R) 

# Example data (replace with your actual data) 
# admitted_ids <- c(1, 3, 5, 7, 10, 12) # Example admitted student IDs 
# waitlisted_ids <- c(15, 18, 20, 22, 25, 30) # Example waitlisted student IDs 

# Combine data into a data frame for plotting 
data <- data.frame( 
ID = c(admitted_ids, waitlisted_ids), 
Status = factor(c(rep("Admitted", length(admitted_ids)), 
rep("Waitlisted", length(waitlisted_ids)))) 
) 

# 1. Plot histograms with density 
ggplot(data, aes(x = ID, fill = Status)) + 
geom_histogram(aes(y = ..density..), alpha = 0.5, position = "identity") + 
labs(title = "Distribution of Student IDs", x = "Student ID", y = "Density") + 
theme_minimal() 

# 2. Box plot to compare medians and spread 
ggplot(data, aes(x = Status, y = ID, fill = Status)) + 
geom_boxplot() + 
labs(title = "Box Plot of Student IDs by Status", y = "Student ID") + 
theme_minimal() 

# 3. Mann-Whitney U Test (non-parametric, good for skewed data) 
mw_test <- wilcox.test(admitted_ids, waitlisted_ids, alternative = "two.sided") 
print("Mann-Whitney U Test:") 
print(mw_test) 

# 4. Kolmogorov-Smirnov Test (compare distributions) 
ks_test <- ks.test(admitted_ids, waitlisted_ids) 
print("Kolmogorov-Smirnov Test:") 
print(ks_test) 

# 5. Compare means 
mean_admitted <- mean(admitted_ids) 
mean_waitlisted <- mean(waitlisted_ids) 
cat("Mean ID (Admitted):", mean_admitted, "\n") 
cat("Mean ID (Waitlisted):", mean_waitlisted, "\n") 

# 6. Optional: T-Test (if data is roughly normal) 
t_test <- t.test(admitted_ids, waitlisted_ids) 
print("Two-Sample T-Test:") 
print(t_test) 

# 7. Quantify skewness (requires 'moments' package) 
# Install if needed: install.packages("moments") 
library(moments) 
skew_admitted <- skewness(admitted_ids) 
skew_waitlisted <- skewness(waitlisted_ids) 
cat("Skewness (Admitted):", skew_admitted, "\n") 
cat("Skewness (Waitlisted):", skew_waitlisted, "\n") 

# 8. Logistic regression (modeling probability of admission) 
model <- glm(Status ~ ID, data = data, family = "binomial") 
summary(model) 

From: Friam <friam-bounces at redfish.com> on behalf of cody dooderson <d00d3rs0n at gmail.com>
Date: Thursday, March 13, 2025 at 1:28 PM
To: The Friday Morning Applied Complexity Coffee Group <friam at redfish.com>
Subject: [FRIAM] statistics question 

I have a question concerning preschool admissions. The kindergarten that my daughter went to for preschool has a "random lottery" for admissions. They published a list of all of the student ids of the students who got in and the ones who did not and were put on a waitlist. 

She did not get in, so I decided that it was unfair and plotted the data. What statistical tricks should I use to figure out if the lottery was random or not? 

I have attached a plot of the data in question. To me, the plot looks slightly skewed towards the low numbers. The lower numbers are kids that signed up for the lottery earlier and I hypothesise have favorable connections in the school. 








_ Cody Smith _ 
d00d3rs0n at gmail.com <mailto:d00d3rs0n at gmail.com> 






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