[FRIAM] statistics question

[Russell Standish]

A simple check you could do is check for Benford's law: https://en.wikipedia.org/wiki/Benford%27s_law

On Thu, Mar 13, 2025 at 08:33:09PM +0000, Marcus Daniels wrote:
> 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.
> 
>  
> 
> [cid]
> 
> 
> _ Cody Smith _
> 
> d00d3rs0n at gmail.com
> 





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Dr Russell Standish                    Phone 0425 253119 (mobile)
Principal, High Performance Coders     hpcoder at hpcoders.com.au
                      http://www.hpcoders.com.au
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