[FRIAM] statistics question

Thu Mar 13 17:25:32 EDT 2025

Marcus;

Thank you for that. I blindly applied a few of those tests using scipy and
it looks like my null hypothesis failed, though the kolmogorov test was
very close.

Mann-Whitney U Statistic: 1020.0 P-Value: 0.09382801322415955 The accepted
list is random (fail to reject null hypothesis).

Kolmogorov-Smirnov Statistic: 0.3109090909090909 P-Value:
0.05816781698348724 The accepted list is random (fail to reject null
hypothesis).

_ Cody Smith _
d00d3rs0n at gmail.com

On Thu, Mar 13, 2025 at 2:56 PM Russell Standish <lists at hpcoders.com.au>
wrote:

> 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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