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 _ [email protected] On Thu, Mar 13, 2025 at 2:56 PM Russell Standish <[email protected]> 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 <[email protected]> on behalf of cody dooderson > > <[email protected]> > > Date: Thursday, March 13, 2025 at 1:28 PM > > To: The Friday Morning Applied Complexity Coffee Group < > [email protected]> > > 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 _ > > > > [email protected] > > > > > > > > > .- .-.. .-.. / ..-. --- --- - . .-. ... / .- .-. . / .-- .-. --- -. --. > / ... --- -- . / .- .-. . / ..- ... . ..-. ..- .-.. > > FRIAM Applied Complexity Group listserv > > Fridays 9a-12p Friday St. Johns Cafe / Thursdays 9a-12p Zoom > https://bit.ly/virtualfriam > > to (un)subscribe http://redfish.com/mailman/listinfo/friam_redfish.com > > FRIAM-COMIC http://friam-comic.blogspot.com/ > > archives: 5/2017 thru present > https://redfish.com/pipermail/friam_redfish.com/ > > 1/2003 thru 6/2021 http://friam.383.s1.nabble.com/ > > > -- > > > ---------------------------------------------------------------------------- > Dr Russell Standish Phone 0425 253119 (mobile) > Principal, High Performance Coders [email protected] > http://www.hpcoders.com.au > > ---------------------------------------------------------------------------- > > .- .-.. .-.. / ..-. --- --- - . .-. ... / .- .-. . / .-- .-. --- -. --. / > ... --- -- . / .- .-. . / ..- ... . ..-. ..- .-.. > FRIAM Applied Complexity Group listserv > Fridays 9a-12p Friday St. Johns Cafe / Thursdays 9a-12p Zoom > https://bit.ly/virtualfriam > to (un)subscribe http://redfish.com/mailman/listinfo/friam_redfish.com > FRIAM-COMIC http://friam-comic.blogspot.com/ > archives: 5/2017 thru present > https://redfish.com/pipermail/friam_redfish.com/ > 1/2003 thru 6/2021 http://friam.383.s1.nabble.com/ >
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