11.1 t-test for a paired difference in marble masses

Students select two marbles from a box, one from each side of a divided box. One side includes marbles less than or equal to 5.2 grams, the other side contains marbles greater than 5.2 grams. 



Data from spring 2026 demonstrated that students could distinguish which marble was more massive using a paired t-test and an alpha of 0.05.


The ability of Desmos to display the t-distribution graphically (and calculate t-ciritical from data) allows for the graphical display of the result.


The t-test capability displays the p-value based directly on the data. Desmos has become a powerful tool for displaying statistical results graphically.


Calculating t-critical involves using tdist(n-1).inversecdf(0.975) for a 95% confidence interval. In the above example the test is an independent samples t-test, not a pairwise test of the differences. 

Desmos

To do a pairwise t-test the data has to be the pairwise differences, which can also be done as seen above. 

Desmos


This term the inversecdf input was altered to display the confidence interval. Once again the pairwise difference was significant.


A chi square test, which is perhaps more appropriate in this situation, concurs.

Comments

Post a Comment

Popular posts from this blog

Moodle bulk grading of manually marked quiz and test questions

Image
Manual marking of an essay type question on a quiz or test in Moodle can be done student by student but that process involves a lot of clicking and scrolling as one has to open each student's submission. There is a bulk marking screen available. In the test or quiz click on Results. At the upper left side is a stealth drop down list menu under the word "Grades" that includes the option "Manual grading." Choose manual grading. On the far right click on the blue "grade all" hyperlink. That will open up a all of the submissions for question one on a single page. One can now mark all of the question one submissions manually for all students in the course. 
Read more

Experimenting with the PlantNet and iNaturalist apps

Image
The application of image recognition technologies as the back end to botany apps is providing increasingly relevant search results. Over the recent winter break I began looking at whether the apps now available might be useful to the ethnobotany class here on Pohnpei. Some apps had a more regional focus in the past and were better at north american or european plants. Pohnpei has a both unique indigenous plants and many introduced plants from around the world -  a challenging environment for any image recognition system. A student working with a plant identification app for the first time My criterion was that the app had to be appropriate for use in my classroom. The app could not contain advertising and the app had to be free, my students typically do not have the ability to pay for an app. The app would also have to be fairly small as my students often use phones with limited memory and processing power. I settled on PlantNet and was impressed with the ability of the a...
Read more

From Canvas to Moodle

Image
Migration  There is no option to migrate from Instructure Canvas to Moodle by exporting courses from Canvas and importing those courses into Moodle. Canvas exports courses as Instructional Management Systems Common Cartridge version 1.1 files. Moodle only imports IMS Common Cartridge 1.0 files. The versions are incompatible and as far as this author is aware there are no converters between the versions.  IMSCC 1.0 is a 2008 standard and IMSCC 1.1 dates back to 2011 or earlier. In other words, both versions are out of date. The current version is IMSCC 1.3 and IMSCC 1.4 is under development. Neither Instructure nor Moodle appear to be working on code to handle any newer IMS CC version. The inability to easily move courses between learning management systems benefits vendor lock in.  As a result, migration is a heavy lift manual process of rebuilding element-by-element from a blank sheet. Or one can pay a third party significant sums of money to handle the migration. T...
Read more