MCB111: Mathematics in Biology (Fall 2023)

week 04:

Significance: The Student’s t-test and p-values


Present all your reasoning, derivations, plots and code as part of the homework. Imagine that you are writing a short paper that anyone in class should to be able to understand. If you are stuck in some point, please describe the issue and how far you got. A jupyter notebook if you are working in Python is not required, but recommended.

How many types of dopaminergic neurons?

Dopaminergic neurons are thought to be involved in reward, and they appear to signal the difference between expected and actual reward. In order to investigate this, we have recorded firing rates from optogenetically-identified dopamine neurons in the lateral ventral tegmental area (VTA).

One set of recordings corresponds to mouse trained in a conditional task such that the reward always matched the expected rewards: data.0. In another set of experiments, the reward was always smaller than expected: data.1

You are given two other data sets: data.2 and data.3.

The role of dopaminergic neurons in reward is real see for instance this paper by the Uchida lab. The observation that there are different types of dopaminergic neurons is also documented. The data of this exercise is fake.