Statistics

Statistics is an inevitable part of research but not necessarily an inevitable or significant part of undergraduate education.

Since neuroscientists come from a diverse range of backgrounds, knowledge and understanding of statistics can vary greatly from person to person so here are some resources on statistics in neuroscience flavor.

Applied Statistics for Neuroscience (UC Berkeley)

The materials for a UC Berkeley course called Applied Statistics for Neuroscientists are available on GitHub. The course is an intensive introduction to statistics and provides an opportunity to gain a solid understanding of frequently used statistical methods in neuroscience which are not always explained in depth.

The course constitutes of tutorials and labs in Jupyter notebooks, which are organized into three parts:

Part 00: Setup and Review

  • 00 - Setup

  • 01 - Probability and Statistics Review

    • Lab A - Probability and Python
    • Lab B - Statistics with Pandas and Seaborn

Part 01: Statistical Testing

  • 02 - Inferential Statistics and Error Bars

    • Lab A - Inferential Statistics
    • Lab B - Error Bars

  • 03 - Hypothesis Testing

    • Tutorial - Hypothesis Testing
    • Lab - Hypothesis Testing

  • 04 - Tests for 2-Sample Data

    • Tutorial - Tests for 2-Sample Data
    • Lab A - Unpaired t-tests
    • Lab B - Paired t-tests and Non-Parametric Tests

  • 05 - ANOVA I

    • Tutorial - ANOVA by Hand
    • Lab - One-Way ANOVA

  • 06 - ANOVA II

    • Tutorial - Two-Way Anove by Hand
    • Lab A - Two-Way ANOVA
    • Lab B - Multiple Comparisons and ANOVA

Part 02: Statistical Modeling

  • 07 - Linear Algebra

    • Tutorial - Linear Algebra for Neuroscientists
    • Lab - Linear Transformations

  • 08 - Bootstraping and Correlation

    • Tutorial A - Sampling and Bootstrapping
    • Lab A - Visualizing Bootstrapping and One-Sample Tests
    • Tutorial B - Dependence and Correlation
    • Lab B - Computing and Bootstrapping Correlation

  • 09 - Model Specification

    • Lab - Visualizing Models

  • 10 - Model Fitting

    • Lab -Fitting Models

  • 11 - Model Accuracy and Reliability

    • Lab - Model Accuracy and Reliability

  • 12 - Classification

    • Lab - Classification

  • 13 - Clustering

    • Tutorial - Clustering

Since the code used for examples is written in Python, familiarity with the language would be helpful and is therefore recommended.

Attention

To prevent errors while running the notebooks, ensure the latest versions of matplotlib and seaborn are installed on your computer. Enter the command

$ pip install --upgrade --user matplotlib

into Terminal or Command Prompt.

Error

Before you start Part 02-10: Model Fitting, open utils.py in the util folder and comment out all instances of ax.set_aspect('equal'). This command does not apply to 3D plots and will therefore prevent them from rendering.

An equivalent function called axis_equal_3d was included instead, which was written by Stack Overflow user Ben as a response to this post.

Statistics and Data Analysis Tutorial (Center for Brains, Minds and Machines)

The Brains, Minds and Machines (BMM) Summer Course by The Center for Brains, Minds and Machines (CBMM) at MIT is a three-week course on computation, neuroscience, and cognition in the fields of human and machine intelligence research.

The Statistics and Data Analysis tutorial from the 2018 BMM summer course is available on Youtube. It is a quick overview of the basics of statistics by Ethan Meyers.

00:00-10:13:Introduction
10:14-12:22:Box and violin plots
12:23-13:42:Joy plots
13:43-14:52:Dynamite plots
14:53-16:40:What is a statistic?
16:41-18:26:Correlation coefficient
18:27-19:22:Descriptive statistics
19:23-19:48:Population/process parameters
19:49_-20:11:Statistical Inference
20:12-20:24:Estimation
20:25-22:27:Regression
22:28-23:56:Sampling Distribution
23:57-24:29:Estimation (continued)
24:30-27:17:Confidence intervals
27:18-33:17:Bootstrapping, 95% confidence interval
33:18-35:05:What is a p-value?
35:06-40:34:Hypothesis testing
40:35-41:34:Permutation tests, parametric tests
41:35-43:29:Visual hypothesis tests
43:30-53:50:Permutation test example
53:51-58:28:Type I and Type II errors
58:29-1:03:44:Multiple hypothesis tests
1:03:45-end:Data Science

Statistics for Brain and Cognitive Science (MIT)

Statistics for Brain and Cognitive Science is an MIT course that covers three main topics: probability theory, statistical theory, and the linear model. It includes topics such as estimation, Bayesian methods, bootstrap, hypothesis testing, and confidence intervals.

The course materials from fall 2016, including the syllabus, lecture notes, and assignments, are available for download on MIT OpenCourseWare.