Prerequisites: HCS 6312, Research Methods I

(may be waived with instructor permission)

Course Description:

This course will provide instruction in the fundamentals of advanced statistical analysis as the basis for selection and application of appropriate tests widely employed for neuroscience research. The course will review specific examples of published studies that illustrate the proper application of these tests and their particular advantages for neuroscience research. The course will also review other quantitative methods that are frequently employed in neuroscience research and must be understood in detail to fully appreciate the power of such methods and the significance of such research.

Contemporary research in the neurosciences employs a wide range of mathematical tools in addition to the statistical methods that quantify the reliability of experimental results. Every neuroscientist needs a basic understanding of the mathematical underpinnings of these tools to appreciate the particular insights they may provide, as well as their limitations and proper uses in neuroscience research.

In addition to the topics listed in the following tentative outline, particular attention will be given to quantitative methods that appear prominently in published research identified by students enrolled in the course:

1st half Instructor Dr. Larry Cauller

1. The Practice of Statistics in the Neurosciences – Overcoming the inferiority complex most researcher’s suffer when it comes to statistics.

a. ‘Descriptive’ Statistics – taking a good look at your sample distribution as a reflection of the population.

b. ‘Inferential’ Statistics and the power of the ‘Central Limit Theorem’.

c. Assumptions and Robustness

d. The weakness of Statistical ‘Power’ – why science is only built upon positive result.

e. Decision-based versus experiment-wise error rates – Bonnferonni’s correction

f. The a priori demands of Spartan Statisticians versus the post-hoc realities of research in the real world.

g. The limitations of multi-level ANOVA tests and the dangers of multi-factor interactions – Dr. Cauller’s biggest pet peeve about statistics.

h. The necessity of specific contrasts to overcome the limitations of ANOVA tests.

i. Types of data in the neurosciences: When it’s best to use non-parametric statistics – those pesty outliers.

2. Specific contrast (multiple comparison) methods

a. Including: Tukey’s, Newmann-Keuls and good ol’ Student’s t-test (Dr. Cauller’s favorite – non-conservative and high power)

b. Choosing a good comparison test – conservative versus powerful

c. Non-parametric comparison tests – Rank-sums, Mann-Whitney U, Sign-test

d. Why t-tests can handle just about anything without assuming equal variance

e. Pitfalls and rules.

3. Specific applications of statistical methods in published neuroscience research

a. Review of statistical methods commonly found in published neuroscience research.

b. Special attention to statistical methods the students find in their own readings

4. Electrophysiological data analysis: Looking through the neuro-electric keyhole?

a. Bio-electric signal generation: current-source density

b. Neural electrodes: where the metal meets the mush: Electro-chemical Impedance

c. Electrometers: Amplification and the effects of filtering

d. Levels of neuro-electric analysis – from inside neurons to the surface of scalp

5. Digital Signal Analysis - From wet neurons to computers

a. Discrete sampling of continuous neural signals – Sampling rate and bit precision

b. Time-locked averaging and evoked potentials – detecting faint messages amidst the roar of a noisy brain

c. Spike signals – the least ambiguous measure of neuron activity

i. Introduction to NeuroExplorer – state-of-the-art software for spike signal analysis

ii. peri-stimulus time histograms (PSTH)

iii. inter-spike-intervals (ISI)

iv. auto- and cross-correlograms

v. Information theory and the analysis of confusion

6. Quantitative analysis of microscopic neural structure

a. Introduction to ImagePro – state-of-the-art software for tissue image analysis

b. Matching the spectra of fluorochromes and filters – contemporary microscope methods

c. Effective sampling methods for counting and measuring neurons with statistical confidence

d. Quantitative analysis of relative label intensity

7. The Euler constant and nature’s pivotal difference equation – its pervasive role in neuroscience theory and methods

a. Length and time constants

b. Kinetics and active bio-physics

8. Numerical simulation versus analytical solutions

a. The limits of simplification

b. Dynamical systems and intractability

2nd half instructor Dr. Marco Atzori

1) Elements of calculus

2) Fourier Transforms: formant analysis

3) Auto- and cross-correlation function: NMR decay time, synchronization in neuronal ensembles

4) Distributions / Dirac-d function / random number generation/ binomial and Poisson distributions

5) Quantal analysis in synaptic transmission (Salgado)

6) Coefficient of variation analysis in synaptic transmission

7) Noise analysis in single-channel conductance measurement

8) Wavelet analysis

9) Single-cell, single-compartment Hodgkin and Huxley model (Lu Dinh)

10) Multiple compartment HH, interneuronal network (Tram Nguyen)

Student Learning Objectives:

After completing the course, students should be able to:

1.1 Identify and select statistical tests appropriate for the majority of uses in neuroscience research.

1.2 Explain the importance of descriptive statistics and employ such statistics to characterize the sample distributions of neuroscience data..

1.3. Describe the limitations and pitfalls of ANOVA tests with respect to multi-factor and multi-level experimental designs.

1.4. Explain the importance of multiple comparison tests and employ such tests to overcome the limitations of ANOVA tests.

2.1 Describe the mathematical underpinnings of a wide range of quantitative methods, in addition to statistics, commonly employed in the neurosciences.

2.2 Characterize major types of neuroscience data from neuro-electric signals to microscopic images of neural structures.

2.3 Identify the particular quantitative methods employed in contemporary neuroscience research for the analysis of these major types of data.

3. Interpret and criticize published applications of advanced statistical and other quantitative methods.

4. Identify and describe the capabilities of state-of-the-art software applications widely available for statistical and other quantitative analyses useful for neuroscience research.

Textbooks and materials:

No textbooks are required for this course.

Students are encouraged to find a friendly statistics textbook with an emphasis upon practical applications and step-by-step calculations. (Students are invited to study excerpts from Dr. Cauller’s out-of-date text.)

The course will require students to make extensive use of PubMed search tools and access electronic neuroscience journals on-line.

Exams and student assignments

Exams: Students will be required to take two exams, a mid-term exam related to topics presented by Dr. Cauller, and a final exam related to the topics presented by Dr. Atzori Each exam will be administered during a single class period. Student will be expected to describe and interpret analytical methods related to figures taken from published neuroscience studies.

Assignments: Students will be asked to find specific examples of published applications of both statistical and other quantitative methods from the contemporary neuroscience literature and discuss these examples in class.

Attendance: Student attendance and participation in each class will be directly noted by the instructors.

Grading Policy

20% of the overall grade will be based upon student attendance and participation.

40% of the overall grade will be based upon student performance on each of the two exams.

Course policy

Professionalism: In appreciation of the multidisciplinary nature of this course, students will be expected to respect the importance of every topic by participating in each class with as much enthusiasm as they have for topics specifically related to their personal interests.

Downloads

16 Jan –

AQMdesStatsI.xls

AQMdesStatsII_moments.xls

AQMdesStatsIII_flat.xls

AQMdesStatsIII_normalized_flat.xls

AQMinfStatsV_CentralLimitTheorem.xls

18 Jan –

AQM_PracticalStatistics_Para.pdf

AdvQuantMeth_SquaredDeviationDerivation.doc

23 Jan –

AQM_PracticalStatistics_nonPara.pdf

Link to Wikipedia_on_Statistics – beware, Mann-Whitney U-table link is simply wrong.

Advanced methods demonstrated with Excel

Student's t-test

Correlation and Trend analysis

non-parametric vs t-tests

FFTdigitalFiltering

Discrete Sampling and Sampling Errors

Percentage Transform

ANOVA power

Advanced methods

Correlogram

Effect Magnitude and Data Transformation

Link to Statistical Power Analysis Java Applets (sophisticated)

Link to ANOVA Power Analysis (simple)

ImmunoHistoChemistry Methods

Quantitative Double Labeling

Selecting Fluorochromes

These descriptions and timelines are subject to change at the discretion of the Professor.

Date	Topic	Assignments and Due Dates
Week 1 Jan. 9	Dr. Cauller – Introduction and Orientation to the Course Introduction to using MS Excel for class demonstrations	Find a published application of statistics in your research area
Jan. 11	Practical Statistics in the Neurosciences Descriptive Statistics and Population Distributions The Limitations of ANOVA
Week 2 Jan. 16	Application of Statistics in Neuroscience Research Inferential Statistics and The Power of the Central Limit Theorem Assumptions, Robustness and Pitfalls The Impractical Notion of Statistical Power – Why science is only built upon positive results. Types of Neuroscience Data – Non-parametric statistics.
Jan. 18	Using Specific Contrast Statistical Tests – Beyond ANOVA
Week 3 Jan. 23	Applications of Statistics in Published Neuroscience Research Review of examples of published applications of statistics
Jan. 25	Student-led discussion of specific examples of published statistical applications related to their individual neuroscience interests	Presentation of published applications of statistics in neuroscience research
Week 4 Jan. 30	Quantitative Methods for the Analysis of Neuro-Electric Signals Principles of Neuro-Electric signal generation Levels of Neuro-Electric analysis – intracellular to EEG	Find a published study that employs quantitative tools for the analysis of neuro-electric signals
Feb. 1	Digital Signal Analysis – Analog-to-Digital Conversion The Power of Time-locked Signal Averaging Quantitative Analysis of Spike Signals – Intro to NeuroExplorer
Week 5 Feb. 6	Student-led discussion of published examples of quantitative neuro-electric signal analysis	Presentation of published examples of neuro-electric signal analysis
Feb. 8	Quantitative Analysis of Microscopic Neural Structure Fluorescence microscopy – experimental design and controls Sampling methods for counting and measuring labeled neurons	Find example of quantitative micro-structure analysis in published neuroscience research
Week 6 Feb. 13	Introduction to ImagePro – state-of-the-art software from the NIH Quantifying relative label intensity
Feb. 15	Student-led discussion of published applications of quantitative micro-structure analysis in neuroscience research	Presentation of published neuroscience research that employed micro-structure analysis

Date

Topic

Assignments and Due Dates