Quantitative Biology

in the Classroom

# Tutorials

Below are links to videos and pdf tutorials for core mathematical and statistical concepts used in biology. Enjoy!

Topic Sub-Topic Description
Area/Volume
pdf review of all sub-topics
1 Why surface area and volume matter in biology. Area and perimeter for circles and squares.
2 Volume of a cylinder. Volume and surface area of a rectangular prism.
3 Effect of changing side length on surface area and volume... different rates of growth.
4 Example of surface area and volume and their ratio

Proportions
pdf review of all sub-topics
1 Direct proportionality
2 Solving proportions, cross-multiplication
3 Using proportions in population estimation of wild animals: Capture (Mark)-Recapture explanation and example
4 Capture (Mark)-Recapture example

Ratios/Percents
pdf review of all sub-topics
1 Defining a ratio, with two examples
2 Normalizing data as a ratio, with example
3 What is a percent?
4 Example of percent calculations
5 Effective percent, or percents as a measure of change
6 Percent change and percent error

Exponentials
pdf review of all sub-topics
Introduction Introduction to exponential growth
Growth vs. Decay Growth or decay, with growth example

Decay example

Decay example
More examples You are going to have to click it.
Doubling time How long will it take a population to double in size?You are going to have to click to find out!

Logarithms
pdf review of all sub-topics
Introduction Basics of logs and the "common" logarithm
Logs and exponents examples Relationship between logs and exponents
Investigating logs graphically Basic graph of a logarithmic relationship with some observations
Properties of logs Using logs to solve exponential equations
pH and logs Why is pH measured on a logarithmic scale, and how do we interpret it?
Earthquakes and logs The intensity of earthquakes are measured on a logarithmic scale - why?

pdf review of all sub-topics
2 Three examples using the quadratic formula
3 Solving a quadratic equation in a biological example.
4 Solving a quadratic equation in a physical example.

Probability
pdf review of all sub-topics
General definitions Need a refresher on basic probability rules?
Basic examples Practice, practice, practice!
Punnett squares - probability in genetics See how probability can help us understand the inheritance of allells.
Tree diagrams to understand probabilities This video shows how a simple visual diagram can help us track compound probabilities.
Sampling w/ and w/o replacement When we sample, do we include individuals already selected as candidates for the next sample? Does it matter?

Binomial distribution
pdf review of all sub-topics
Factorials: Definition and examples Before we get to the binomial, we need to understand factorials.
Combinations ...and we also need to understand how the same result can be produced by several differen combinations of events.
Binomial distribution - formula How do we compute expected outcomes?
Binomial distribution - example How can we use the binomial formula in the real world?
Binomial distribution - multipart example Another example for you to practice...

Statistics

Why statistics?
Why do we need stats? Why do biology students need to understand statistics? Start here if you aren't sure why!
Sampling
Populations versus samples Why do we sample, and what implications does that have for our understanding?
Data types
Categorical versus quantitative Data come in many forms. Learn about the basic data types here.

Summary statistics

Central tendency
Mean, median Review the concepts of mean and median here.

Variability
Random processes What processes contribute to the "noise" we see in real data? Why is this important to know? What does a biologist mean when they talk about "random error", "measurement error", or "uncertainty"?
Why is variability important in biology? Consider why variability in measurements is vitally important for the biologist, and learn how to calculate variance.
Standard deviation Review how to calculate the standard deviation.

Data distributions
Normal and Uniform distributions Data can have very different basic properties. Learn about the normal and uniform distributions.
Poisson and Negative Binomial distributions - counts Many data in biology are counts - counts of individuals, events, outcomes, etc. Counts often have their own unique kind of distribution.
Binomial distribution When there are several events, each with either a yes/no, success/failure outcome, the data will often be distributed according to the binomial.

Graphing
Single variables
Frequency histogram Learn why and how to display the frequency of different values of a single variable.
Frequency histogram mechanics in Excel Need to make a frequency histogram in Excel? Learn how.
Frequency histogram mechanics in JMP Need to make a frequency histogram in JMP? Learn how.

Several variables
Introduction There are lots of ways to explore and display relationships between two or more variables. We cover the basic approaches here.

Scatterplot mechanics in Excel

Need to make a scatterplot in Excel? Learn how.
Scatterplot mechanics in JMP Need to make a scatterplot in JMP? Learn how, and along the way learn how to conduct a linear regression analysis on the same data.
Bar chart mechanics in Excel ... I bet you can guess...
Bar chart mechanics in JMP :-)
Line graph mechanics in Excel ... I bet you can guess...
Line graph mechanics in JMP :-)

Inferential statistics
Standard error amd confidence intervals What are confidence intervals and why/how do we use them? What are these things, and how can we interpret them?
How do we calculate confidence intervals? How to calculate a simple confidence interval assuming normally distributed data... and see the standard error of the mean along the way

p-values
What is a p-value? What are these things, and how can we interpret them?

Linear Regression
Introduction What is it, and why do we use it so much?
Strength and confidence How can we assess the strength of a relationship between two quantitative variables, and how confident can we be that an apparent relationship is real?
Higher-level thinking about regression I Applying regression in meaningful and appropriate ways requires one to have a nuanced understanding of what we are doing... learn more here.
Higher-level thinking about regression II Yeah, watch this one too.
Regression mechanics in Excel Just need a refresher on how to get Excel to calculate and plot a regression?
Regression mechanics in JMP Just need a refresher on how to get JMP to calculate and plot a regression?

t-tests
Introduction coming soon...
Examples coming soon...
t-test mechanics in Excel Learn how to get Excel to calculate a t-test on your behalf...
t-test mechanics in JMP coming soon...

ANOVA
introduction coming soon...
Example coming soon...
ANOVA mechanics in Excel coming soon...
ANOVA mechanics in JMP coming soon...

Chi-square
Chi-square calculations in JMP Need to perform a chi-square test? Want to use JMP? Start here...

Other stuff...
Image analysis
The basics... Setting the scale and making linear measurements
Labeling.. Leave a mark after each measurement to track which objects have been measured
Exporting data... Get your data out of ImageJ and into Excel or JMP

Formatting Data
Entering and formatting data in JMP The basics of getting started with JMP
Using Pivot Tables in Excel Need to get summary statistics, rearrange data, or avoid lots of cutting and pasting? Pivot Tables offer a powerful approach to do some complicated things, FAST.