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!
	6	Do it. Learn more. Go ahead...
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?
Quadratics
	pdf review of all sub-topics
	1	What is a quadratic equation? Solving quadratics using the quadratic formula.
	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.