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

Area/Volume  
pdf review of all subtopics  
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 subtopics  
1  Direct proportionality  
2  Solving proportions, crossmultiplication  
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 subtopics  
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 subtopics  
Introduction  Introduction to exponential growth  
Growth vs. Decay  Growth or decay, with growth 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 subtopics  
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 subtopics  
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 subtopics  
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 subtopics  
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.  


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.  
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  
pvalues  
What is a pvalue?  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?  
Higherlevel 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.  
Higherlevel 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?  
ttests  
Introduction  coming soon...  
Examples  coming soon...  
ttest mechanics in Excel  Learn how to get Excel to calculate a ttest on your behalf...  
ttest mechanics in JMP  coming soon...  
ANOVA  
introduction  coming soon...  
Example  coming soon...  
ANOVA mechanics in Excel  coming soon...  
ANOVA mechanics in JMP  coming soon...  
Chisquare  
Chisquare calculations in JMP  Need to perform a chisquare 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. 