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