∞ generated and posted on 2020.12.19 ∞
This module considers the basics of probability theory, graphing, and determination of variance.
| The goals of the associated laboratory exercise are to gain an appreciation for the concepts of variance and stochasticity, the basics of probability theory, the difference between a prediction and an observation, and to provide practice in the drawing of graphs and the generation of tables. Here also considered is that of biases in thinking. |
The above video simply shows a dice rolling in slow motion.
This learning module considers the basics of probability theory such as can be seen when using one or more six-sided dice (or die, whichever you prefer as the singular). We also will take a look at the independence of events as well as what changes, in terms of probabilities, when events instead are dependent. Note regardless that everything is easier given independence so, if at all possible, scientists tend to concentrate on independent events, at least to start with, only finding themselves dragged into non-independence when they absolutely have to and/or because a lack of independence appears to underlie an interesting phenomenon.
We will consider in association with independent events what is known as the Multiplication Rule (which, unfortunately, happens to be a different thing from the Rule of Product or Multiplication Principle). We also will consider what is known as the Addition Rule. Lastly, we will finish up with the consideration of basics of graphing, variance, and what sorts of biases can enter into the scientific process.
We start with the Multiplication Rule.
The above video introduces the probability theory Multiplication Rule. Note the importance here of statistical independence.
The following videos introduce us to the Addition Rule, which is a more challenging concept than the Multiplication Rule.
The above video introduces the probability theory, Addition Rule, considering both mutually exclusive and not mutually exclusive events; we're interested particularly in the mutually exclusive, which is equivalent to the "when order does not matter" example.
The above video is a bit 'dry', but all examples are based on rolling dice.
The following video is a reiteration of the Addition Rule as applied to when order does not matter (odds of rolling, e.g., a 6). It also brings us back to doing biology.
Why do we care about probability theory? Genetics for one, which this video considers.
The next two videos introduce graphing, which is a really important life skill completely 'independent' of whether you care anything about science. Key concepts are those of independent variable (usually the x axis) and dependent variable (usually the y axis) as well as an appreciation of how to fully utilize the "real estate" found on your graph.
The above video is also very dry, but makes its point reasonably well.
The above video describes how to graph. Very simple stuff, and (ironically) poor graphics, but the video makes all of the right points.
OK, totally corny, but also totally worth watching. ☺
The following video provides a brief introduction to the idea of variance.
This video describes how to calculate the variance associated with a data set.
Niall Ferguson in his book, the The Ascent of Money, suggests that we, as humans, have a lot of biases. Here the point is that therefore we do not tend to make for highly effective economic creatures but many of these points (or perhaps even all) also are relevant to why, without proper training and discipline, we also don't tend to make for highly effective scientists. Indeed, the whole point of science, really, is to better understand the world through a striving towards reducing such biases – in our own personal as well as collective perspectives – as the following (pp. 345-346):