Closeness and Confidence
Here is my summary of Meaning from Data: Statistics Made Clear Lecture Three. I made it using a combination of GIMP and Inkscape, so it’s not quite up to Photoshop standards. It shows a sample of stars randomly taken from a larger pool of stars. The information that can be inferred from the smaller sample about the larger one (that is, it’s shape, centre and spread) is limited in terms of ‘closeness’ and ‘confidence’. The aim of an experiment is to enable us to infer the characteristics of the complete data set with high closeness and high confidence. If closeness is high but confidence low then we will find that the estimates will often be outside the closeness limits. If the closeness is low but the confidence high then the estimates will be too vague to rely upon.
Workchoices Advertisements
In what appears to be a waste of money, the Federal Government is running an advertisement campaign promoting their workplace relations laws (known as Workchoices) whilst the Victorian Government is simultaneously running a campaign against the policy. I guess one could argue that this allows voters to get ‘both sides’ of the issue but the ad’s really don’t give much information in that respect, so it seems to me to be a waste of money.
The Federal Government ad has a lady who appears to be a senior bureaucrat dispelling ‘myths’ surrounding the new laws.
The Victorian Government ad has ‘victims’ of the new laws giving their stories, in sombre black-and-white.
And the political disclaimer.
Data and Distributions
The following picture is a summary of lecture two of the Teaching Company series Meaning from Data: Statistics Made Clear. I produced it using Rationale and Photoshop. It has been saved in the Portable Network Graphics (PNG) format because that format is the most efficient for storing diagrams such as the one reproduced below.
The Scope of Reason
I here describe a model of argumentation that places arguments at various points along a continuum rather in one of two categories: right or wrong. An argument is assessed to determine how close it lies to the middle of a one dimensional representation of reasonableness. If it is close then it is considered reasonable. If it is outside the middle area then it is considered unreasonable. The diagram immediately below shows the scope of reason. The diagram immediately below that shows an argument (represented as a blue circle) that lies within the scope of reason. The third diagram shows a less reasonable argument and the final one shows an unreasonable argument.
Sometimes several inconsistent arguments lie within the scope of reason. Given the human intolerance for cognitive dissonance, the inconsistent arguments are either reconciled in some manner or one or more arguments are chosen over the others.
It’s also possible that we process ideas in two phases: a low resolution phase that is simple and less detailed and a high resolution and more detailed phase. Using the aforementioned concept of argument, the first phase would be a ‘blurry’ categorisation based upon quick reasoning that involves stereotyping and appeals to consequences. Those arguments that pass this phase then move to a second and more detailed one. I am not sure how to visually represent this so I will leave that for a later post.
Emotion and Argument
People often accept a weak argument when they want a claim to be true and reject a strong argument when they want a claim to be false. I have thought about this and have a simple explanation. By simple I mean simplistic. I don’t understand the relevant cognitive science at all so the actual underlying process is probably a lot more complex.
I have drawn a diagram of a model of a simple argument below. The magnifying glass is the evidence and the exclamation mark is the claim or conclusion. The black arrow is the inference connecting the two.
Below is a weak argument. The weakness of the argument is shown by a lightly shaded arrow. If the claim is one that a listener has an emotional stake in, they will ‘emotionally fortify’ the connection between the claim and the evidence. I have represented this by drawing a swirly red line in the same direction as the black arrow. The listener will perceive the argument as being far stronger than it really is.
The process can also work in reverse. As shown below, a strong argument (represented by a darker black arrow connecting the evidence and the claim) is being weakened by the emotional resistance of a listener that has an emotional stake in the claim not being true. For them, it is as though the argument is much weaker than it really is.
It appears to me that this is an invisible process. Everyone is affected to some degree. But awareness of your own tendency in this regard may help you to ‘factor in’ your own biases. If you see many people accepting claims that you regard as very weak, extra caution should be exercised to ensure that it is not your own emotional bias that is weakening the appearance of the arguments. Conversely, if you accept claims that others regard as very weak, you should double check your reasoning (perhaps by writing it down) to ensure that your emotions are not strengthening an otherwise weak argument. Of course, the emotional strengthening and weakening is occuring in others to so you cannot rely upon most people to get things right either.
Now that I have this basic framework down, I can analyse it in a little more detail.
