PSYC 210 Chapter Notes - Chapter 5: Carl Friedrich Gauss, Adolphe Quetelet, Standard Deviation
Psychology 210 Chapter 5
Galton
Galton was one of the first experimental psychologists, and the founder of the field of enquiry
now called Differential Psychology, which concerns itself with psychological differences
between people, rather than on common traits.
- Darwin's cousin
- Correct treatment of population and variance despite statisticians incorrect
- He was not a mathematician
The Laws of Error
- Issues with the measuring device
- The notion that every time you measure you will get a slightly different measure (i.e.
weight on the scale)
- We will assume that all tools have the same degree of accuracy
What is the !true value
- The more times you measure the better
- Add all measurements and divide by 1000 will give us the mean or average of this
distribution
- We take this value as the closest to the true value
What is the !deviation
- The deviation from the true value must be due to some kind of error - sloppy measure,
or imperfection in the instrument or both
Bell shaped appearance
- The frequency
- The middle of the distribution is the most !frequently occurring observation
- The X is the variation measurements - in this example it the heights
- The values on either side are either above or below the average
- To the left of right the values are very infrequent
The blue arrow indicates the the value of the measurements are one standard deviation above
the mean
- 34.1% of our measurements will be less than or equal to the value that is 1 standard
deviation above the mean (to the right)
- And the same below the mean (34.1%)
- An additional 13.6% of the measurements vary above or below the mean but between 1
and 2 standard deviations
The law of errors is called a LAW because the deviation (i.e. errors) of a distribution of values
around the mean has a very particular profile which I have just described
Concept of the Average Person
The Gaussian (or normal) distribution was considered obeying the laws of error
- The bell-shaped curve was used by the mathematician Carl Friedrich Gauss to model
errors in astronomical observations and the errors always clustered in a particular
pattern
Adolphe Quetelet and the Concept of Average Human Being
- Plotted the large population of individuals - where each individual is only measured
once and invented the concept of the !average person
- Measured soldiers
- Amazed that the plot looked exactly like the bell shape that was predicted by the
Gaussian law of errors
Used the evidence that the bell shape appeared to make the assumptions
- Guass’s law of error applied to the difference between a population of individuals is
indeed a law !about
!
!
errors
- The !average
!
score (mean) is the !true value
!
of the group, which represents the !idealized
type
- Deviations from the mean are the result of !accidental causes
!
that are fundamentally
unanalyzable
In other words the variation of a particular anthropometric characteristic (in this case, bright is a
population of individuals is distributed in precisely the same way as the measurement errors
that Gauss analyzed, made by astronomers
This confirmed the assumption:
- We know that the mean of a large number of observations provides an estimate of the
true value
- Deviations from the mean are the results from errors in measurement
- Noise obscuring the ideal value
Document Summary
Galton was one of the rst experimental psychologists, and the founder of the eld of enquiry now called di erential psychology, which concerns itself with psychological di erences between people, rather than on common traits. Correct treatment of population and variance despite statisticians incorrect. The notion that every time you measure you will get a slightly di erent measure (i. e. weight on the scale) We will assume that all tools have the same degree of accuracy. Add all measurements and divide by 1000 will give us the mean or average of this distribution. We take this value as the closest to the true value. The deviation from the true value must be due to some kind of error - sloppy measure, or imperfection in the instrument or both. The middle of the distribution is the most frequently occurring observation. The x is the variation measurements - in this example it the heights.
