Descriptive Statistics and Law of Large Numbers Flashcards
If we want to represent an entire distribution or at least some special characteristic of it, by means of a single, summary numerical index or a pair of such indices, what is this called?
Descriptive Statistics
What is the two major categories of summary statistics (descriptive statistics)?
- Indices of location 2, Indices of dispersion
Indices where some nameable part of a distribution is on the horizontal axis are?
Indices of location
This tells us how spread out the distribution is according to some criterion
Indices of dispersion
What is another term for regularity?
The mean
What is another term for diversity?
Variance
What is statistically described via regularity?
– pattern, consistency, shape
– regularity allows for existence of science
– measures of central tendency or location
What is statisically described by diversity?
– differences, uniqueness, individuality
– diversity makes for interesting science
– measures of dispersion
What are the different types of indicies of location?
- Mode
- Median
- Mean
What is the crudest index of location?
Mode
Define the mode?
the value that occurs with the greatest
frequency.
In other words, the value that is
possessed by the greatest number of units
in the set.
If a data set has two or more values may be tied for the
greatest frequency, what is this called?
Biomodal (2)
Multimodal (2+)
What is the value of the middle unit?
Median
How do we define the median?
N units arranged in a line in order
of increasing value, the median is the middle one between the highest and lowest value
note that this is unit middle NOT value
How do we calculate the median if we have an even # of units in a data set?
Average the 2 middle values
What is the 50th percentile?
Median
How do we determine a percentile value rank given a data set?
i.e. we are given the data set and the percentile and we are trying to find the value that corresponds to the percentile
THIS IS A BONUS QUESTION NOT COVERED IN THE LECTURE
Given a score and a data set how do we determine the percentile rank of a score?
THIS IS A BONUS QUESTION NOT COVERED IN THE LECTURE
The best known index of location is….?
THE MEAN
What is the formula for the mean?
Which index of location is sensitive to extreme score?
The mean
What are positive attributes of the mean?
- IT is the LEAST subject to sampling variation!
- It IS SENSITIVE TO the exact value of all the scores in the distribution
- mathematically tractable
- It is the best guess for the value of any unit drawn at random from a distribution.
- this depends on the types of units being selected
Define this term?
The deviation score
(which is the ammount that event x deviates from the mean–x with a line over the top)
What is the squared deviation score?
Why do we square the deviation score?
Because we want a postive number (sometimes it can be negative if the value is less than the mean)
What does this equation define?
The sum of the squared deviation scores
OTHERWISE KNOWN AS
sum of squares
- What is the sum of the deviations about the mean equal to?
- Always or just some of the time?
- Why?
- 0
- ALL of the time
- Because each deviation above the mean is canceled out by a deviation below the mean. This always ends up at zero because the mean is the “center of gravity” or “balance point” of the data set.
The sum of the squared devations is a?
A minimum
Variance is?
Average squared deviation from the mean
What is the most common index of dispersion?
The Variance
*sigh* again
What is the square root of the variance?
Standard deviation
What are common indicies of dispersion?
Range
Variance
Standard Deviation
Range is defined as?
The difference between the higest and lowest values
Range = High - Low
What is the simplest index of dispersion?
The Range
According to Goldsmith what is the single most important concept in behavioral statistics?
Also, which type is good and bad?
Variance
Good variance – the difference between independent variables–seek to maximize this (inter-group variance)
Bad variance – the differnce between members of each variable–seek to minimize this (intra-group variance)
The following are what?
- the variance of a random variable is a measure of its statistical
- dispersion, indicating how far from the expected value its values
- typically are
- – a measure of the variation shown by a set of observations defined by
- the sum of the squares of deviations from the mean, divided by the
- number of degrees of freedom in the set of observations
- – a measure of the spread of the values in a distribution
- – a measure of variability
- – deviation from a standard or norm
- – the square of the standard deviation
- – a measure of the spread or dispersion of a variable about its mean
- – the variance of a real-valued random variable is its second central
- moment
Some definitions of variance
Which defintion is a very important concept to understand?
– the variance of a real-valued random variable is its second central moment
What is the advantage of the standard deviation?
Compared to what?
The values are expressed in the orginal units of measurment.
As opposed to the variance which does not express them in the orginal values of measurment (because the values are squared)
In most other respects which measure of dispersion is more advantageous?
The variance
What is the formula for variance?
What is this an example of?
Variance of a theoretical distribution
What are the properties of variance?
- gives us a measure of dispersion relative to
- the mean
- sensitive to each score in the distribution
- stable with regard to sampling fluctuations
- mathematically tractable
- variance is directly proportional to the average
- squared deviation between all pairs of
- observations
What does this formual signify?
variance is directly proportional to the average
squared deviation between all pairs of
observations
How do we seperate population variance and sample variance?
Why do we do this?
Via two slighlty different formulas
Is variance change with respect to location (addition of a constant)?
No it is invariant
If you want to multiply some constant to the variance what do you have to do?
You must square the constant.
