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What is variance?

A measure of how diverse scores are.

This type of measurement scale is just an arbitrary label to put things into categoreies. There is no information about the difference between categories.

Nominal Scale

This measurement scale tells who is more than whom but does not know how much more. You know the order, but not the distance between each category.

Ordinal Scale
(Rank Order) 
In this measurement scale, it is known who is above whom and by how far. The distance between 1 and 2 is equivalent to the distance between 6 and 7. Order and distance are known.

Equal Interval Scale

On this scale, it is possible to distinguish if 100 is twice as much as 50.

Rational Zero Scale

What is Measurement Theory?

Measurement Theory is the link between the numbers we assign and the meaning we place on them.
The methods and rules used to assign numbers to objects AND the meaning we place on numbers. 
Discuss 4 reasons to put a number on diversity.

To know how well the mean represents the group.
low diversity  mean is good rep of group. high diversity  mean is poor rep of group. To measuring the difference between 2 groups. To examine causal effects. To figure out how much a variable has an impact, take it away and measure the difference between the groups. To calculate if a predictor variable is valid, ie, does A predict B and how well? 
What is an analysis of variance used for?

An analysis of variance is used to see how much the means of two diffrent groups differ. If there is a big difference around the grand mean, there is a difference between the groups.

What is a weakness in using the absolute deviation?

Taking the absolute deviation (using absolute value)  Diversity in a popuiation may be the same but the value gets bigger just because there are more numbers.

What is a weakness in using the average absolute deviation?

There is no way to reverse absolute value.
Cannot use absolute value in integrals. 
Which is a measure of diversity that gets bigger just because there are more numbers, not necessarily because the values are more spread out?

Average Absolute Deviation

Explain the following statement: Zero was not just invented and automatically used. Include Babylonians and Greeks.

Babylonians around 1700 BC used context to disinguish between 216 and 2106. Around 400 BC used wedges to distinguish between 216 and 21"6. Saw the concept as punctuation.
Greek accomplishments were in geometry but Greek astronomers used 0 around 130 AD. First place where symbol is O but fell out of use. 
Discuss India's contributions to the path to Zero.

Numerals and number system was born in India but used some of the Greeks ideas.
650 AD they used a place value system and O was used to denote empty space. 876 AD  first agreen upon Zero in garden measurements. 
What did Brahmagupta contribute to the path to O?

He is creditied with introducing zero into math and discovering the rules that govern its use.
He gave rules for addition, subtraction, and multiplication involving Zero Extended arithmetic to negative numbers and Zero. A number minus itself is 0. A number doesn't change if add 0. A number times Zero equals 0. Mistake: Zero can be in denominator. Did not understand what happens when you divide by zero. 
What mistake did India make with respect to operations on Zero?

For 500 years they thought that n/0 was defined.

What rules did Basakra contribute to the Path to Zero?

Zero squared = 0 and 0/0 = 0

What are some of Brahmagupta's contributions?

Developed algebraic notation and gave rules to solve some quadratic equations.
Algorithm for computing square roots. Rules for summing series. Length of day, solar and lunar eclipses. 
Subtracting the mean score from a participant's score yields the _________

Deviation score

What information is needed to calculate a ZScore

How many points your score is from the mean.
Number of points in a standard deviation. 
What information does a raw score on a depression test give?

The raw score tells you the number of points you earned above zero.
Limited interpretation. In comparing raw scores, cannot say which is the greater problem, anxiety or depression 
What information is contained in a deviation score?

A deviation score tells how far your score is above or below the mean.

In order to compare scores from a depression scale to an anxiety scale, use the ___ Score.

Z Score.
Raw scores and deviation scores do not allow for crossscale comparision 
What is the difference between a raw score, a deviation score, and a Z score?

Raw Score  # points above 0.
Deviation Score  X  Mean Z Score  X  Mean / Std dev A Z score allows comparison across measures. If you know how many standard deviations you are from the mean, you know how much more rare you are compared to the population (ie, percent of population above or below you). 
Why is there value in knowing if X is correlated with Y?

a) practical value application
(social class and intelligence.) b) One piece of evidence in looking for evidence to see if X causes Y. c) measure the size of causal effects. 
What is covariance?

Covariance is a measure of association.

What contributions were made by SS Stevens?

Discussed the differences between nominal, rank order, equal interval, and rational zero levels of measurement.
Can perform arithmetic operations and calculate mean but be careful about interpretation. performing operations on scores/numbers can break the link between the numbers and the meaning we place on them. 
Discuss characteristics of the ordinal scale.

A Most to Least Scale.
BUT no indication of HOW MUCH more No indication of HOW FAR apart. (do NOT know distance between) Not meaningful to calculate mean or standard deviation. 
Discuss characteristics of the Interval Scale.

Know rank AND how far apart.
(distance between attributes has meaning). BUT no information available for absolute magnitude. Can work with distances above or below the mean. No ZERO point. Can average, calculate mean. e.g. temperature. Ratios do NOT make sense, 80 degrees is not twice as much as 40 degrees. 
Discuss attributes of the Ratio Scale.

Rank Order is known
Distance between intervals is known. Distance from an absolute ZERO is known. Distances are stated from rational ZERO, not the mean. Absolute Zero is meaningful. Ratios have meaning, 40 is twice 20. Weight, number of clients 
What is measurement theory?

The connection between the numbers we use and the meaning we want.
Need to be clever so that numbers convey desired meaning. 
Discuss 4 reasons to put a number on diversity.

To see how well the mean represents the group. The average may not be telling you about anyone in the group especially if diversity is high.
To measure the difference between groups. Look at how much the means differ when comparing 2 different treatments. Figure out if a factor is a causal effect. Take cause away to see if there is a measureable difference without it. To see if A predicts B and how well. 
The average squared distance from the mean is called _______

Variance

What is the weakness of using a Raw Score for comparison across scales?

Raw Score is the number of points scored above Zero. Can only be used for limited interpretation because there is no rational Zero.

What is the weakness of using a Deviation Score for comparison across scales?

A Deviation Score tells how many points you are from the mean but 3 from the mean on a depression scale is different than 3 from the mean on an anxiety scale.

What 2 numbers must you know to calculate a Z Score?

# points UR from Mean
Standard Deviation 
Why can't you just multiply X and Y to see if there is association?

Product is sensitive to the means. (Subtract mean).
Sensitive to the number of subjects. (Divide by # subj) Sensitive to the units of measurement (Use ZScore). 
Why is it useful to know if X predicts Y?

Practical to plan for the future or predict.
Part of the case to prove that X predicts Y. Evaluate the size of causal effects. 
What are 3 elements to prove causation?

Prediction
Plausible mechanism Cause occurs before effect 
The mean product of deviation scores is called ________. Explain this concept.

Covariance.
It is a measure of the degree of correspondence or association between scores on X and Y. if Cov (XY) is large, the corresponcence of XY is high. 
Define a Pearson Correspondence of 1, 0, and 1.

1=Correspondence is perfect
0=no correspondence at all 1=reverse correspondence 
The mean of ZScores is ____
The Std Dev of ZScores is __ 
Mean = 0
Std Dev = 1 
What is covariance and can it be used to compare across different sets of numbers?

Covariance is a measure of the degree of correspondence or association between scores on X and Y. Cov (XY) is bigger if the correspondence of X and Y is high. You can't compare covariance across different sets of numbers unless they have the same diversity. Using covariance takes away effects of means, sample size, and diversity.

What is a weakness of Raw Scores?

Raw Score is how far you are from zero, measured in points.
Don't tell how far the person is from having none of the underlying trait. Don't tell where the person stands relative to other people. Can't be compared across different measures. 
What makes a deviation score more meaningful than a raw score?

The deviation score tells how far the score is from the mean.
Positive deviation scores indicate that the person is above the mean. Negative deviation scores indicate that the person is below the mean. Still not clear because you don't know how much 10 above the mean is. But at least can get an idea if the person's score is higher or lower than most people's. Don't tell us how many points are a little and how many are a lot. 
What is a ZScore?

A ZScore is a measure of how many standard deviations the person is above the mean.
Range from +3 to 3. Mean of ZScores is 0 and Std Dev is 1. 
What is variance?

The variance of a set of scores is how far the typical person is from the mean.

What information is locked up in a ZScore?

Where the subject stands relative to the mean.
Tells you if subject is close to the mean (0), close to the maximum (+3) or min. Can be translated into exact information about where the subject stands relative to all others. 
Define a ZScore of 0, 1, 2, 3.

0=mean
1=exceeds 64% scores 2=exceeds 95% scores 3=exceeds 99.9% scores 
Differentiate Raw, Deviation, and Standard Scores.

Raw = how many points more than none.
Deviation = how many points away from the mean. Standard = how many standard deviations from the mean. 
Can a ZScore be used to say that a person is more extreme on depression than on anxiety?

Yes
