Z - Scores
As a student, you probably have figured out that the 58 on the French test is bad compared to every one else and that the 58 on the Physics test may be pretty good compared to everyone else.
Our physics major roommate, says "That great old Prof. - she curved the test!".
We need to be more precise - To do that we need to review the Normal Distribution!
That's how we will compare the French and Physics tests.
Finding Yourself on the Normal Curve
Remember the normal curve. It is the shape that quite a lot of measurement data distributions have. That means that the frequency of the scores tend to fall in a very specific shape.
The normal curve is described by its mean (average) and standard deviation.
Hints:
· This is the normal curve and the line in the middle is the mean.
Mean - SX/N or the average.
· Many frequency distributions in Psychology are normal.
· A little box on the graph represent a score. In our case it will be an exam score of a particular individual.
· The red arrow represents the standard deviation.
A measure of the width of a measurement data distribution
Ö [S(X-mean)2/N]
So What Does This Have to do with the French and Physics Test!
The Big Idea!!
A A A
Where You are in the Distribution Determines How Well You Did!
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Since the Physics test was very difficult with a mean of 50, one roommate did better than most (score of 70) in the class as was quite pleased with herself. You can see that most people in the distribution are below here.
It is the opposite for our French-taking roommate. She is scored below most.
The 2nd Big Idea!!
We can quantify your place in the distribution. You don't have to always draw a picture.
We will do this with the Z-Score.
The 3rd Big Idea!!
The Standard Deviation is a Ruler.
Consider the Z - score as the Inch Marks of the Ruler.
A Z-Score Equals the Number of Standard Deviations, the score is from the Mean
Z = (Score - Mean)/ Standard Deviation
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