PSYC 1010 Chapter Notes - Chapter 6: Sample Size Determination, Central Limit Theorem, Standard Score
29 Jun 2018
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THE NORMAL CURVE, STANDARDIZATION AND Z SCORE CHAPTER 6
-Normal curve: a specific bell-shaped curve that is unimodal, symmetric, and defined
mathematically
STANDARDIZATION, Z SCORE AND THE NORMAL CURVE
-When data are normally distributed, we can compare one particular score to an entire
distortion of scores. To do this, we convert a raw score to a standardized score
-Standardization: is way to convert individual scores from different normal distribution
to a shared normal distribution with a known mean, standard deviation and percentiles
THE NEED FOR STANDARDIZATION
-One problem with making meaningful comparisons is that variables are measured on
different scales (ex. weight and height use different units)
-We can standardize different variables by using their means and standard deviations to
convert any raw score into a z score
-Z score: the number of standard deviations a particular score is from the mean
-Example: standardizing the weights and comparing them on the same measure. A dram is
1/256 of a pound, so 8 drams is 1/32= 0.03125 of a pound. One pound equals 435 grams
TRANSFORMING RAW SCORE INTO Z SCORE
-Only info we need to convert any raw score to a z score is the mean and standard deviation
of the population of interest
-Example: midterm,interested in comparing our grade with the grades of others in this
course. Statistic class is the population of interest. Your score is 2 standard deviations above
the mean of the midterm. z score is 2. Friend is 1.6 standard deviation below the mean( z-
score is-1.6). At the mean the z score is 0
-Example: If the mean is 70% of test the standard deviation is 10 and your score is 80. 1
standard deviation away from the mean, z score is 1. If your score was 50, which is 2 standard
deviation below mean, z score is -2.0.
-Formula for z score:
X= -0.44(4.086)+64.886=63.09
=1.25
1.79= (X-64.886)
4.086
= (70-64.886)
4.086
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EXAMPLE 6.4:
-The mean height for the population of sophomores is 64.88, standard deviation of 4.086. If
you are 70 inches, whats your z score.
You1.25 are standard deviations above the mean if you r were 62 then you would be -0.71
EXAMPLE 6.6:
-The mean of the z distribution is always 0 and the standard deviation is always 1. The mean
is 64.886 the standard deviation is 4.086
-If someone is exactly 1 standard deviation above the mean, his or her score would be
64.886+4.086= 68.97. What would the z score be:
TRANSFORMING Z SCORES INTO RAW SCORES
-If we already know the z score we can reverse the calculation to determine the raw score
EXAMPLE:!
-Population mean is 64.886 with a standard deviation of 4.086, if you have a z score of 1.79.
what is the height
- As long as we know the mean and standard deviation of the population, we can do two
things: (1) calculate the raw score from its z score and (2) calculate the z score from its raw score
-With standardization we can compare anything each relative to its own group
-Make more specific comparisons, we convert raw scores to z scores and z scores to
percentiles using the z score distribution
-The z distribution: is a normal distribution of standardized score
-Standard normal distribution: is a normal distribution of z score
= (70-64.886)
4.086
=1.25
= (64.886-64.886)
4.086
=0
=(68.972-64.886)
4.086
=1
1.79= (X-64.886)
4.086
X= -0.44(4.086)+64.886=63.09
=1.14
=1.76
=( 8.1 - 6.8)
1.76
=(92 - 78.1)
12.2
Document Summary
The normal curve, standardization and z score chapter 6. Normal curve: a specific bell-shaped curve that is unimodal, symmetric, and defined mathematically. When data are normally distributed, we can compare one particular score to an entire distortion of scores. To do this, we convert a raw score to a standardized score. Standardization: is way to convert individual scores from different normal distribution to a shared normal distribution with a known mean, standard deviation and percentiles. One problem with making meaningful comparisons is that variables are measured on different scales (ex. weight and height use different units) We can standardize different variables by using their means and standard deviations to convert any raw score into a z score. Z score: the number of standard deviations a particular score is from the mean. Example: standardizing the weights and comparing them on the same measure. 1/256 of a pound, so 8 drams is 1/32= 0. 03125 of a pound.
