false

Textbook Notes
(369,072)

Canada
(162,366)

University of Toronto St. George
(10,716)

Psychology
(2,981)

PSY201H1
(45)

Kristie Dukewich
(20)

Chapter 5

Department

Psychology

Course Code

PSY201H1

Professor

Kristie Dukewich

Description

PSY201: Chapter 5: The Normal Curve and Standard Scores
Introduction:
– Normal curve
+ a very important distribution in behavior sciences
+ three principal reasons why...
- 1. many of the variables measured in behavioral science research have distributions that quite closely
approximate the normal curve (ie: height, weight, intelligence and achievement are few examples)
- 2. many of the inference tests used in analyzing experiments have sampling distributions that become normally
distributed with increasing sample size. (ie: sign test & Mann-Whitney U test)
- 3. many inference tests require sampling distributions that are normally distributed. The z test, Student's t test,
and the F test are examples of inference tests that depend on this point → much of importance of normal curve
occurs in conjunction with inferential statistics.
The Normal Curve:
– normal curve is a theoretical distribution of population scores.
+ a theoretical curve and is only approximated by real data
+ bell-shaped curve that is described by equation:
– curve has two inflection points, one on each side of the mean
+ inflection points are located where the curvature changes direction
+ ie: inflection points are located where curve changes from being convex downward to being convex upward
- if the bell-shaped curve is a normal curve, inflection points are at 1 standard deviation from the mean (
and )
- as the curve approaches the horizontal axis, it is slowly changing its Y value.
- the curve never quite reaches the axis
- it approaches the horizontal axis and gets closer and closer to it, but it never quite touches it.
- curve is asymptotic to the horizontal axis
– infection points under the curve, horizontal... in the diagram on page 97
Area Contained Under the Normal Curve:
– in distributions that are normally shaped, there is a special relationship between the mean and the standard
deviation with regard to the area contained under the curve
– when a set of scores is normally distributed, 34.13% of the area under the curve is contained between the mean
(u) and a score that is equal to u + 1o ; 13.59% of the area is contained between a score equal to + 1 and a
score of u+ 2 o; 2.15%of the area is contained between scores of u+ 2o and u + 3o ; and 0.13% of the area
exists beyond u+ 3o . This accounts for 50% of the area
+ since curve is symmetrical, same percentages hold for scores below the mean
+ since frequency is plotted on vertical axis, these percentages represent the percentage of scores contained
within the area – ie:
+ have a population of 10,000 IQ scores
+ distribution normally shaped with u = 100 and o = 16
+ since scores are normally distributed, 34.13% of scores are contained between scores of 100 and 116 ( u+ 1o
= 100 + 16 = 116), 13.59% between 116 and 132 ( u+ 2o = 100+32 = 132), 2.15% between 132 and 148, and
0.13% above 148
+ similarly, 34.13% of scores fall between 84 and 100, 13.59% between 68 and 84, 2.15% between 52 and 68,
and 0.13% below 52.
– to calculate the number of scores in each area, multiply the relevant percentage by the total number of scores →
there are 34.13% x 10,000 = 3413 scores between 100 and 116, 13.59% x 10.000 = 1359 scores between 116
and 132, and 215 scores between 132 and 148; 13 scores are greater than 148.
+ for other half of distribution, there are 3413 scores between 84 and 100, 1359 scores between 68 and 84, and
215 scores between 52 and 68; there are 13 scores below 52.
+ these frequencies would be true only if distribution is exactly normally distributed
+ in actual practice, the frequencies would vary slightly depending on how close the distribution is to this
theoretical model
Standard Scores (z Scores):
– IQ of 132...
+ a score is meaningless unless you have a reference group to compare against
+ without one, can't tell whether the score is high, average, or low
– score is one of the 10,000 scores of distributions → gives IQ of 132 some meaning
+ ie: can determine the percentage of scores in distribution that are lower than 132 → determining the percentile
rank of score of 132 (percentile rank of a score is defined as the percentage of scores that is below the score in
question)
– 132 is 2 standard deviations above the mean
+ in normal curve, there are 34.13 + 13.59 = 47.72% of the scores between the mean and a score that is 2
standard deviations above the mean
+ to fine percentile rank of 132, need to add this percentage the 50.00% that lie below the mean → 97.72%
(47.72 + 50.00) of the scores fall below your IQ score of 132.
+ should be happy to be intelligent
– to solve problem, had to determine how many standard deviations the raw score of 132 was above or below the
mean
+ transformed the raw score into a standard score, also called a z score
– a z score is a transformed score that designated how many standard deviation units the corresponding raw score
is above or below the mean – process which by the raw score is altered – score transformation
+ z transformation results in a distribution having a mean of 0 and a standard deviation of 1
+ reason z scores are called standard deviation is they are expressed relative to a distribution mean of 0 and a
standard deviation of 1
– in conjunction with a normal curve, z scores allow to determine the number or percentages of scores that fall
above or below any score in the distribution
+ z scor

More
Less
Unlock Document

Related notes for PSY201H1

Only pages 1 and half of page 2 are available for preview. Some parts have been intentionally blurred.

Unlock DocumentJoin OneClass

Access over 10 million pages of study

documents for 1.3 million courses.

Sign up

Join to view

Continue

Continue
OR

By registering, I agree to the
Terms
and
Privacy Policies

Already have an account?
Log in

Just a few more details

So we can recommend you notes for your school.

Reset Password

Please enter below the email address you registered with and we will send you a link to reset your password.