CH2 Flashcards
why we need statistics
- First, statistics are used for purposes of description.
–Numbers provide convenient
summaries and allow us to evaluate some observations relative to others - we can use statistics to make inferences,
–e logical deductions about events that cannot be observed directly
exploratory data analysis
the detective work of gathering and displaying clues
confirmatory data analysis
when the clues are evaluated against rigid statistical rules
This latter phase
is like the work done by judges and juries.
Descriptive statistics
e methods used to provide a concise description of a collection of quantitative information.
Inferential statistics
methods used to make inferences
from observations of a small group of people known as a sample to a larger group
of individuals known as a population
Typically, the psychologist wants to make
statements about the larger group but cannot possibly make all the necessary
observations. Instead, he or she observes a relatively small group of subjects (sample)
and uses inferential statistics to estimate the characteristics of the larger group
measurement
application of rules for assigning numbers to
objects
The rules are the specific procedures used to transform qualities of attributes into numbers
Magnitude
Magnitude is the property of “moreness.” A scale has the property of magnitude if
we can say that a particular instance of the attribute represents more, less, or equal
amounts of the given quantity than does another instance
If the coach were to rank the teams by the number of games they have won, then the new numbering system (games won) would have the property of magnitude
Equal Intervals
difference between two points at any
place on the scale has the same meaning as the difference between two other points
that differ by the same number of scale units.
When a scale has the property of equal intervals, the relationship between the
measured units and some outcome can be described by a straight line or a linear
equation in the form Y = a +bX
Absolute 0
obtained when nothing of the property being measured exists
measuring heart rate and observe that your patient has a rate of 0 and has died, then you would conclude that there is no heart rate at all.
Nominal scales
not scales at all;
their only purpose is to name objects. For example, the numbers on the backs of
football players’ uniforms are nominal.
ordinal scale
A scale with the property of magnitude but not equal intervals or an absolute 0
rank individuals or objects but not to
say anything about the meaning of the differences between the ranks.
interval scale
When a scale has the properties of magnitude and equal intervals but not
absolute 0
most common example of an
interval scale is the measurement of temperature in degrees Fahrenheit.
ratio scale
A scale that has all three properties (magnitude, equal intervals, and an absolute 0)
distribution of scores
summarizes the scores for a group of individuals. In testing, there are many
ways to record a distribution of scores.
frequency distribution
displays scores on a variable or a measure to reflect how frequently each value was obtained
one defines all the possible scores and determines how many people obtained each of those scores..
percentile rank
“What percent of the
scores fall below a particular score (Xi)?”
To calculate a percentile rank, you need
only follow these simple steps:
(1) determine how many cases fall below the score of interest,
(2) determine how many cases are in the group, (3) divide the number of cases below the score of interest (Step 1) by the total number of cases in the group (Step 2), and
(4) multiply the result of Step 3 by 100.
variance.
average squared deviation around the mean,
where (X - Xbar) is the deviation of a score from the mean.
standard deviation
square root of the average squared deviation around the mean.
knowing the standard deviation of a normally distributed batch of data allows us to
make precise statements about the
distribution.
One problem with means and standard deviations
do not convey enough information for us to make meaningful assessments or accurate interpretations of data
Z score
transforms data into standardized units that are easier to interpret. A Z score is the difference between a score and the mean, divided by the standard deviation
Any variable transformed into Z score units takes on special properties
Z scores have a mean of 0 and a standard deviation of 1.0.
McCall’s T
mean of the distribution would be set at 50 to correspond with the 50th percentile. standard deviation was set at 10.
T = 10z + 50
stanine system
Another system developed in the U.S. Air Force during World War II
converts any set of scores into a transformed
scale, which ranges from 1 to 9.
Norms
performances by defined groups on particular tests
The norms for a test are based on the
distribution of scores obtained by some defined sample of individual
When applying an IQ test, the tester’s task is to determine
the mental age of the person being tested. This is accomplished through various exercises that help locate the age-level norm at which a child is performing.
tracking
This tendency to stay at about the same level relative to one’s peers
norm-referenced test
compares each person with a norm
Many critics have objected that this use of tests forces competition among people.
Young children exposed to many norm-referenced tests in elementary school can
get caught up in a never-ending battle to perform better than average
criterion-referenced test
describes the specific types of skills, tasks, or
knowledge that the test taker can demonstrate such as mathematical skills
tests that are applied to determine whether students know specific information. These tests
do not compare students with one another; they compare each student’s performance with a criterion or an expected level of performance
