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chapter 2: Describing and Presenting a Distribution of Scores
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Terms in this set (47)
Data
collected numerical or verbal results
variable
trait or characteristic of something that can assume more than one value
population
all subjects within a defined group
sample
a part or subgroup of the population from which the data is collected
random sample
every personal has a equal chance of being chosen or included
parameter
a value or measurable characteristic that refers to the population
descriptive statistics
-every member of the group is measure and no attempt is made to generalize to a larger group, the methods used to describe the group
-conclusions related ONLY to this group
inferential statistics
a random sample of collected data is projected or generalized about a large group (beyond those truly evaluated/tested)
discrete data
data having specific vaules
ex) sex, # of hits, # of shots
continuous data
measures within a range (timing or throwing events)
statistical terms
data
variable
population
sample
random sample
parameter
descriptive statistics
inferential statistics
discrete data
continuous data
scales of meaurement
nominal, ordinal, interval, ratio
nominal scale
lowest and most elementary, categorical, naming level only, reporting frequencies, no comparison of categories
ex) division by gender, race, eye color
ordinal scale
order or rank, no indication of how much better one score is than another
ex) order of finish in race, grades for achievement
interval scale
order or rank; same distance exists between each division (possible to say how much better one number is than another)
ex) temperature, year
ratio scale
numbers represent equal units between measurements and there is an absolute zero point
ex) height, weight
normal ditribution
-assumption that the distribution of scores is normal
-graphically represented by the normal curve (bell-shaped)
-theoretical
distribution contains and infinite number of scores
characteristics of normal curve
-bell shape curve
-symmetrical
-greatest number found in middle
-all measures of central tendency at vertical axis
score rank
-listing the scores in numerical order starting with the largest (best) to the smallest (lowest) score.
-ranking is not something to consistently share with subjects
central tendency
a measure that represents the typical response or the behavior of a group as a whole
measures of central tendency
mean, median, mode
mean
average of a distribution of scores; mostgenerally used measure of central tendency
characteristics of mean
-most sensitive of all measures of central tendency
-Most appropriate measure of central tendency to use for ratio data
-Considers all information about the data and is used to perform other statistical calculations
-Influenced by extreme scores
X (with a line above)
the mean
Σ
the sum of
X
individual score
N
the total number of scores in distribution
mean formula
Σx/n
median
score that represents the exact middle of the distribution
median characteristics
-Not affected by extreme scores.
-A measure of position.
-Not used for additional statistical calculations.
-Represented by Mdn or P50.
mode
the most frequent number
mode characteristics
-Least used measure of central tendency.
-Not used for additional statistics.
-Not affected by extreme scores.
which measure of central tendency is best for interpretation of test results?
-The mean and median are both useful measures.
-In most testing, the mean is the most reliable and useful measure of central tendency; it is also used in many other statistical procedures.
variability
the spread, or scatter, of scores; terms of dispersion(how spread out) and deviation(how far do they go from the middle score) are often used
types of variability
range and standard deviation
range
determined by subtracting the lowest score from the highest score; represents on the extreme score
characteristics of range
1. Dependent on the two extreme scores.
2. Least useful measure of variability.
standarad deviation
-Most useful and sophisticated measure of variability.
-Describes the scatter of scores around the mean.
Standard Deviation formula
(n-1)
characteristics of standard deviation
-Is applicable to interval and ratio data, includes all scores, and is the most reliable measure of variability.
-a relatively small standard deviation indicates that the group being tested has little variability (performed homogeneously).
-A relatively large standard deviation indicates the group has much variability (performed heterogeneously).
percentile
a point in a distribution of scores below which a given percentage of scores fall
Percentile rank
percentage of the total scores that fall below a given score in a distribution; determined by beginning with the raw scores and calculating the percentile ranks for the scores
displaying statistics
1) interpret data without reading raw data or tables
2) different graphs are used
3) guidelines should be standard
standard scores
Provide method for comparing unlike scores; can obtain an average score, or total score for unlike scores
standard scores examples
z-score and t-scale
z-score
represents the number of standard deviations a raw score deviated from the mean
T-scale
-sets the mean at 50
-standard deviation at 10 to remove the decimal found in z scores and to make all scores positive
-May extend from 0-100
-Unlikely that any t-score will be beyond 20 or 80
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