Chapter 3: A Statistic Refresher Flashcards
Scales of Measurement
Nominal Scales - Discrete scale
Ordinal Scales - Discrete scale
Interval Scales - Continuous scale
Ratio Scales - Continuous scale
If, for example, research subjects were to be categorized as either female or male, the categorization scale would be said to be _____ because it would not be meaningful to categorize a subject as anything other than female or male.
Ex. hospitalized or not, no division, more on quali
discrete
A _____ scale exists when it is theoretically possible to
divide any of the values of the scale.
Ex. ruler, pwede hatiin, quanti
continuous
Measurement always involves _____. In the language of assessment, _____ refers to the collective influence of all of the factors on a test score or measurement beyond those specifically measured by the test or measurement.
error
Measurement using _____ scales always involves error.
Most scales used in psychological and educational assessment are continuous and therefore can be expected to contain this sort of error. The number or score used to characterize the trait being measured on a continuous scale should be thought of as an approximation of the “real” number.
continuous
_____ scales are the simplest form of measurement. These scales involve classification or categorization based on one or more distinguishing characteristics, where all things measured must be
placed into mutually exclusive and exhaustive categories.
Male or female, yes or no
Ex. 1=catholic, 2=inc
Nominal
Like nominal scales, _____ permit classification. However, in addition to classification, rank-ordering on some characteristic is also permissible with _____.
Alfred Binet, a developer of the intelligence test that today bears his name, believed strongly that the data derived from an intelligence test are ordinal in nature. He emphasized that what he tried to do in the test was not to measure people, as one might measure a person’s height, but merely to classify (and rank) people on the basis of their performance on the tasks.
Ex. IQ, may measures of high and low, average
ordinal scales
In addition to the features of nominal and ordinal scales, _____ contain equal intervals between numbers. Each unit on the scale is exactly equal to any other unit on the scale. But like ordinal scales, _____ contain no absolute zero point.
Scores on many tests, such as tests of intelligence, are analyzed statistically in ways appropriate for data at the _____ level of measurement.
No 0 measurement, like IQ test. its 112. yan lang walang average chuchu
interval scales
In addition to all the properties of nominal, ordinal, and interval measurement, a _____ has a true zero point. All mathematical operations can meaningfully be performed because there exist equal intervals between the numbers on the scale as well as a true or absolute zero point.
In psychology, _____-level measurement is employed in some types of tests and test items, perhaps most notably those involving assessment of neurological functioning.
ratio scale
The _____ level of measurement is most frequently used in psychology. As Kerlinger put it: “Intelligence, aptitude, and personality test scores are, basically and strictly speaking, _____.
ordinal
A _____ may be defined as a set of test scores arrayed for recording or study.
distribution
The 25 scores in this distribution are referred to as _____ scores. As its name implies, a raw score is a straightforward, unmodified accounting of performance that is usually numerical.
raw
The data from the test could be organized into a distribution of the raw scores. One way the scores could be distributed is by the _____ with which they occur. In a _____, all scores are listed alongside the number of times each score occurred. The scores might be listed in tabular or graphic form.
frequency distribution
In a _____, test-score intervals, also called class intervals, replace the actual test scores. The number of class intervals used and the size or width of each class interval (i.e., the range of test scores contained in each class interval) are for the test user to decide.
grouped frequency distribution
A _____ is a diagram or chart composed of lines, points, bars, or other symbols that describe and illustrate data.
graph
A _____ is a graph with vertical lines drawn at the true limits of each test score (or class interval), forming a series of contiguous rectangles.
histogram
In a _____, numbers indicative of frequency also appear on the Y -axis, and reference to some categorization (e.g., yes/no/maybe, male/female) appears on the X -axis. Here the rectangular bars typically are not contiguous.
bar graph
Data illustrated in a _____ are expressed by a continuous line connecting the points where test scores or class intervals (as indicated on the X -axis) meet frequencies (as indicated on the Y -axis)
frequency polygon
A _____ is a statistic that indicates the average or midmost score between the extreme scores in a distribution.
Problem, is what if the score is malayo sa central tendency. iba iba and scores at malayo ang agwat
measure of central tendency
Measures of Central Tendency:
- The arithmetic mean
- The median
- The mode
The _____, denoted by the symbol X (pronounced “X bar”), is equal to the sum of the observations (or test scores in this case) divided by the number of observations.
The _____ is typically the most appropriate measure of central tendency for interval or ratio data when the distributions are believed to be approximately normal.
arithmetic mean
The _____, defined as the middle score in a distribution, is another commonly used measure of central tendency. We determine the median of a distribution of scores by ordering the scores in a
list by magnitude, in either ascending or descending order.
The _____ is an appropriate measure of central tendency for ordinal, interval, and ratio data.
median
The most frequently occurring score in a distribution of scores is the mode.
The mode
1) The range
2) The interquartile and semi-interquartile ranges
3) The average deviation
4) The standard deviation
Measures of Variability
_____ is an indication of how scores in a distribution are scattered or dispersed.
May bumuhat sa scores or variable, nahila yung mababa. saktong hindi extreme scores and mababa scores. Thus need of
Variability
Two or more distributions of test scores can have the same _____ even though differences in the dispersion of scores around the mean can be wide.
mean
Statistics that describe the amount of variation in a distribution are referred to as _____. Some _____ include the range, the interquartile range, the semi-interquartile range, the average deviation, the standard deviation, and the variance.
measures of variability
Measures of Variability:
_____ means that the scores are homogenous (similar) and solid.
Low variability
Measures of Variability:
_____ means that the scores are heterogenous and does not prove what the scores are supposed to represent.
means that the scores differ by a lot.
High variability
Measures of Variability: How to measure V?
The _____ of a distribution is equal to the difference between the highest and the lowest scores.
_____ is not used often because it is influenced so much by extreme values.
Exclusive are the values in an ungrouped data.
Inclusive are the values in a grouped data.
Highest minus lowest, x axis
range
Measures of Variability:
As illustrated below, the dividing points between the four quarters in the distribution are the _____. There are three of them, respectively labeled Q 1 , Q 2 , and Q 3.
Hatiin lang sa apat yung range
quartiles
Measures of Variability:
A _____ provides information regarding how the data items are spread over the interval from the lowest value to the highest value.
percentile
Measures of Variability:
_____ is the spread of a data set by breaking the data into quarters.
Quartile
Measures of Variability:
Q1 is the middle value of the lower half of the data
Q2 is the middle value up to the half of the data
Q3 is the middle value of the upper half (above the median) of the data
Q4 is the highest 25% of the data
Quartile
Measures of Variability:
The _____ gives the difference between Q3 and Q1.
interquartile range (IQR)
Measures of Variability:
_____ measures how far a set of numbers are spread out from the mean.
This is the average squared deviation from the mean.
This is when mean is used and the distribution is symmetric.
Variance
Measures of Variability:
_____ refers to the typical distance of the observations from the mean.
This is the square root of the variance.
Larger standard deviations produce distributions that are more spread out.
This defines the normal distribution. X axis lang.
Standard Deviation (SD)
_____ summarize the scores for a group of individuals.
Distribution of scores
_____ displays scores on a variable or a measure to reflect how frequently each value was obtained.
_____ can be represented in a bell-shaped, with the greatest frequency of scores toward the center of the distribution and decreasing scores as the values become greater or less than the value in the center of the distribution.
Frequency Distribution
Distributions can be characterized by their _____, or the nature and extent to which symmetry is absent.
The equilibrium of distribution.
The indication of how the measurements in distribution are distributed.
skewness
A distribution has a _____ when relatively few of the scores fall at the high end of the distribution. _____ examination results may indicate that the test was too difficult.
More items that were easier would have been desirable in order to better discriminate at the lower end of the distribution of test scores.
positive skew (right-skewed)
A distribution has a _____ when relatively few of the scores fall at the low end of the distribution. _____ examination results may indicate that the test was too easy.
In this case, more items of a higher level of difficulty would make it possible to better discriminate between scores at the upper end of the distribution.
negative skew (left-skewed)
Extreme skewness is not desirable for a distribution and _____ may be employed to make the skewed data closer to a normal distribution.
log information
A _____ is the steepness of a distribution in its center.
How many of the scores are shown frequently?
Distributions are generally described as platykurtic (relatively flat), leptokurtic (relatively peaked), or somewhere in the middle mesokurtic.
Kurtosis
Development of the concept of a normal curve began in the middle of the eighteenth century with the work of Abraham DeMoivre and, later, the Marquis de Laplace. At the beginning of the nineteenth century, Karl Friedrich Gauss made some substantial contributions. Through the early nineteenth century, scientists referred to it as the _____.
“Laplace-Gaussian curve.”
_____ is credited with being the first to refer to the curve as the normal curve, perhaps in an effort to be diplomatic to all of the people who helped develop it.
Karl Pearson
Theoretically, the _____ is a bell-shaped, smooth, mathematically defined curve that is highest at its center.
has symmetry when it is folded, the mean, median, and mode lie exactly on top of another.
The central tendencies are equal.
normal curve
A _____ is a normal distribution.
Theorized that it ranges from negative infinity to positive infinity.
Bell Curve
Simply stated, a _____ is a raw score that has been converted from one scale to another scale, where the latter scale has some arbitrarily set mean and standard deviation.
Raw scores may be converted to _____ because standard scores are more easily interpretable than raw scores. With a standard score, the position of a testtaker’s performance relative to other testtakers is readily apparent.
standard score
In essence, a _____ is equal to the difference between a particular raw score and the mean divided by the standard deviation.
A _____ of 1.5 is 1.5 standard deviations above and below the mean.
z score
If the scale used in the computation of z scores is called a zero plus or minus one scale, then the scale used in the computation of _____ can be called a fifty plus or minus ten scale; that is, a scale with a mean set at 50 and a standard deviation set at 10.
T scores
Devised by W. A. McCall and named a _____ in honor of his professor E. L. Thorndike
T score
One advantage in using T scores is that none of the scores is _____. By contrast, in a z score distribution, scores can be positive and negative; this can make further computation cumbersome in some instances.
negative
Other Standard Scores:
1) Stanine
2) Scholastic Aptitude Test (SAT) and Graduate Record Examination (GRE)
3) Deviation IQ scores
1) Stanine
2) Scholastic Aptitude Test (SAT) and Graduate Record Examination (GRE)
3) Deviation IQ scores
Other Standard Scores:
Other Standard Scores:
Numerous other standard scoring systems exist. Researchers during World War II developed a standard score with a mean of 5 and a standard deviation of approximately 2. Divided into nine units, the scale was christened a _____, a term that was a contraction of the words standard and nine.
mean=5, SD=2
Stanine
Other Standard Scores:
mean=500, SD=100
Scholastic Aptitude Test (SAT) and Graduate Record Examination (GRE)
Other Standard Scores:
mean=100, SD=15
IQ
Standard scores converted from raw scores may involve either _____ or _____.
linear transformation, nonlinear transformation
A standard score obtained by a _____ is one that retains a direct numerical relationship to the original raw score. The magnitude of differences between such standard scores exactly parallels the differences between corresponding raw scores.
linear transformation
A standard score obtained by a _____ is one that retains a direct numerical relationship to the original raw score. The magnitude of differences between such standard scores exactly parallels the differences between corresponding raw scores.
linear transformation
A _____ may be required when the data under consideration are not normally distributed yet comparisons with normal distributions need to be made. In a nonlinear transformation, the resulting standard score does not necessarily have a direct numerical relationship to the original, raw score. As the result of a nonlinear transformation, the original distribution is said to have been
normalized.
The original distribution has been normalized.
nonlinear transformation
Many test developers hope that the test they are working on will yield a normal distribution of scores. Yet even after very large samples have been tested with the instrument under development, skewed distributions result. What should be done?
Normalized standard scores
The process of conversion is called _____ that allows to compare observations and calculate probabilities across different populations.
standardization
