Chapter 3: A Statistics Refresher

Question 1

Statistical Tools

Answer 1

Used to describe, make inferences from, and draw conclusions about numbers

Question 2

Measurement

Answer 2

Act of assigning numbers or symbols to characteristics of things (people, events, etc) according to rules

Question 3

Rules Used to Assign Numbers

Answer 3

Guidelines for representing the magnitude (or some other characteristic) of the object being measured

Question 4

Scale

Answer 4

Set of numbers (or other symbols) whose properties model empirical properties of the objects to which the numbers are assigned

Question 5

Ways to Categorize Scales

Answer 5

Continuous Scale

Discrete Scale

Question 6

Continuous Scale

Answer 6

A scale used to measure a continuous variable; exists when it is theoretically possible to divide any of the values of the scale

Question 7

Discrete Scale

Answer 7

A scale used to measure a discrete variable; example, male or female

Question 8

Units into which a continuous scale will be divided

Answer 8

Depends on factors such as the purpose of the measurement and practicality

Question 9

Error

Answer 9

Refers to the collective influence of all of the factors on a test score or measurement beoynd those specifically measured by the test or measurement

Question 10

Sources of Error

Answer 10

A distracting thunderstorm

Particular selection of test items the instructor chose to use for the test

Question 11

Measuring Scale

Answer 11

Continuous if used for psychological and educational assessment and therefore can be expected to contain this sort of error

Question 12

Four levels or Scales of Measurement

Answer 12

Nominal, Ordinal, Interval, and Ratio Scales; Within these, different levels or scales of measurement, assigned numbers convey different kinds of information;

Question 13

Statistical Manipulation

Answer 13

May or may not be appropriate, depending upon the leel or scale of measurement

Question 14

Nominal Scales

Answer 14

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

Question 15

Arithmetic Operations

Answer 15

That can be performed with norminal data include counting for the purpose of determining how many cases fall into each category and a resulting determination of proportion or percentages

Question 16

Ordinal Scales

Answer 16

Permits classification rank ordering on some characteristic is also permissible with ordinal scales; have no absolute zero point; notes how much greater one ranking is than another; limited statistical analysis

Question 17

Alfred Binet

Answer 17

Developer of the intelligence test that bears his name, believed strongly that the data derived from an intelligence test are ordinal in nature; Emphasized that what he tried to do in the test was not to measure people but merely to classify (and rank) people on the basis of their performance on the tasks.

Question 18

Rokeach Value Survey

Answer 18

Uses ordinal form of measurement

Question 19

Zero in a Survey

Answer 19

Without meaning in such a test because the number of units that separate one testtaker’s score from another’s is simply not known

Question 20

Interval Scales

Answer 20

Contain equal intervals between numbers; each unit on the scale is exactly equal to any other unit on the scale; contain no absolute zero point; it is possible to average a set of measure ments and obtain a meaningful result

Question 21

Ratio Scales

Answer 21

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

Question 22

Ratio-Level Measurement

Answer 22

Employed in some types of tests and test items, especially those involving assessment of neurological functioning; Test of hand grip, timed test of perceptual-motor ability (completion of a puzzle); no testtaker can ever obtain a score of zero on an assembly task

Question 23

Measurement used in Psychology

Answer 23

Ordinal level of measurement; intelligence, aptitude, and personality tests are basically and strictly speaking, ordinal; these tests indicate with more or less accuracy not the amount of intelligence, aptitude, and personality traits of individuals, but rather the rank-order positions of individuals

Question 24

Distribution

Answer 24

Defined as a set of test scores arrayed for recording or study

Question 25

Raw Score

Answer 25

Straighforward, unmodified accounting of performance that is usually numberical; may reflect a simple tally, as in the number of items responded to correctly on an achievement test

Question 26

Frequency Distribution

Answer 26

All scores are listed alongside the number of times each score occurred; scores may be listed the frequency of occurrence of each score in one column and the score itself in the other column

Question 27

Simple Frequency Distribution

Answer 27

What a frequency distribution is referred to, to indicate that individual scores have been used and the data have not been grouped

Question 28

Grouped Frequency Distribution

Answer 28

Test-score intervals replace the actual test scores

Question 29

Class Intervals

Answer 29

Test-score intervals

Question 30

Graph

Answer 30

A diagram or chart composed of lines, points, bars, or other symbols that describe and illustrate data

Question 31

Good Graph

Answer 31

The place of a single score in relation to a distribution of test scores can be understood easily

Question 32

Types of Graphs

Answer 32

Histogram Bar Graph Frequency Polygon

Question 33

Histogram

Answer 33

Graph with vertical lines drawn at the true limits of each test score (or class interval), forming a series of contiguous rectangles; customary for the test scores to be placed along the graph's horizontal axis (x) and for numbers indicative of the frequency of occurrence to be placed along the graph's vertical axis

Question 34

Abcissa

Answer 34

X axis, the graph's horizontal axis; where test scores should be placed

Question 35

Ordinate

Answer 35

Y axis, the graph's vertical axis; where numbers indicative of the frequency of occurrence should be placed

Question 36

Bar Graph

Answer 36

Numbers indicative of frequency also appear on the Y axis, and reference to some categorization appears on the x-axis; rectangular bars are not contiguous

Question 37

Frequency Polygon

Answer 37

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)

Question 38

Bell-Shaped Curve

Answer 38

Normal graphic representation of data

Question 39

Measure of Central Tendency

Answer 39

Statistic that indicates the average or midmost score between the extreme scores in a distribution

Question 40

Center of a Distribution

Answer 40

Arithmetic Mean Median Mode

Question 41

Mean

Answer 41

The average, takes into account the actual numerical value of every score; Sum of observations divided by the number of ebservations or test scores; most appropriate measure of central tendency for interval or ratio data when distributions are believed to be approximately normal; the most stable and useful measure of a central tendency

Question 42

Median

Answer 42

Defined as the middle score in a distribution; scores are ordered in a list by magnitude, in either ascending or descending order. If the total number of scores ordered is an odd number, then the median will be the score that is exactly in the middle, with one-half of the remaining scores lying above it and the other half of the scores lying below it; average calculated by obtaining the average of the two middle scores; appropriate measure of central tendency for ordinal, interval, and ratio data

Question 43

When Median is Useful to measure Central Tendency

Answer 43

In cases where relatively few scores fall at the high end of the distribution or relatively few scores fall at the low end of the distribution

Question 44

Mode

Answer 44

Most frequenctly occurring score in a distribution of scores;

Question 45

Bimodal Distribution

Answer 45

When there are two scores that occur with the highest frequency; not a commonly used measure of central tendency; not calculated; one merely counts and determines which score occurs most frequently; not necessarily a unique point in a distribution; useful in conveying certain types of information; useful in analyses of a qualitative or verbal nature; useful to convey information IN ADDITION to the mean;

Question 46

Variability

Answer 46

Indication of how scores in a distribution are scattered or dispersed

Question 47

Measures of Variability

Answer 47

Include the range, the interquartile range, the semi-interquartile range, the average deviation, the standard deviation and the variance

Question 48

Range

Answer 48

Equal to the difference between the highest and the lowest scores; simplest measure of variability to calculate; Because it is based on values of the lowest and highest scores, one extreme score can radically alter the value of the range; provides a quick but gross description of the spread of scores

Question 49

Nature of the Range

Answer 49

When its value is based on extreme scores in a distribution, the resulting description of variation may be understated or overstated. Better measures include interquartile range and the semiquartile range

Question 50

Quartiles

Answer 50

Dividing test scores into four parts such that 25% of the test scores occur in each quarter; refers to a specific point

Question 51

Quarter

Answer 51

Refers to an interval

Question 52

Interquartile Range

Answer 52

Measure of variability equal to the difference between Q3 and Q1; ordinal statistic

Question 53

Semi-Interquartile Range

Answer 53

Equal to the interquartle range divided by 2;

Question 54

Shape of distribution

Answer 54

Provided by the relative distances from Q1 and Q3 from Q2 (the median)

Question 55

Perfectly symmetrical Distribution

Answer 55

Q1 and Q3 will be esactly the same distance from the median

Question 56

Skewness

Answer 56

Lack of symmetry

Question 57

Average Deviation (AD)

Answer 57

Tool that could be used to describe the amount of variability in a distribution; Deviation scored are added and divided by the total number of scores to arrive at the average deviation

Question 58

Standard Deviation

Answer 58

Square of each score is used; a measure of variability equal to the square root of the average squared deviations about the mean; Equal to the square root of the variance; Standard deviation measures how much - on average - individual scores of a given group vary (or deviate) from the average (or mean) score for this same group. In other words, the value of standard deviation helps show how many subjects in the group score within a certain range of variation from the mean score for the entire group. Still other way to explain it is that standard deviation measures the spread of individual results around a mean of all the results;

Question 59

Variance

Answer 59

Equal to the arithmetic mean of the squares of the differences between the scores in a distribution and their mean; squaring and summing all the deviation scores and then dividing by the total number of scores

Question 60

If Standard Deviation is 14.10

Answer 60

1 Standard Deviation Unit is approximately equal to 14 units of measurement or to 14 test-score points

Question 61

n-1

Answer 61

only makes a difference if n is 10 or more

Question 62

Skewness

Answer 62

The nature and extent to which symmetry is absent; indication of how the measurements in a distribution are distributed

Question 63

Positively Skewed Distribution

Answer 63

When relatively few of the scores fall at the high end of the distribution; for examination result, may indicate that the test was too difficult;the distance between Q3-Q2 > Q2-Q1

Question 64

Negatively Skewed Distribution

Answer 64

When relatively few of the scores fall at the low end of the distribution; for examination results, may indicate that the test was too easy; Q3-Q2

Question 65

Symmetrical Distribution

Answer 65

Distances from Q1 and Q3 to the median are the sme

Question 66

Kurtosis

Answer 66

Used to refer to the steepness of a distribution in its center;

Question 67

Descriptions of Distributions

Answer 67

Platykurtic Leptokurtic Mesokrtic

Question 68

Platykurtic

Answer 68

Relatively flat

Question 69

Leptokurtic

Answer 69

Relatively peaked

Question 70

Mesokurtic

Answer 70

Somewhere in the middle

Question 71

Abraham DeMoivre & Marquis de Laplace

Answer 71

First ones to develop the concept of normal curve

Question 72

Karl Friedrich Gauss

Answer 72

Made some substantial contributions to the concept of normal curve; LaPlace-Gaussian Curve

Question 73

Karl Pearson

Answer 73

Credited with being the first to refer to the curve as the normal curve; Gaussian curve

Question 74

Normal Curve

Answer 74

Bell-shaped, smooth, mathematically defined curve that is at its center. From the center, it tapers on both sides apporaching the X-axis asymptotically; symettrical, the mean, median, and mode all have the same exact value; has two tails

Question 75

Asymptotically

Answer 75

It approaches but never touches the axis

Question 76

Distribution of a normal curve

Answer 76

Ranges from negative infinity to positive infinity

Question 77

Characteristics of all Normal Distributions

Answer 77

50% occur above the mean and 50% of the scores occur below the mean Approximately 34% of all scores occur between the mean and 1 standard deviation above the mean Approximately 34% of all scores occur between the mean and 1 standard deviation below the mean Approximately 68% of all scores occur between the mean and +_ 1 standard deviation Approximately 95% of all scores occur between the mean and +-2 standard deviations

Question 78

Tail

Answer 78

The area on the normal curve between 2 and 3 standard deviations above the mean; the area on the normal curve between -2 and -3 standard deviations below the mean

Question 79

Standard Score

Answer 79

Raw score that has been converted from one scale to another scale, where the latter scale has some arbitrarily set mean and standard deviation

Question 80

Why convert raw scores to standard scores

Answer 80

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

Question 81

Systems for Standard Scores

Answer 81

z Scores T Scores Stanines Other standard scores

Question 82

Zero Plus or Minus One Scale

Answer 82

Type of standard score scale that may be thought of as the zero plus or minus one scale

Question 83

z Score

Answer 83

Results from the conversion of a raw score into a number indicating how many standard deviation units the raw score is below or above the mean of the distribution; provides a convenient context for comparing scores on the same and different tests; zero plus or minus one scale

Question 84

T Scores

Answer 84

Fifty plus or minus ten scale; a scale with a mean set at 50 and a standard deviation set at 10; discovered by W.A. McCall named it as such in honor of EL Thorndike; standard score system composed of a scale that ranges from 5 standard deviations below the mean to 5 standard deviations above the mean;

Question 85

Stanine

Answer 85

Contraction of words standard and nine; test scores are often represented as stanines; they take on whole values from 1 to 9 which represent a range of performance that is half of a standard deviation width

Question 86

Scores Obtained By Linear Transformation

Answer 86

One that retains a direct numerical relationship to the original raw score; the magnitude of difference between standard scores exactly parallels the differences between corresponding raw scores

Question 87

Nonlinear Transformation

Answer 87

May be required when the data under consideration are not normally distributed yet comparisons with normal distributions need to be made; resulting standard score does not necessarily have a direct numerical relationship to the original, raw score

Question 88

Normalizing the Distribution

Answer 88

Involves stretching the skewed curve into the shape of a normal curve and creating a corresponding scale of standard scores

Question 89

Normalized standard Score Scale

Answer 89

Corresponding scale of standard scores