CHAPTER 3: A STATISTICS REFRESHER

Question 1

The act of assigning numbers or symbols to characteristics of things (people, events, whatever) according to rules. The rules used in assigning numbers are guidelines for representing the magnitude (or some other characteristic) of the object being measured.

Answer 1

Measurement

Question 2

It is a set of numbers (or other symbols) whose properties model empirical properties of the objects to which the numbers are assigned.

Answer 2

Scale

Question 3

A scale used to measure a continuous variable. These are variables that can take on any value within a range, including fractions or decimals.

Answer 3

Continuous Scale

Question 4

A scale used to measure a discrete variable. These are variables that can only take on specific, separate values, usually whole numbers.

Answer 4

Discrete Scale

Question 5

It 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.

Answer 5

Error

Question 6

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.

Answer 6

Nominal Scale

Question 7

It permits classification. However, in addition to classification, rank ordering on some characteristic is also permissible with this kind of scale. (It ranks things in order)

Answer 7

Ordinal Scale

Question 8

It contains equal intervals between numbers. Each unit on the scale is exactly equal to any other unit on the scale. (Measures in equal units, but no true zero.)

Answer 8

Interval Scale

Question 9

This scale 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. (Like interval, but has a true zero)

Answer 9

Ratio Scale

Question 10

What are the four major types of measurement scales?

Answer 10

Nominal
Ordinal
Interval
Ratio

Question 11

It is defined as a set of test scores arrayed for recording or study.

Answer 11

Distribution

Question 12

It is a straightforward, unmodified accounting of performance that is usually numerical. It may reflect a simple tally.

Answer 12

Raw Score

Question 13

It pertains to all scores that are listed alongside the number of times each score occurred. The scores might be listed in tabular or graphic form.

Answer 13

Frequency Distribution

Question 14

It refers to the test-score intervals, also called class intervals, that replace the actual test scores. The number of class intervals used and the size or width of each class interval (or the range of test scores contained in each class interval) are for the test user to decide.

Answer 14

Grouped Frequency Distribution

Question 15

Test-score intervals are also called?

Answer 15

Class intervals

Question 16

It is a diagram or chart composed of lines, points, bars, or other symbols that describe and illustrate data.

Answer 16

Graph

Question 17

It is similar to a bar graph but used for continuous data, showing the frequency distribution of data intervals. It is a graph with vertical lines drawn at the true limits of each test score (or class interval), forming a series of contiguous rectangles.

Answer 17

Histogram

Question 18

It uses rectangular bars to represent categorical data, where the length of each bar is proportional to the value it represents. It refers to the numbers indicative of frequency that also appear on the Y-axis, and a reference to some categorization (e.g., yes/no/maybe, male/female) appears on the X-axis.

Answer 18

Bar Graph

Question 19

A line graph that shows the shape of a data distribution. These 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).

Answer 19

Frequency Polygon

Question 20

A graph that uses lines to show trends or changes over time.

Answer 20

Line Graph

Question 21

A graph that shows the median, quartiles, and outliers of a dataset.

Answer 21

Box Plot (Box-and-Whisker Plot)

Question 22

A chart that organizes data to show its shape and individual values.

Answer 22

Stem-and-Leaf Plot

Question 23

A graph that uses dots to represent the frequency of individual values in a dataset.

Answer 23

Dot Plot

Question 24

It is a statistic that indicates the average or midmost score between the extreme scores in a distribution.

Answer 24

Measure of Central Tendency

Question 25

It refers to the average score. The sum of all test scores divided by the number of scores. It represents the "typical" score, and is used when data is normally distributed.

Answer 25

Mean (x̄)

Question 26

The formula for the _________ is X = Σ(X/n), where n equals the number of observations or test scores.

Answer 26

Mean (x̄)

Question 27

It is defined as the middle score in a distribution, and 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. It could be calculated by obtaining the average (or the arithmetic mean) of the two middle scores.

Answer 27

Median (x̃)

Question 28

The most frequently occurring score in a distribution of scores.

Answer 28

Mode

Question 29

It is a type of frequency distribution that has two distinct peaks or modes — meaning there are two scores or ranges of scores that occur more frequently than others. This can happen when: You have two groups within a population that perform very differently on a test.

Answer 29

Bimodal Distribution

Question 30

What are the measures of central tendency?

Answer 30

Mean Median Mode

Question 31

It is an indication of how scores in a distribution are scattered or dispersed.

Answer 31

Variability

Question 32

It refers to the Statistics that describe the amount of variation in a distribution.

Answer 32

Measures of Variability

Question 33

It pertains to a distribution that is equal to the difference between the highest and the lowest scores.

Answer 33

Range

Question 34

Note that _____ refers to a specific point whereas ______ refers to an interval.

Answer 34

quartile;quarter

Question 35

It is a statistical value that helps you understand how scores are distributed in a test or dataset by dividing the data into four equal parts. Each _____ marks the boundary between quarters of the data. This helps assess how an individual's test score compares to others in the sample.

Answer 35

Quartile

Question 36

It is a measure of variability equal to the difference between Q3 and Q1. The difference between the third quartile (Q3) and the first quartile (Q1). It also means that it tells you how wide the range is for the middle 50% of scores — where most people's test results typically fall.

Answer 36

Interquartile Range

Question 37

Determine the range formula: IQR = Q3 - Q1

Answer 37

Interquartile Range

Question 38

Half of the IQR; it gives a measure of variability centered around the median. It offers a more stable estimate of variability by ignoring extreme scores.

Answer 38

Semi-interquartile Range (SIQR)

Question 39

A circular chart divided into slices to show proportions of a whole.

Answer 39

Pie Chart

Question 40

Determine the range formula: SIQR = (Q3 - Q1) / 2

Answer 40

Semi-interquartile Range (SIQR)

Question 41

A tool that could be used to describe the amount of variability in a distribution and how spread out scores are around the mean (average) score of a test. It also tells us, on average, how far each individual score is from the mean of the group.

Answer 41

Average Deviation

Question 42

It is a measure of variability equal to the square root of the average squared deviations about the mean. More succinctly, it is equal to the square root of the variance.

Answer 42

Standard Deviation (SD σ)

Question 43

It is equal to the arithmetic mean of the squares of the differences between the scores in a distribution and their mean.

Answer 43

Variance (s2)

Question 44

It is the nature and extent to which symmetry is absent. It is an indication of how the measurements in a distribution are distributed.

Answer 44

Skewness

Question 45

It illustrates when relatively few of the scores fall at the high end of the distribution. __________ examination results may indicate that the test was too difficult.

Answer 45

Positive Skew

Question 46

It illustrates when relatively few of the scores fall at the low end of the distribution. __________ examination results may indicate that the test was too easy.

Answer 46

Negative Skew

Question 47

The term testing professionals use to refer to the steepness of a distribution in its center, to describe the peakedness/flatness of three general types of curves.

Answer 47

Kurtosis

Question 48

A flat distribution with light tails. Interpretation: Scores are more spread out; fewer extreme values. Example: A test where most people score around the middle and there are very few very high or very low scores.

Answer 48

Platykurtic

Question 49

A distribution with moderate peak and tails, similar to the normal (bell-shaped) distribution. Interpretation: This is considered the "standard" shape. The normal distribution is __________. Example: IQ scores typically follow a mesokurtic distribution.

Answer 49

Mesokurtic

Question 50

A tall and narrow distribution with heavy tails. Interpretation: More scores are clustered around the mean, but there are also more extreme scores (outliers). Example: A test where many people score similarly, but a few score very high or very low.

Answer 50

Leptokurtic

Question 51

It is a bell-shaped, smooth, mathematically defined curve that is highest at its center. From the center, it tapers on both sides approaching the X-axis asymptotically (meaning that it approaches, but never touches, the axis).

Answer 51

Normal Curve

Question 52

Development of the concept of a normal curve began in the middle of the eighteenth century with the work of A____ D_____ and, later, the M_____ d_ L_______.

Answer 52

Abraham DeMoivre & Marquis de Laplace

Question 53

Through the early nineteenth century, scientists referred to it as?

Answer 53

Laplace-Gaussian curve

Question 54

He 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.

Answer 54

Karl Pearson

Question 55

It refers to the far left or far right end of the curve, where the values become very small and stretch out toward the horizontal axis but never actually touch it.

Answer 55

Tail

Question 56

The ____ tail contains extremely low scores

Answer 56

Left Tail

Question 57

It 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.

Answer 57

Standard Score

Question 58

It 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 (zero plus or minus one scale).

Answer 58

Z-score

Question 59

It 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.

Answer 59

T-score

Question 60

It is a term that was a contraction of the words standard and nine. They are different from other standard scores in that they take on whole values from 1 to 9, which represent a range of performance that is half of a standard deviation in width.

Answer 60

Stanine

Question 61

A way to convert raw scores into standard scores (like z-scores or T-scores) while keeping the same relative distance between scores.

Answer 61

Linear Transformation

Question 62

This may be required when the data under consideration are not normally distributed, yet comparisons with normal distributions need to be made. It converts scores using a method that does not preserve exact distances between raw scores.

Answer 62

Nonlinear Transformation

Question 63

It is the process of reshaping a skewed (non-normal) score distribution to approximate a normal distribution, to make the scores easier to interpret and compare, especially when we want to use standard scores like z-scores, T-scores, or percentiles.

Answer 63

Normalizing a Distribution

Question 64

A scale of scores created from a non-normal distribution that has been transformed into a normal one. The resulting scores are called _____________. It allows fair comparison between test takers or even between different tests.

Answer 64

Normalized Standard Score Scale

Question 65

It is a number that provides us with an index of the strength of the relationship between two things. It expresses a linear relationship between two (and only two) variables, usually continuous in nature.

Answer 65

Coefficient of Correlation (Correlation Coefficient)

Question 66

It is an expression of the degree and direction of correspondence between two things.

Answer 66

Correlation

Question 67

As one variable increases, the other also increases. As one decreases, the other also decreases.

Answer 67

Positive Correlation

Question 68

As one variable increases, the other decreases, and vice versa.

Answer 68

Negative Correlation

Question 69

A statistical tool of choice when the relationship between the variables is linear and when the two variables being correlated are continuous (or, they can theoretically take any value). A statistical measure used to express the strength and direction of the linear relationship between two continuous variables, and tells us how much two things go together, like height and weight, or test scores and study time.

Answer 69

Pearson r (r)

Question 70

It is derived from the Pearson correlation coefficient (r) and provides a measure of how much variance in one variable is explained by the other variable in the context of statistical analysis, including psychological assessment. It is an indication of how much variance is shared by the X- and the Y-variables.

Answer 70

Coefficient of determination (r2)

Question 71

It is a non-parametric measure of correlation developed by Charles Spearman, used to assess the strength and direction of the monotonic relationship between two variables that are measured on ordinal scales or can be ranked.

Answer 71

Spearman Rho (ρ)

Question 72

Definition: The average of the deviations from the mean. Meaning: Always equals zero, because positive and negative deviations cancel out. Interpretation: Not very informative by itself.

Answer 72

First Moment

Question 73

Also known as the variance. Meaning: Measures the spread or dispersion of the data. Interpretation: The larger the second moment, the more spread out the data is.

Answer 73

Second Moment

Question 74

Meaning: Measures skewness, or the asymmetry of the distribution. Interpretation: Positive → skewed to the right Negative → skewed to the left

Answer 74

Third Moment

Question 75

Meaning: Measures kurtosis, or the "peakedness" and tail heaviness of the distribution. Interpretation: High kurtosis → sharp peak and heavy tails (leptokurtic) Low kurtosis → flat peak and light tails (platykurtic)

Answer 75

Fourth Moment

Question 76

A graph that displays the relationship between two continuous variables using dots. A graph with dots representing paired values (X, Y). X-values go on the horizontal axis, Y-values on the vertical axis.

Answer 76

Scatterplot

Question 77

It refers to the degree to which the relationship between two variables forms a curve rather than a straight line. It also means that the relationship between variables is nonlinear — the data points form a curve instead of a straight line.

Answer 77

Curvilinearity

Question 78

A data point that lies far away from the rest of the points in a scatterplot — it doesn't follow the general pattern or trend of the data. It can distort statistical results — especially correlation coefficients like Pearson’s r, they might include: A measurement error, A unique case (e.g., a gifted or severely impaired individual), an unusual condition or situation.

Answer 78

Outlier

Question 79

A key characteristic in an outlier that does not fit the overall pattern or line formed by the majority of the data.

Answer 79

Atypical

Question 80

A key characteristic in an outlier that shows a very high or very low value on one or both variables.

Answer 80

Extreme

Question 81

A key characteristic in an outlier that lies at a noticeable distance from the cluster of points.

Answer 81

Isolated

Question 82

It may be defined as a family of techniques used to statistically combine information across studies to produce single estimates of the data under study.

Answer 82

Meta-analysis

Question 83

It is a quantitative estimate of the magnitude or strength of a relationship, difference, or effect found in a study.

Answer 83

Effect size

Question 84

Measures the strength of association between two variables; Used in correlational studies, including meta-analyses

Answer 84

Correlation coefficient (r)

Question 85

Measures the difference between two means in standard deviation units, and used in experimental studies or group comparisons

Answer 85

Cohen’s d

Question 86

Proportion of variance explained in ANOVA, and is used in ANOVA designs

Answer 86

Eta squared (η²)

Question 87

Compares odds of outcomes between groups, and is used in logistic regression, health studies

Answer 87

Odds ratio