CHAPTER 3: STATISTICS REFRESHER 1
The PROCESS of ASSIGNING NUMBERS or SYMBOLS to CHARACTERISTICS of THINGS (PEOPLE, EVENTS, whatever) according to rules.
measurement
What is example of a measurement rule?
Assign the number 12 to all lengths that
are exactly the same length as a 12-inch ruler.
is a SET of NUMBERS (or OTHER SYMBOLS) whose PROPERTIES model EMPIRICAL PROPERTIES of the objects to which the NUMBERS are assigned
scale
What is the correct definition of a SAMPLE SPACE in the context of a variable?
The sample space refers to the possible values that a variable can take on.
it has a SAMPLE SPACE that can be COUNTED.
discrete scale
Which of the following correctly represents the SAMPLE SPACE for a CATEGORICAL VARIABLE like "year in high school"?
The sample space is {freshman, sophomore, junior, senior}.
Why is the NUMBER of PREVIOUS HOSPITALIZATIONS A PATIENT has considered a DISCRETE VARIABLE?
Because the sample space is countable and includes values like {0, 1, 2, 3, . . .}.
Which of the following statements best describes a CONTINUOUS SCALE?
Values can be any real number in the scale’s sample space, including fractions, numbers with many decimals, and irrational numbers like the square root of 2 or π.
In the language of assessment, what does "ERROR" refer to?
The collective influence of all factors on a test score or measurement beyond those specifically measured by the test or measurement.
What does the text suggest about the ROLE OF ERROR IN ALL MEASUREMENT?
Error is an inherent element of all measurement and must be accounted for in any theory of measurement.
Why is there always ERROR INVOLVED IN MEASUREMENT using CONTINUOUS SCALES?
Continuous scales are marked off in gradations that may not capture the exact value, leading to approximation errors.
How should a score on a CONTINUOUS SCALE, like a TEST SCORE, be INTERPRETED according to the text?
The score should be considered an approximation of the "real" score, not a precise measure.
Which of the following lists the FOUR LEVELS OF MEASUREMENT?
Nominal scale, ordinal scale, interval scale, and ratio.
the SIMPLEST FORM of MEASUREMENT.
nominal scale
What is the primary CHARACTERISTIC of a NOMINAL SCALE?
It involves classification or categorization based on one or more distinguishing characteristics, with no inherent order.
How are NOMINAL VARIABLES typically ANALYZED?
By verifying equality or difference between categories and counting cases within each category.
Which of the following statements is true about NOMINAL SCALES?
Numbers assigned to nominal variables are used exclusively for classification and cannot be meaningfully added or averaged.
What distinguishes ordinal scales from nominal scales?
Ordinal scales have categories with a clear and uncontroversial order, while nominal scales do not.
What does ALFRED BINET’S perspective on INTELLIGENCE TESTING highlight about ORDINAL SCALES?
Binet viewed intelligence testing as a method of classification and ranking, not as a precise measurement of ability.
What does the ROKEACH VALUE SURVEY illustrate about ORDINAL SCALES?
The survey uses ordinal scales to rank personal values according to their perceived importance, with numbers indicating their order but not the magnitude of differences between ranks.
Which of the following statements is true about ORDINAL SCALES?
Ordinal scales allow the use of relational operators such as <, ≤, >, and ≥, but do not indicate the exact magnitude of differences between ranks.
Why is ZERO WITHOUT MEANING on an ordinal scale, such as a test of JOB PERFORMANCE ABILITY?
Because ordinal scales do not have an absolute zero point, and the number of units separating scores is not known.
Which of the following statements is true about INTERVAL SCALES?
Interval scales have meaningful distances between numbers but lack an absolute zero point.
Why is TEMPERATURE measured in DEGREES CELSIUS considered an INTERVAL SCALE?
Because zero degrees Celsius does not represent an absence of heat, and distances between temperatures are consistent.
Which of the following is an example of a true INTERVAL SCALE?
Calendar years, because the distance between years is consistent.
What distinguishes a ratio scale from other types of measurement scales?
A ratio scale has a true zero point that indicates the absence of the quantity being measured, allowing for meaningful comparisons of ratios and proportions.
In the context of using a DYNAMOMETER to MEASURE HAND GRIP STRENGTH, which of the following statements accurately describes the implications of achieving a score of 0 pounds of pressure on a ratio scale?
A score of 0 pounds indicates a complete lack of exerted pressure and could result from various factors such as genuine paralysis, non-compliance, or malingering. Interpretation of the test data requires careful consideration of these factors.
What does the term "RAW SCORES" refer to in the context of TEST RESULTS?
The straightforward, unmodified numerical representation of performance on a test.
When you have a SET OF RAW SCORES from a TEST and want to EFFECTIVELY COMMUNICATE the RESULTS to your students, what is one of the FIRST STEPS you should take?
Transform the raw scores into a more organized format that conveys additional information about how each student's performance compares to others.
This is may be defined as a SET OF TEST SCORES ARRAYED for RECORDING or STUDY.
distribution
What distinguishes a grouped frequency distribution from a simple frequency distribution?
In a grouped frequency distribution, scores are organized into intervals or groups rather than listed individually.
In a GROUPED FREQUENCY DISTRIBUTION, what REPLACES INDIVIDUAL TEST SCORES?
Test-score intervals or class intervals.i
What is a HISTOGRAM USED for in the context of FREQUENCY DISTRIBUTIONS?
To display test scores or class intervals as contiguous rectangles, showing the frequency of each score.
How does a bar graph differ from a histogram in representing data?
In a bar graph, the bars are not contiguous and represent categorical data, whereas in a histogram, the bars are contiguous and represent numerical data.
What does a FREQUENCY POLYGON illustrate?
Data using a continuous line connecting points where test scores or class intervals (as indicated on the
X-axis) meet frequencies (as indicated on the Y-axis).
What is the ARITHMETIC MEAN, and how is it calculated?
The arithmetic mean is the sum of all test scores divided by the number of test scores, denoted by X̄ = ΣX / n.
In what type of data distribution is the ARITHMETIC MEAN MOST EFFECTIVE?
Interval or ratio data distributions that are approximately normal.
What SYMBOL is used to represent the ARITHMETIC MEAN in statistical formulas?
X̄ (pronounced "X bar")
What is a LIMITATION of determining the MEDIAN in a very LARGE dataset, such as tens of thousands of scores?
It is impractical to manually order the data and find the middle scores.
How is the MEDIAN determined in a distribution of scores when the total number of scores is ODD?
The median is the middle score with an equal number of scores above and below it.
What is the correct method for finding the MEDIAN when the total number of scores is EVEN?
Calculate the arithmetic mean of the two middle scores
How is the MODE determined in a distribution of scores? and identify the mode here Given the scores 43, 34, 45, 51, 42, 31, 51
The mode is the score that occurs most frequently in the distribution. The mode is 51
What is a distribution called when it has TWO MODES?
Bimodal
What is one practical APPLICATION of the MODE in research?
Identifying the most frequently mentioned word in interviews about a commercial.
What does the range measure in a distribution?
The difference between the highest and lowest scores in the distribution.
What does the interquartile range measure in a distribution?
The difference between the third quartile (Q3) and the first quartile (Q1).
What is the semi-interquartile range?
Half of the interquartile range.
What does it mean if Q1 and Q3 are not equidistant from the median?
The distribution is skewed.