Psychological Testing: Statistics Refresher

• Psychological tests and test scores impact everyday life
• Tests can identify strengths and weaknesses
• Tests influence job interviews and career choices
• Understanding the theory and principles behind test use and score interpretation is important whether you are a test taker or a test user
• Statistical tools are used to describe, interpret, and draw conclusions from test scores

Statistics Refresher Topics

• Scales of measurement
• Data presentation (tabular and graphic)
• Measures of central tendency
• Measures of variability
• Aspects of the normal curve
• Standard scores

Scales of Measurement

• Measurement is assigning numbers or symbols to characteristics based on rules
• Rules represent the magnitude or characteristic being measured
• A scale consists of numbers or symbols modeling empirical object properties

Categorizing Scales

• Scales can be categorized by the variable type being measured
• A continuous scale measures continuous variables
• A discrete scale measures discrete variables
• Continuous scales divide values theoretically, but practical considerations may limit divisions
• Measurement always involves error, influenced by factors beyond what is being measured

Error in Measurement

• Error also includes factors that should be accounted for in measurement theory
• Error sources vary, such as distractions or test item selection
• The number used on a continuous scale to characterize a trait should be thought of as an approximation
• There are four different levels/scales of measurement, each providing distinct information

NOIR Acronym

• The French word "noir" (black) will help you remember scales from least to most rigorous for
• N: Nominal
• O: Ordinal
• I: Interval
• R: Ratio

Nominal Scales

• Nominal scales are the simplest measurement form
• Data is categorized based on characteristics, with mutually exclusive and exhaustive categories
• An example of a nominal scale is the Diagnostic and Statistical Manual of Mental Disorders
• Each disorder is assigned a number used for classification
• Numbers cannot be added, subtracted, ranked, or averaged
• Individual test items, such as yes/no responses, can use nominal scaling
• Arithmetic operations are limited - but nominal data includes counting cases in each category and determining proportions/percentages

Ordinal Scales

• Ordinal scales classify and rank order characteristics
• In business, job applicants can be rank-ordered by desirability
• In clinical settings, people can be rank-ordered according to their need for treatment
• Alfred Binet believed intelligence test data to be ordinal
• The assessment instruments like the Rokeach Value Survey use an ordinal form of measurement
• Ordinal scales don't indicate how much greater one ranking is than another
• Numbers don't represent measurement units
• Ordinal scales also have no absolute zero point, since every test taker will have some ability
• Data analysis from ordinal scales is limited, because you can't average and there is no information regarding units

Interval Scales

• Interval scales build on nominal and ordinal scales with equal intervals between numbers
• Each unit on the scale is exactly equal to any other
• Interval scales don't have an absolute zero point
• Interval scales allow averaging measurements for a meaningful result
• Many tests, such as intelligence tests, are analyzed statistically at the interval measurement level
• Because interval scales have no absolute zero point, their use assumes no test taker has none of the ability being measured

Ratio Scales

• In addition to all properties/measurements above
• A ratio scale has a true zero point
• All mathematical operations can be performed meaningfully
• Ratio-level measurement used in some psychology tests involving neurological functioning assessment
• An assessment includes hand grip strength or a timed perceptual-motor ability test/assessments
• No test taker can ever obtain a score of zero
• The ordinal level of measurement is most frequently used in psychology
• Most psychological and education scales are close in interval equality
• "Intelligence, aptitude, and personality test scores are, basically and strictly speaking, ordinal"
• Users must use and treat test data with caution

Describing Data

• A distribution is a set of test scores arranged for recording/study
• Scores in the distribution are referred to as raw scores
• A raw score is usually numerical
• A raw score's number of items responded to correctly on an achievement test
• Transforming scores is done in a way that will help students understand how their performance compared to that of the others

Frequency Distributions

• The data from the test can be organized into a distribution of the raw scores
• One way the scores could be distributed is by the frequency in which they occur
• All sores are listed along side number of times each score occurred
• Often called the simple frequency distribution to indicate individual scores have been used, and data was not grouped
• A grouped frequency distribution summarizes data, test-score intervals and is called a class interval, replaces test scores
• In most instances, the decision about the interval has convenience
• Easy to read, convenient summary of data is a trade off for a loss of detail
• The test scores have been grouped into twelve class intervals where each test interval equal to five points

Illustrated Graphically

• Frequency distributions of test scores can be illustrated graphically, with the use of:
• Lines
• Points
• Bars
• Symbols

Types of Graphs for Descriptive Statics

• Histogram
• It is the test score
• Bar Graph
• Numbers indicative of frequency to be placed along the y- axis.
• Frequency Polygon
• Data illustrated with 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. Regardless of the shape, there must be a good idea of a consumer
• The normal or bell shaped curve is used to better get a graphic representation of the data of a measurement

Measures of Central Tendency

• Measure of central tendency, is a statistic that indicates average or midmost score between extreme scores in distribution
• The most commonly used measure that is easily and simply the ''mean''
• The mean takes into account actual numerical value of every score
• Other measures of central tendency - median, and the mode . Greek uppercase letter ∑ is symbol used to '' sum ''
• Sigma is use to signify ''sum'', if x , represents test score then the expression ∑ X means ''add all the test scores''

Arithmetic Mean

• The arithmetic mean denoted X , pronounced the " X- bar''
• It is equal to the sum of the observations divided by the number of observations X= ∑(X /n), where n = the number of observations or test scores
• Formula = X =∑(fx)/n where ∑ (fX) means ''multiply the frequency with each number by its corresponding score and then sum"
• Technicallity there's range
• Another common used measure = The Median - middle score is determined by ordering all the scores
• If the numbers of the scores are odd then it is easy to measure the median as will be the score
• If the scores are even , the median was found from obtaining average which would be the aerthemtic

Modal Score

• The most frequently occurring score in a distribution of scores is the mode
• Mode is nominal
• However its important that it stay central
• Measure of variability, can be found with help of understanding the scores in a distribution

Variability

• Variability describes the measure of scores which happen scattered

Types of Distribution

• Distribution A & B
• Test scores could range 0-100 in b oth.
• Range, distribution is equal to the differences of between the highest and the lowest sores.
• It based on the entire values ranging from the lowest and the highest scores- one extreme score is in the values

The interquartile and semi-interquartile range.

• a distribution test scores matter, divide into four such that 25% the test scores occur in the quarters
• As illustrated the dividing point can be done within the four of the quarter in the distribution
• Interquartile range is a measure of the ability equal of the diff between the mean and Q1 Averaged Distribution
• Another tool, describe of the volume of its distributions.
• AD for short
• The lower cases italic , x , in the Formula signifies a score in the division of of a mean.
• In average deviation scores, a problem, where the sum, equals zero, , is the same
• Used to calculate the average, in the mean time will solving for the average.the numbers with 0's do the same
• As its always be the same

standard deviation.

• It equals to the square root means
• By definition to a measure equal by it.

Normal Curve

• Karl Pearson- credited with 1st to refer to the curve that it can be diplomatic for those who help

Understanding psychological test

• The data comes from the normal bell shaped tests that test at the same average, that it would seem normal to understand
• The most tested in average, and it would get results better more stable

z Scores

• The result is the conversion of a raw score indicates how many scores, standard deviations in the units, the raw score can be below or above the test.
• z+x-x/s

T Scores

• Scale used-zero, plus of minus one. Scale used in scores, T = 50 and the mean will be set at 50 . One advantage will using , T scores of the scores is in the test and the by contrast
• z-score of 2 - also positive in both.
• If someone has a great sense with both - will get easier the most standard
• scores the great world during the world war 2 (approximately ) 2. divided into - the term.nine of the units.a term, with its a contraction in 9-2-50, with some test it, and can be done