statistics refresher

statistics

• are used for purposes of description.

• Numbers provide convenient summaries and allow us to evaluate some observations relative to others

• For example, if you get a score of 54 on a psychology examination, you probably want to know what 54 means

• Is 54 lower than the average score or is it about the same?

• Knowing the answer can make the feedback you get from your examination more meaningful. If you discover that the 54 puts you in the top 5% of the class, then you might assume you have a good chance for an A. If it puts you in the bottom 5%, then you will feel indifferently

statistics

• can be utilized to make inferences, which are logical deductions about events that cannot be observed directly

• For example, you do not know how many people watched a particular television movie unless you ask everyone.

• However, by using scientific sample surveys, you can infer the percentage of people who saw the film

Two Kinds of Statistics

• Descriptive Statistics

• Inferential Statistics

Descriptive Statistics

• These are methods used to provide a concise description of a collection of quantitative information

• brief informational coefficients that summarize a given data set, which can be either a representation of the entire population or a sample of a population

• broken down into measures of central tendency and measures of variability (spread)

• mean, median, mode

Inferential Statistics

• These are methods used to make inferences from observations of a small group of people known as a sample to a larger group of individuals known as the population

• Typically, the psychologist wants to make statements about the larger group but cannot possibly make all the necessary observations. Instead, he or she observes a relatively small group of subjects (sample) and uses inferential statistics to estimate the characteristics of the larger group

Properties of Scales

• make scales of measurement different from one another which are:

• Magnitude

• Equal Intervals

• Absolute 0 (Zero)

magnitude

• property of “moreness”

• A scale has the property of magnitude if we can say that a particular instance of the attribute represents more, less, or equal amounts of the given quantity than does another instance

• On a scale of height for example, if we can say Michael is shorter than Denzel, then the scale has the property of?

magnitude

• There are scales that do not have the property of?

• For example, a coach assigning identification numbers to teams such as Team 1, Team 2, and Team 3 does not have the property of magnitude

• However, if these teams are ranked based on the number of games they have won, then the new numbering system would have the property of?

Equal Intervals

• A scale has the property of equal intervals if the difference between two points at any place on the scale has the same meaning as the difference between two other points that differ by the same number of scale units

• For example, the difference between inch 2 and inch 4 on a ruler represents the same quantity as the difference between inch 10 and inch 12: exactly 2 inches

Absolute 0 (Zero)

• Absolute 0 (Zero) is obtained when nothing of the property being measured exists

• For example, if you are measuring heart rate and observe that your patient has a rate of 0 and has died, then you would conclude that there is no heart rate at all

• For many psychological properties, it is extremely difficult, if not impossible, to define an absolute 0 point

• For example, if one measures shyness on a scale from 0 to 10, then it is hard to define what it means for a person to have absolutely no shyness

Nominal

• does not have the property of magnitude, equal intervals, or an absolute 0

• really not scales at all; their only purpose is to name objects

• For example, the numbers in the back of the jersey of basketball or football players are nominal because they are not used to quantify, they are only used to label the player

Ordinal

• A scale with the property of magnitude but not equal intervals or an absolute 0

• This scale allows you to rank individuals or objects but not say anything about the meaning of the differences between ranks

• If you were to rank the members of your class by height, then you would have an ordinal scale. For example, if Vin is the tallest, Rovi the second tallest, and Peter the third tallest, you would assign them the ranks of 1, 2, & 3, respectively but you would not give consideration as to how many inches are their difference between each other

Interval

• When a scale has the properties of magnitude and equal intervals but not absolute 0

• the measurement of temperature in degrees Fahrenheit. This temperature scale clearly has the property of magnitude, because 35°F is warmer than 32°F

• Also, the difference between 90°F and 80°F is equal to a similar difference of 10 degrees at any point on the scale. There is no absolute 0 because 0° in Fahrenheit still refers to a degree of temperature which is a temperature that is very cold

Ratio

• A scale that has all three properties (magnitude, equal intervals, and an absolute 0)

• For example, consider the number of yards gained by running backs in football teams. Zero yards actually mean that the player has gained no yards at all

• If one player has gained 1000 yards and another has gained only 500, then we can say that the first athlete has gained twice as many yards as the second

• Another example is the speed of travel. For instance, 0 miles per hour (mph) is the point at which there is no speed at all. If you are driving onto a highway at 30 mph and increase your speed to 60 when you merge, then you have doubled your speed

DISTRIBUTION OF SCORES

• A single test score means more if one relates it to other test scores

• summarizes the scores for a group of individuals.

Frequency Distribution

• It displays scores on a variable or a measure to reflect how frequently each value was obtained

• one defines all the possible scores and determines how many people obtained each of those scores

• Usually, scores are arranged on the horizontal axis from the lowest to the highest value.

• The vertical axis reflects how many times each of the values on the horizontal axis was observed

• 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

Class Interval

Whenever you draw a frequency distribution or a frequency polygon, you must decide on the width of this

• This answers the question “What percent of the scores fall below a particular score”

• the percentage of scores in its frequency distribution that are equal to or lower than it.

• For example, a test score that is greater than 75% of the scores of people taking the test is said to be at the 75th percentile, where 75 is the percentile rank

Describing Distributions

• Statistics are used to summarize data. If you consider a set of scores, the mass of information may be too much to interpret all at once.

• That is why we need these numerical conveniences to help summarize the information:

• Mean

• Standard Deviation

• Z-Score

• Standard Normal Deviation

• T-Score

• Quartiles and Deciles

mean

• The arithmetic average score in a distribution

• To calculate the mean, we total the scores, and we divide the sum with the number of cases

Standard Deviation

• This is an approximation of the average deviation around the mean.

• This is basically the degree of variation in test scores

Z-Score

• One problem with means and standard deviations is that they do not convey enough information for us to make meaningful assessments or accurate interpretations of data

• transforms data into standardized units that are easier to interpret.

• This describes a value’s relationship to the mean of a group of values

• have a mean of 0 and a standard deviation of ±1

T-Score

• to transforms data into standardized units that are easier to interpret.

• This describes a value’s relationship to the mean of a group of values

• have a mean of 50 and a standard deviation of 10

Quartiles

• These are points that divide the frequency distribution into equal fourths.

• The first quartile is the 25th percentile, the second quartile is the 50th percentile, the third is the 75th percentile

Deciles

These are similar to quartiles except that they use points that mark 10% rather than 25% intervals

Correlation

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

• For example, a test administrator would like to know the correlation between the scores of a Brief Resilience Scale and Mental Toughness Scale. If the scores on BRS are mostly high and the scores on the MTS also show the same trend, we can say that there is a correlation between the two variables

coefficient of correlation (r)

expresses a linear relationship between two (and only two) variables, usually continuous in nature

Positive Correlation

• refers to when the Scores in BRS are high while the scores in MTS high as well.

• This can also happen when both scores are low

• both high or both low

Negative Correlation

• happens when the two scores contradict with each other.

• When one is high, the other score is low

Regression

• This may be defined broadly as the analysis of relationships among variables for the purpose of understanding how one variable may predict another

• The statistical tool that can be utilized for this is the ANOVA

Simple Regression

• involves one independent variable, which is typically referred to as the predictor variable, and one dependent variable typically referred to as the outcome variable.

• The statistical tool utilized for this is the T-Test

Multiple Regression

the statistical technique that can be used to analyze the relationship between a single dependent variable and several independent variables

Multimethod Assessment

• No measure of personality or behavior is perfect.

• Some have excellent reliability, validity, and clinical utility, but even these have their limitations.

• For that reason, it is important for clinical psychologists not to rely exclusively on any single assessment method.

• Instead, personality is best assessed by using multiple methods, including tests of different types, interview data, observations, or other sources.

Multimethod Assessment

Evidence-Based Assessment

• Clinical psychologists who practice evidence-based assessment select only those methods that have strong psychometrics, including reliability, validity, and clinical utility

• They typically target their assessment strategies toward a particular diagnosis or problem, such that “what works” for assessing attention-deficit/ hyperactivity disorder (ADHD) might be a different set of assessment tools than “what works” for assessing panic disorder, schizophrenia, bulimia, PTSD, or any other clinical issue

• Some of its advocates hope it will influence not only current graduate students in clinical psychology but also experienced psychologists “who use assessment instruments because they learned them in graduate school, rather than because there is strong evidence that they work.

Culturally Competent Assessment

• essential across all activities of clinical psychologists, especially personality assessment.

• Simply put, every culture has its own perception of “normal” and its own variations of “abnormal” as well

• A personality assessment conducted without knowledge or sensitivity to these cultural specifics can be a dangerous thing; in fact, it has been labeled “cultural malpractice” by some

• A primary danger lies in the possibility of overpathologizing—that is, viewing as abnormal that which is culturally normal

• In other words, the clinical psychologist must appreciate the meaning of a behavior, thought, or feeling within the context of the client’s culture, which may differ from the context of the psychologist’s own culture

Objective Personality Tests

• unambiguous test items, offer clients a limited range of responses, and are objectively scored.

• Most often, the objective personality tests that clinical psychologists use are questionnaires that clients complete with pencil and paper

• They typically involve a series of direct, brief statements or questions and either true/false or multiple-choice response options in which clients indicate the extent to which the statement or question applies to them

Minnesota Multiphasic Personality Inventory-2

• When creating a personality test, it is relatively easy for an author to create a list of items that should, theoretically, elicit different responses from “normal” and “abnormal” people of various categories

• Hathaway and McKinley chose to take on a greater challenge: to create a list of items that empirically elicit different responses from people in these normal and abnormal groups

• Hathaway and McKinley succeeded in creating such a list of items by using a method of test construction called empirical criterion keying

Empirical Criterion Keying

• Essentially, this method involves identifying distinct groups of people, asking them all to respond to the same test items, and comparing responses between groups

• If an item elicits different responses from one group than from another, it’s a worthy item and should be included on the final version of the test

• If the groups answer an item similarly, the item is discarded because it does not help categorize a client in one group or the other

Hypochondriasis

• scale number: 1

• abbreviation: Hs

• description of high scale scores: Somatic problems, excessive bodily concern, weakness, ailments, complaining and whining

Depression

• scale number: 2

• abbreviation: D

• description of high scale scores: Depressed, unhappy, low confidence, pessimistic

Hysteria

• scale number: 3

• abbreviation: Hy

• description of high scale scores: Vague medical reactions to stress, somatic symptoms, denial of conflict and anger

Psychopathic Deviate

• scale number: 4

• abbreviation: Pd

• description of high scale scores: Antisocial, rebellious, blaming others, poor consideration of consequences of actions

Masculinity-Femininity

• scale number: 5

• abbreviation: Mf

• description of high scale scores: Rejection of traditional gender roles, effeminate men, masculine women

Paranoia

• scale number: 6

• abbreviation: Pa

• description of high scale scores: Suspicious, guarded, hypersensitive, belief that others intend to harm

Psychasthenia

• scale number: 7

• abbreviation: Pt

• description of high scale scores: Anxious, nervous, tense, worrisome, obsessive

Schizophrenia

• scale number: 8

• abbreviation: Sc

• description of high scale scores: Psychotic, disorganized, or bizarre thought process, unconventional, hallucinations, delusions, alienated

Mania

• scale number: 9

• abbreviation: Ma

• description of high scale scores: Manic, elevated mood, energetic, overactive, accelerated movement and speech, flight of ideas

Social Introversion

• scale number: 10

• abbreviation: Si

• description of high scale scores: Introverted, shy, reserved, more comfortable alone than with others

Personality Assessment Inventory (PAI)

• contains 344 items, each of which offers four responses: totally false, slightly true, mainly true, and very true.

• It is appropriate for clients 18 to 89 years old, but an adolescent version, the PAI-A, can be used for clients as young as 12.

• It includes 11 clinical scales, some that match with those of the MMPI but others that are more uniquely tied to specific diagnoses or problems, like Borderline Features, Antisocial Features, Anxiety- Related Disorders, Alcohol Problems, and Drug Problems.

Millon Clinical Multiaxial Inventory-IV

• like the MMPI-2 and PAI in many ways: It is a comprehensive personality test in a self-report, pencil-and paper, true/false format.

• The primary difference between the tests is its emphasis on personality disorders

• features separate clinical scales corresponding to each of the 10 current personality disorders (e.g., antisocial, borderline, narcissistic, paranoid)

• It also includes clinical scales for other forms of personality pathology, many of which have been considered for inclusion as disorders in DSM but are currently omitted (e.g., self-defeating personality, negativistic/passive-aggressive personality, depressive personality, turbulent personality

NEO Personality Inventory-3

The authors, Paul Costa and Robert McCrae, sought to create a personality measure that assesses “normal” personality characteristics

In short, the authors of the NEO-PI-3 (who also put forth the corresponding five-factor model of personality or “Big Five”) argue that the many words our language offers for describing personality traits “cluster” into five fundamental traits of personality that characterize everyone in varying degrees.

These traits—Neuroticism, Extraversion, Openness, Agreeableness, and Conscientiousness— are the five primary scales yielded

Neuroticism

Extraversion

Openness

Agreeableness

Conscientiousness

Beck Depression Inventory - II

• self-report, pencil-and-paper test that assesses depressive symptoms in adults and adolescents

• brief—only 21 items, usually requiring a total of 5 to 10 minutes to complete.

• Each item is a set of four statements regarding a particular symptom of depression, listed in order of increasing severity.

• The clients choose the one sentence in each set that best describes their personal experience during the previous 2 weeks (a time period chosen to match DSM criteria)

Beck Depression Inventory - II

• The 21 item scores are summed to produce a total score, which reflects the client’s overall level of depression

• consider the following set of statements, of which the client would choose one:

• I never think about dying. (0 points)

• I occasionally think about dying. (1 point)

• I frequently think about dying. (2 points)

• I constantly think about dying. (3 points)

Projective Personality Tests

• based on a fundamentally different assumption: People will “project” their personalities if presented with unstructured, ambiguous stimuli and an unrestricted opportunity to respond

• Imagine a group of people lying on the ground, looking up at the same series of vaguely shaped clouds in the sky.

• The way each person makes sense of the series of clouds implies something about that person’s personality

Projective Personality Tests

• To extend this analogy, projective personality tests are similar to a series of “clouds” that psychologists display to clients.

• The lack of objectivity, especially in scoring and interpreting, highlights the most frequently cited shortcoming

• Critics stress that they are far too inferential to be empirically sound; that is, they rely too heavily on a psychologist’s unique way of scoring and interpreting a client’s responses

Rorschach Inkblot Method

• In 1921, Hermann Rorschach created

• Rorschach was a Swiss psychiatrist who, as a child, played a game in which participants looked at vague blots of ink and said what they saw in the blots

• As an adult, he decided to apply a similar method to his patients, with the hypothesis that their responses would reveal their personality characteristics

Rorschach created 10 inkblots, 5 with only

black ink and the other 5 with multiple colors.

Administration occurs in two phases. In the “response”

or “free association” phase, the psychologist presents

one inkblot card at a time, asks, “What might this be?”

and writes down the client’s responses verbatim.

After the client has responded to all 10 cards, the

“inquiry” phase begins, in which the psychologist reads

the client’s responses aloud and asks the client to

describe exactly where in the inkblot each response

was located and what features of the inkblot caused

the client to offer that response.

Thematic Apperception Test

• feature interpersonal scenes rather than inkblots. The client’s task is to create a story to go along with each scene

• They are asked to consider not only what is happening in the scene at the moment but also what happened before and what may happen after the scene.

• They are also asked to describe what the characters may be thinking and feeling

• Although it is considered a global measure of personality by many, its strength may lie in its ability to measure interpersonal relationship tendencies

Thematic Apperception Test

• includes a total of 31 cards, but psychologists typically select their own subset of cards—often about 10 or so—to administer to a particular client

• As the client tells stories aloud and the psychologist writes them down, the psychologist may ask questions during a client’s story to solicit more information and can remind the client of the initial instructions as well.

• often analyzed without formal scoring at all.

• Thus, interpretation is frequently more art than science.

• A client’s story may be interpreted one way by one psychologist but very differently by another.

Sentence Completion Tests

• the ambiguous stimuli are neither inkblots nor interpersonal scenes; instead, they are the beginnings of sentences

• The assumption is that clients’ personalities are revealed by the endings they add and the sentences they create

Intelligence Tests

Measure a client’s intellectual activities

Neuropsychological Tests

Focuses on issues of cognitive or brain dysfunction, including the effects of brain injuries and illnesses

Charles Spearman

• To him, Intelligence is One Thing.

• In other words, intelligence is a singular characteristic

• he labeled this characteristic “g” for general intelligence and argued that it represented a person’s global, overall intellectual ability

• he acknowledged that more specific abilities “s” existed, but he argued that they played a relatively minor role in intelligence

Louis Thurstone

• he argued that intelligence should not be understood as a single, unified ability but as numerous distinct abilities that have little relationship to one another

• He was a pioneer of the statistical procedure called multiple-factor analysis, which enabled him to identify underlying factors in a large data set

• Using multiple-factor analysis, he found several independent factors.

• These factors were given labels such as verbal comprehension, numerical ability, spatial reasoning, and memory

• This means that you cannot say confidently that a person performing well in mathematics will also perform well when it comes to verbal skills

Hierarchical Model of Intelligence

raymond cattell

• proposed two separate intelligences:

• Fluid Intelligence: The ability to reason when face with novel problems

• Crystallized Intelligence: The body of knowledge one has accumulated as a result of life experiences

Three-Stratum Theory of Intelligence

General Ability

• can provide a broad and comprehensive assessment of cognitive functioning.

• It is often associated with problem-solving skills, adaptability, and learning ability.

• it may not provide detailed insights into specific skills or aptitudes.

Specific Ability

• provide a detailed and focused assessment of an individual's proficiency in a particular area

• They can be useful for identifying strengths and weaknesses in specific domains.

• may not provide a complete picture of an individual's overall cognitive capacity

• It may also be less applicable in contexts that require a broad understanding or adaptability across different domains.

Task or Goal Specificity

• Consider the specific task or goal of the assessment.

• If you need a broad understanding of overall cognitive ability, general ability assessments may be more appropriate.

• If you are interested in a particular skill or domain, specific ability assessments may be more relevant.

Balanced Approach

incorporates both general and specific ability assessments can provide a more comprehensive understanding of an individual's cognitive profile.

Context and Purpose

• The choice between general and specific abilities also depends on the context of the assessment and the purpose for which the information is being gathered.

• For academic or employment settings, a combination of both may be beneficial.

Wechsler Intelligence Tests

• cover virtually the entire life span.

• They vary slightly from one another, as necessitated by the demands of measuring intelligence at different ages

• They are administered one-on-one and face-to-face.

• cannot be administered to a group of examinees at the same time, nor are they entirely pencil-and-paper tests (e.g., multiple choice, true/false, essay) that examinees simply administer to themselves

Wechsler Intelligence Tests

• They feature large, carefully collected sets of normative data.

• That is, the manual for each Wechsler test includes norms collected from about 2,000 people

• have a number of notable strengths: They have impressive reliability and validity; they feature comprehensive and recent normative data; they cover an extremely wide age range; they provide full-scale, index, and subtest scores that have great clinical utility; and, at this point in their history, they are very familiar to most clinical psychologists.

Wechsler Intelligence Tests

On the other hand, these tests have received criticism for some limitations: Some subtests may be culturally loaded or biased, the connection between the tests and day-to-day life (ecological validity) may be limited, and scoring can be complex or subjective on some subtests

Stanford-Binet Intelligence Scale

• It is administered face-to-face and one-on-one

• It employs a hierarchical model of intelligence and therefore yields a singular measure of full-scale IQ (or “g”), five factor scores, and many more specific subtest scores

• Rather than three separate tests for three different age ranges, it covers the entire life span (ages 2–85+) as a single test

Stanford-Binet Intelligence Scale - 5

Five Specific Factors and Subtests:

•Fluid Reasoning

•Knowledge

•Quantitative Reasoning

•Visual-Spatial Processing

•Working Memory

Fluid Reasoning

the ability to solve novel problems

Knowledge

general information accumulated over time via personal experiences, including education, home, and environment

Quantitative Reasoning

the ability to solve numerical problems

Visual-Spatial Processing

the ability to analyze visually presented information, including relationships between objects, spatial orientation, assembling pieces to make a whole, and detecting visual patterns

Working Memory

the ability to hold and transform information in short-term memory

Wechsler Individual Achievement Test—Third Edition (WIAT-III)

• a comprehensive achievement test for clients aged 4 to 50 years

• administered face-to-face and one-on-one.

• measures achievement in four broad areas:

• Reading, Math, Written Language, Oral Language

• Each of these broad areas is assessed by two to four subtests

Listening Comprehension

Paying attention to orally presented information and answering questions about it

Oral Expression

Using speech to repeat spoken material, create stories about presented pictures, providing direction, etc.)

Word Reading

Reading isolated words

Pseudoword Decoding

Using phonetic skills to sound out nonsense words, such as plore or tharch

Reading Comprehension

Reading sentences or passages and answering questions about their content

Numerical Operations

Written math problems

Math Problem Solving

Word problems, numerical patterns, statistics and probability questions, etc.

Spelling

Increasingly difficult words

Sentence and Essay Composition

Constructing sentences, paragraphs, or essays as instructed