EXAM 2 ch 3-8

Reconstruction Crisis

Studies of the past are being replicated and are not yielding the same results, reliability.

Population

A group of individuals that belong to the same species and live in the same area that we are interested in studying.

Sample

A portion of the universe of people deemed to be representative of the whole population.

* small portion of people chosen in a survey to represent the whole population.

Parameter

Numerical summary/ description (e.g. mean or minimum of population)

Statistic

numerical summary of a sample

Nominal scale

A scale in which objects or individuals are assigned to categories that have no numerical properties.

• simplest form of measurement

• Categorical (e.g. felon or not, suicidal or not)

• Bar graphs

• Cannot compute average

Ordinal Scale

a scale of measurement using ranks rather than actual numbers.

• Classification

• Rank ordering (e.g. 1st, 2nd, gold, silver)

• Bar graphs

• Binet believed that data from intelligence test are ordinal, used to classify people

• Have no absolute zero, every test taker has some ability

• Cannot compute average

• Most frequently used in psychology

Interval Scale

a quantitative measurement scale that has no “true zero”, and in which the numerals represent equal intervals (distances) between levels (e.g. temperature in degrees).

• equal intervals/ distance between data

• Numerical

• Can compute average

• Is possible to average a set of measurements and obtain a meaningful result

• No true zero

• Most psychological testing uses this because of the flexibility w/ which data can be manipulated statistically

Ratio Scale

measurement that has a natural, or absolute, zero and therefore allows the comparison of the numbers

• has absolute zero

• Can compute average

• E.g. height, weight, distance

• All mathematical operations can mean fully be performed because there exists intervals between the numbers on a scale

Dynamometer

Instrument to measure strength of hand grip

* absolute zero is possible

What does statistics allow us to do?

describe and infer

Descriptive statistics

numerical data used to measure and describe characteristics of groups.

• measures of central tendency (the middle)

• Measures of variation (the spread)

Measures of Central Tendency

a statistic that indicates the average or mid most score between the extreme scores in a distribution

• arithmetic mean, median, mode

• Calculating averages

Arithmetic Mean

the same of observations (or test scores) divided by the number of overreactions. X = £ (fX)/n

• interval-level-statistic

• Most useful in central tendency

Median

the middle score in distribution

• ordering the scores in a list by magnitude, either in ascending or descending order

• Ordinal in nature

Mode

the most frequently occurring score in distribution

Bimodal distribution

a distribution w/ two modes; two scores occurring an equal number of times that are most frequently occurring scores in the distribution

• one more can appear at high and low end of the distribution

• Is a nominal statistic

Measures of Variation / Variability

Interquartile / semi-interquartile range, variance, average / standard deviation

* a measure used to describe the distribution of data

Variability

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

Range

a descriptive statistic of variability is equal to the difference between the highest and lowest scores in a distribution

Quartiles

one of the three dividing point between the four quarters of a distribution, each typically labeled Q1, Q2, or Q3

• refers to specific point

• Not quarter which refers to an interval

Interquartile Range

a measure of variability equal to the difference between Q3 and Q1

* is ordinal

Semi-Interquartile Range

a measure of variability equal to the interquartile range divided by 2

Average Deviation

A measure of variability derived by summing the absolute value of all the scores in a distribution and dividing by the total number of scores

* rarely used

Standard Deviation

a measure of variability equal to the square root of the averaged squared deviations about the mean / equal to the square root of the variance

• the sd is the average amount of variability in your dataset

• It tells you, on average, how far each value lies from the mean

Variance

a measure of variability equal to the arithmetic mean of the squares between the scores in a distribution and their mean

• variance is a measure of dispersion, meaning its a measure of how far a set of numbers is spread out from their average value

• Standard deviation squared

• S^2 = £x^2 / n

Skewness

the nature and extent to which symmetry is absent

* is an indication of how the measurements in a distribution are distributed

Positive Skew

when relatively few of the scores fall at the high end of the distribution \n \~ may indicate that the test was too difficult \n \~ ..:''':......... \n \~ Q3 − Q2 will be greater than the distance of Q2 − Q1 \n \~ mode (at peak), median (middle of slope), mean (the end/tail) \n \~ median is considered the best measure of central tendency in a skewed distribution

Negative Skew

when relatively few of the scores fall at the low end of the distribution \n \~ may indicate that the test was too easy \n \~ .......:"':.. \n \~ Q3 − Q2 will be less than the distance of Q2 − Q1 \n \~ mean (the end/tail), mode (at peak), median (middle of slope) \n \~ median is considered the best measure of central tendency in a skewed distribution

Measurement

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

Scale

A set of numbers (or other symbols) whose properties model empirical properties of the objects to which the numbers are assigned \n \~ continuous scale (measure continuous variable; measuring) \n \~ discrete scale (measure a discrete variable; countin)

Error

the collective influence of all of the factors on a test score or measurement beyond those specifically measured by the test or measurement \n \~ measuring using continuous scales always involve error

Distribution

A set of test scores arrayed for recording or study

Raw Score

a straightforward, unmodified accounting of performance that is usually numerical \n \~ may reflect a simple tally

(Simple) Frequency Distribution

A summary chart, showing how frequently each of the various scores in a set of data occurs \n \~ all scores are listed alongside the number of times each score occurred, in columns

Grouped Frequency Distribution

A frequency distribution where scores are grouped into intervals rather than listed as individual values. \n \~ test score intervals, aka class intervals, replace the actual test scores \n \~ size of the class interval is made on the basis of convenience

Graph

A diagram or chart composed of lines, points, bars, or other symbols that describe and illustrate data \n \~ e.g., histogram, bar graph, and frequency polygon

Histogram

A graph with vertical lines drawn at the true limits of each test score (or class interval), forming a series of contiguous rectangles \n \~ usually test scores on horizontal axis, and frequency of occurrence on the vertical axis

Bar Graph

A graphic illustration of data wherein numbers indicative of frequency are set on the vertical axis, categories are set on the horizontal axis, and the rectangular bars that describe the data are typically noncontiguous.

Frequency Polygon

A graphic illustration of data wherein numbers indicating frequency are set on the vertical axis, test scores or categories are set on the horizontal axis, and the data are described by a continuous line connecting the points where the test scores or categories meet frequencies

Kurtosis

An indication of the nature of the steepness (peaked versus flat) of the center of a distribution \n \~ high kurtosis in distributions are characterized by a high peak and "fatter" tails compared to a normal distribution. \n \~ lower kurtosis values indicate a distribution with a rounded peak and thinner tails

Platykurtic

relatively flat distributioin \n \~ great deal of variance \n \~ very spread out

Leptokurtic

relatively peaked distribution \n \~ low deal of variance \n \~ not as spread out

Mesokurtic

somewhere in the middle

Who is credited w/ being the 1st to refer to the curve / Laplace-Gaussian curve as the Normal Curve?

Karl Pearson

Normal Curve/ Distribution aka Gaussian Curve

A bell-shaped, smooth, mathematically defined curve highest at the center and gradually tapered on both sides, approaching but never actually touching the horizontal axis \n \~ perfectly symmetrical, no skewness \n \~ negative infinity to positive infinity \n \~ divided into areas defined in units of standard deviation

Normal Distribution Class Notes

\~ In a normal curve, the mean, median, and mode are all in the same spot \n \~ 2% / 14% / 34% / 34% / 14% / 2% \n \~ A large number of scores fall very close to the mean with progressively fewer cases occurring as scores get further above or below the mean \~ If the data is skewed with outliers then the mean would be in a different place

Why is it important to have a normal curve for your data?

Means are affected by the outliers, and because the mean is the best measure of central tendency in a normal distribution, it must have normal curves for the data to be a good representation of the population (not skewed)

Tail

the area on the normal curve between +/- 2 and +/- 3 standard deviations above or below the mean

Standard Score

A raw score that has been converted from one scale into another, where the latter scale (1) has some arbitrarily set mean and standard deviation and (2) is more widely used and readily interpretable \n \~ allows you to make comparisons to other standard scores and tells you percentile \n \~ e.g., z scores, stanines and T scores

Z-scores

conversion of a raw score into a number indicating how many \n standard deviation units the raw score is below or above the mean of the distribution \n \~ mean set at 0 and standard deviation set at +-1 \n \~ a z score is equal to the difference between a particular raw score and the mean divided by the standard deviation; X - X' / SD \n \~ -2 SD, -1 SD, 0, 1 SD, 2 SD \n \~ positive and negative

T-scores

a standard score calculated using a scale with a mean set at 50 and a standard deviation set at 10; X' = 50, SD = 10 \n \~ 5 standard deviations below and above the mean; 0-100 \n \~ Devised by W. A. McCall, named for Thorndike \n \~ used by developers of the MMPI \n \~ One advantage in using T scores is that none of the scores is negative.

\
Ex: T= 45-50/ 10 = -5/10 = -0.5

Other Standard Scores

\`\`\`\`IQ: X' = 100, SD = 15 \n A score: X' = 500, SD = 100; e.g. SAT

Stanine

a standard score with a mean of 5 and a standard deviation of approximately 2 \n \~developed in WWII \n \~ divided into 9 units \n \~ Stanines 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 \n \~ The 5th stanine indicates performance in the average range, from 1/4 standard deviation below the mean to 1/4 standard deviation above the mean, and captures the middle 20% of the scores in a normal distribution. The 4th and 6th stanines are also 1/2 standard deviation wide and capture the 17% of cases below and above (respectively) the 5th stanine. \n \~ e.g., achievement tests, GRE

Linear Transformation

A standard score obtained by a linear transformation is one that retains a direct numerical relationship to the original raw score \n \~ The magnitude of differences between such standard scores exactly parallels the differences between corresponding raw scores \n \~ used to compare scales

Nonlinear Transformation

A nonlinear transformation may be required when the data under consideration are not normally distributed yet comparisons with normal distributions need to be made. \n \~ If the distribution is not normal, then you must "stretch" (manipulate) the skewed distribution so it looks normal \n \~ In a nonlinear transformation, the resulting standard score does not necessarily have a direct numerical relationship to the original, raw score

“Normalizing” a distribution should only be done when you have?

1. Good reason to believe that the test sample was large and representative enough

2. Failure to obtain normally distributed scores was due to the measuring instrument, not because the population itself is skewed ~ e.g. positive skew is 60%/40%, then you can chop of some of the score/get rid of outlier to make it a normal curve 50%/50%

Normalizing a Distribution

A statistical correction applied to distributions meeting certain criteria for the purpose of approximating a normal distribution, thus making the data more readily comprehensible or manipulable \n \~ involves "stretching" the skewed curve into the shape of a normal curve and creating a corresponding scale of standard scores

Normalized standard scores / scale

Conceptually, the end product of "stretching" a skewed distribution into the shape of a normal curve, usually through nonlinear transformation \n \~ a scale \n \~ advantages of a standard score on one test is that it can readily be compared with a standard score on another test, only when the distributions from which they derived are the same

Coefficient of Correlation / correlation coefficient

is a number that provides us with an index of the strength of the relationship between two things. \n \~ It tells us the extent to which X and Y are "co-related." \n \~ A coefficient of correlation (r) expresses a linear relationship between two (and only two) variables, usually continuous in nature \n \~ The meaning of a correlation coefficient is interpreted by its sign and magnitude \n \~ "plus" (for a positive correlation), "minus" (for a negative correlation), or "none" (in the rare instance that the correlation coefficient was exactly equal to zero). \n \~ magnitude, it would respond with a number anywhere at all between −1 and +1. \n \~ If a correlation coefficient has a value of +1 or −1, then the relationship between the two variables being correlated is perfect—without error in the statistical sense.

Correlation

is an expression of the degree and direction of correspondence between two things \n \~ If two variables simultaneously increase or simultaneously decrease, then those two variables are said to be positively (or directly) correlated \n \~ negative (or inverse) correlation occurs when one variable increases while the other variable decreases. \n \~ If a correlation is zero, then absolutely no relationship exists between the two variables

Pearson r

a widely used statistic for obtaining an index of the relationship between two variables when that relationship is linear and when the two correlated variables are continuous (i.e., theoretically can take any value) \n \~A mean for the sum of the products is calculated, and that mean is the value of the Pearson r. \n \~ also known as the Pearson correlation coefficient and the Pearson product-moment coefficient of correlation \n \~ Devised by Karl Pearson \n \~ The formula for the Pearson r takes into account the relative position of each test score or measurement with respect to the mean of the distribution. \n \~ the sign of the resulting r would be a function of the sign and the magnitude of the standard scores used. \n \~ negative standard score values for measurements of X always corresponded with negative standard score values for Y scores, the resulting r would be positive (because the product of two negative values is positive). \n \~ if positive standard score values on X always corresponded with positive standard score values on Y, the resulting correlation would also be positive. \n \~ However, if positive standard score values for X corresponded with negative standard score values for Y and vice versa, then an inverse relationship would exist and so a negative correlation would result. \n \~ A zero or near-zero correlation could result when some products are positive and some are negative. \n \~ Significance at the .05 level means that the result could have been expected to occur by chance alone five times or less in a hundred

Coefficient of Determination, r^2

is an indication of how much variance is shared by the X- and the Y-variables being calculated \n \~ squaring the obtained correlation coefficient, multiplying by 100, and expressing the result as a percentage, which indicates the amount of variance accounted for by the correlation coefficient

Spearman’s rho aka rank- order/difference correlation

this coefficient of correlation is frequently used when the sample size is small (fewer than 30 pairs of measurements) and especially when both sets of measurements are in ordinal (or rank-order) form \n \~ developed by Charles Spearman

Scatterplot aka Bivariate Distribution / a scatter diagram / a scattergram

this coefficient of correlation is frequently used when the sample size is small (fewer than 30 pairs of measurements) and especially when both sets of measurements are in ordinal (or rank-order) form \n \~ developed by Charles Spearman

Curvilinearity

Usually with regard to graphs or correlation scatterplots, the degree to which the plot or graph is characterized by curvature \n \~ an "eyeball gauge" of how curved a graph is

Outlier

is an extremely atypical point located at a relatively long distance—an outlying distance—from the rest of the coordinate points in a scatterplot \n \~ In some cases, outliers are simply the result of administering a test to a very small sample of testtakers

Meta-Analysis

A family of techniques used to statistically combine information across studies to produce single estimates of the statistics being studied \n \~ advantage: more weight can be given to studies that have larger numbers of subjects, (1) meta-analyses can be replicated; (2) the conclusions of tend to be more reliable and precise than from single studies; (3) there is more focus on effect size rather than statistical significance alone; and (4) meta-analysis promotes evidence-based practice

Effect Size

A statistic used to express the strength of the relationship or the magnitude of the differences in data \n \~ in meta-analysis, this statistic is most typically a correlation coefficient

Evidence-Based practice

which may be defined as professional practice that is based on clinical and research findings

Trait

Any distinguishable, relatively enduring way, in which one individuals varies from another \n \~ contrast to state \n \~ psychological traits only exists as a construct

States

Distinguishes one person from another but are relatively less enduring

What are some assumptions about psychological testing and assessment?

1. Psychological traits and states exist

2. Psychological traits and states can be quantified and measured

3. Test-related behavior predicts non-test related behavior

4. Tests and other measurement techniques have strengths and weaknesses

5. Various sources of error are part of the assessment process

6. Testing and assessment can be conducted in a fair and unbiased manner

7. Testing and assessment benefit society

Over Behavior

An observable action or the product of an observable action, including test- or assessment-related responses

Cumulative Scoring

Point or score accumulated on individual items or sub tests are tallied and then, the higher the total sum, the higher the individual is presumed to be on the ability, trait or other characteristic being measured \n \~ e.g. spelling test score

Domain Sampling

A sample of behaviors from all possible behaviors (OR a sample of test items from all possible items) that could be conceivably be used to measure a particular construct

Error variance

The component of a test score attributable to sources other than the trait or ability measured

Classical Test Theory (CTT) aka True Score Theory

The assumption is made that each test taker has a true score on a test that would be obtained but for the action of measurement error \n \~ observed score = true score + error \n \~ longer tests

True Score

A value that, according to classical test theory, genuinely reflects an individual's ability (or trait) level as measured by a particular test \n \~ One's true score on one test of extraversion, for example, may not bear much resemblance to one's true score on another test of extraversion.

Norm-referenced testing and assessment

A method of evaluation and a way of deriving meaning from test score by evaluating an individual testtaker's score and comparing it to scores of a group of testtakers. \n \~ the meaning of an individuals test score is understood relative to other scores on the same test (ranking or standing)

Norm

In psychometric context, are the test performance data of a particular group of testtakers (broad or narrow) that are designed for use as a reference when evaluating or interpreting individual test scores

Normative Sample

group of people whose performance on a particular test is analyzed for reference in evaluating the performance of individual testtakers

Normative Data

we need to gather information on the "defined" population to which we would like to make inferences \n \~ To obtain normative data, we take a representative sample of the population. \n \~ The best procedure is to get a random sample of the population

Norming

The process of deriving or creating norms \n \~ e.g. race norming

Race Norming

Norming on the basis of race or ethic background \n \~ resulted in the establishment of different cutoff scores for hiring by cultural group \n \~ the practice was outlawed by the Civil Rights act of 1991

User Norms / Program Norms

Consists of descriptive statistics based on a group of testtakers in a given period of time rather than norms obtained by formal sampling methods \n \~ because norming a test with the participation of a nationally representative normative sample an be expensive, some test manuals provide this

Test Standardization

The process of administering a test to a representative sample of testtakers for the purpose of establishing norms

Standardized Test

A test or measure that has undergone standardization; clearly specified procedures for administration, scoring, and interpretation in addition to norms \n \~ a test is standardized when it has clearly specified procedures for administration and scoring, typically normative data

Standardized Testing Characteristics

Normative data \n and Standardized procedures for administration to reduce error variance

Sampling

The process of selecting the portion of the universe/population deemed to be representative of the whole population

Random Sampling

A true random sample consists of a groups of subjects that were randomly selected from the population. Each member of the population must have an equal probability of being selected.

Stratified Sampling

The process of developing a sample based on specific subgroups (strata) based on characteristics they share of a population \n \~ help prevent sampling bias and ultimately aid in the interpretation of the findings \n \~ Samples are stratified across various demographics (gender, ethnicity, level of education, geographic region, urban/rural, etc.) and according to known population data \n \~ Once divided, each subgroup is randomly sampled using another probability sampling method.

Sampling Problems in Research

Don't often has access to random samples \n \~ Over use of incidental samples / samples of convenience (college students) \n \~ Attrition - when people leave studies: can threaten the external/internal validity and reliability if they do not come back in again \n \~ Subject characteristic - characteristics particular to the subject that may influence results \n \~ experimenter characteristics

Experimenter Characteristics

Demand characteristics - participants form an interpretation of the experiment's purpose and subconsciously change their behavior to fit that interpretation \n \~ To fix this use Blind and Double Blind Studies \~ Researchers may not be aware that they are priming results \n \~ The sad case of Facilitative Learning: treatment for autism, the idea that children with autism could learn to communicate through typing / keyboards, parents were the facilitators

Stratified-Random Sampling

The process of developing a sample based on specific subgroups of a population in which every member has the same chance of being included in the sample

Purposive sample

The arbitrary selection of people to be part of a sample because they are thought to be representative of the population being studied \n \~ Manufacturers test the appeal of a new product in one city or market and then make assumptions about how that product would sell nationally \n \~ the danger the city may no longer be representative of the nation and this sample may simply not be representative of national preferences with regard to the particular product being test-marketed.

Incidental/Convenience Sample

the process of arbitrarily selecting some people to be part of a sample because they are readily available, not because they are most representative of the population being studied \n \~ practical instead of ideal

Percentile Norm

the raw data from a test's standardization sample converted to percentile form

Percentile

an expression of the percentage of people whose score on a test or measure falls below a particular score \n \~ is a converted score that refers to a percentage of testtakers \n \~ e.g. the 15th percentile is the score at or below which 15% of the scores in the distribution fall \n \~ .A problem with using percentiles with normally distributed scores is that real differences between raw scores may be minimized near the ends of the distribution and exaggerated in the middle of the distribution

Percentage Correct

the distribution of raw scores—more specifically, to the number of items that were answered correctly multiplied by 100 and divided by the total number of items