Quantitative Reasoning Vocab

Classical test theory

A framework for conceptualizing score reliability that defines a score as being a function of a true score (the average score an individual would get on a measure) and a random error score that moves the true score higher or lower than it would typically be

Concurrent criterion validity

How well a test’s scores correlate with a criterion that exists in the present

Construct-based validity

How well a test score reflects an abstract hard-to-observe concept, such as intelligence or aggression

Content-based validity

A characteristic of items on a test that are a fair representation of the items that could be on the test

Criterion-based validity

A type of validity that examines how well a test correlates with an external criterion that exists in either the present (concurrent) or the future (predictive)

Cronbach’s alpha

A coefficient of reliability that estimates internal consistency among the items on a measure. It generally ranges from .00 to 1.00

Dependent variable

The outcome variable in a research study, or the variable that a researcher believes is affected by some other variable (the independent variable)

Error score

The part of a test score that is random and contributes to the unreliability of a test.

Independent variable

The causal variable in a research study, or the variable that a researcher believes affects some other variable (the dependent variable)

Internal consistency reliability

A type of reliability that reflects how well items on a single test correlate with each other

Interrater reliability

A type of reliability that reflects how well two different human scorers agree

Observed score

The score that an individual gets on a test or measure

Predictive criterion validity

How well a test’s scores correlate with a criterion that will exist in the future

Reliability

the degree to which a test produces stable and consistent results over time

Test–retest reliability

refers to the consistency of test scores when the same test is administered to the same group at two different points in time

True score

The typical score you would get if you took the same test an infinite number of times and averaged all the slightly different scores you would get

Validity

The degree to which scores from a measure represent the abstract concept that a researcher thinks it does

Average

The most representative score in a set of scores

Data

A record of an observation or an event such as a test score, a grade in math class, or response time

Data set

A set of data points

Descriptive statistics

Values that organize and describe the characteristics of a collection of data, sometimes called a data set

Inferential statistics

Tools that are used to infer characteristics of a population based on data from a sample of that population

Mean

A type of average calculated by summing values and dividing that sum by the number of values

Measures of central tendency

The mean, the median, and the mode

Median

The midpoint in a set of values, such that 50% of the cases in a distribution fall below the median and 50% fall above it

Mode

The most frequently occurring score in a distribution

Outliers

Those scores in a distribution that are noticeably much more extreme than the majority of scores. Whether a score is an outlier or not is usually an arbitrary decision made by the researcher

Percentile rank

The percentage of cases equal to and below a particular score in a distribution or set of scores

Population

All the possible subjects or cases of interest

Sample

A subset of a population

Skew

The degree of asymmetry of a distribution indicating more scores on one side than the other

Statistics

Quantitative tools and techniques that are used for describing, organizing, and interpreting information

Alternative hypothesis

Represents one of two possible truths: Either the null hypothesis is more likely, or its alternative, the research hypothesis, is more likely

Directional research hypothesis

A research hypothesis that posits a statistical result that is in a particular direction, such as a positive correlation or a mean difference in favor of a particular group

Hypothesis

A statement of relationship between two or more variables. It is the guessed answer to a research question

Nondirectional research hypothesis

A research hypothesis that posits a relationship among variables but not the direction of the relationship. For instance, it might predict a difference between groups but not which group will score higher

Null hypothesis

A statement of equality between groups or the absence of relationship among variables

Parameter

A value that describes a population

Population

All the possible subjects or cases of interest

Research hypothesis

A statement of relationship among variables

Sample

A subset of a population meant to represent the population

Bar chart

A graph where the length or height of a bar represents values

Class interval

A fixed range of values, used in the creation of a frequency distribution

Difference score

The result of subtracting the mean in a distribution from a single score. Difference scores can be positive or negative

Frequency distribution

A method for illustrating how often each score or group of scores occurs in a distribution

Frequency polygon

A graphical representation of a frequency distribution that uses a continuous line to show the number of values that fall within a class interval

Histogram

A graphical representation of a frequency distribution that uses bars of different heights or lengths to show the number of values that fall within each class interval

Interval level of measurement

A level of measurement that places a variable’s values into categories that are equidistant from each other, as when points are evenly spaced along a scale

Levels of measurement

The four ways that numbers can have meaning when used as scores—nominal, ordinal, interval and ratio. The level of measurement determines the methods that can reasonably be used to summarize scores mathematically

Line chart

A graph where the height of a line represents values

Measurement

A procedure that assigns scores to the values of a variable in a meaningful way

Midpoint

The central point in a class interval

Nominal level of measurement

A low level of measurement that involves using numbers only as names for categories, not as quantities

Ordinal level of measurement

A level of measurement that places a variable’s value into a category and assigns that category an order with respect to other categories

Pie chart

A circular graph that resembles a pie with various slices. Each slice shows the percentage of things that are in each category of a nominal-level variable. The percentages add up to 100%

Range

The difference between the highest and lowest score in a distribution

Ratio level of measurement

A level of measurement defined by the presence of an absolute zero on the scale

Standard deviation

The average amount of variability in a set of scores or the scores’ average distance from the mean

Variability

How much scores differ from one another. The amount of spread or dispersion in a set of scores

Variance

The standard deviation squared

Asymptotic

The quality of some distributions, such as the normal curve, where the tails approach, but never touch the horizontal axis

Distribution

The pattern of how a sample of scores are arranged across all possible values, showing the frequency or likelihood of each score. Distributions are often represented by line graphs

Kurtosis

The quality of a distribution that defines how flat or peaked it is

Leptokurtic

The quality of a distribution that is more peaked than a normal distribution

Normal curve

A symmetrical, bell-shaped distribution where most scores are near the mean or center and they decrease in frequency as they move further from the center

Platykurtic

The quality of a curve that is flatter than a normal distribution

Skewness

The degree of asymmetry of a distribution indicating more scores on one side than the other

Standardized scores

Scores transformed to show their position in a distribution compared to the mean

Z score

A raw score that is adjusted by subtracting the distribution’s mean from it and expressing that difference in standard deviations. A z score = (score – mean) / standard deviation

Coefficient of alienation

The amount of variance in one variable that is not accounted for by the variance in another variable. It is 1, the coefficient of determination

Coefficient of determination

The amount of variance in one variable that is accounted for by the variance in another variable

Confounding variable

An external variable, often unmeasured, that explains the apparent relationship between two other variables. If the variable comes between the two other variables in a cause-and-effect path, it is called a mediating variable

Controlling

Equalizing or removing the effects of some variable on the relationship between two other variables. This can be done statistically or through research design choices

Correlation coefficient

A numerical index that reflects the relationship or consistency between two variables. Values range between –1.0, which indicates a strong negative relationship, and +1.0, which indicates a strong positive relationship

Correlation matrix

A table showing correlation coefficients among more than two variables

Effect size

An index of the strength of the relationship among variables

A quantity that represents the strength of a relationship between variables

Mediating variable

A variable that comes between two other variables in a causal path. In this diagram, B is a mediator that explains the correlation between A and C: A→B→C

Negative correlation

An indirect correlation, which means the values of two variables move in opposite directions

Partial correlation

A numerical index that reflects the relationship between two variables after statistically removing the influence of a third variable

Pearson product-moment correlation

The correlation between two variables that are both at the interval level of measurement

Positive correlation

A direct correlation, which means the values of two variables move in the same direction

Scatterplot

A graph of data points representing the scores of two variables—one on the x-axis and one on the y-axis. It visually represents their correlation

Clinically significant

The practical importance or meaningfulness of a treatment effect in real-world settings, regardless of statistical significance

Confidence interval (CI)

A range of values, derived from sample data, that is likely to contain the true population parameter with a specified level of confidence (e.g., 95%)

Critical value

The threshold in a statistical test that determines whether to reject the null hypothesis, based on the significance level

Obtained value/Test statistic value

The value that results from the application of a statistical test

Power

The probability of correctly rejecting the null hypothesis when the alternative hypothesis is true, or detecting a true effect (power = 1 – probability of Type II error)

Sampling error

The natural variation or difference between a sample statistic and the true population parameter

Significance level

The predefined probability (α or alpha, often set at 0.05) of rejecting the null hypothesis when it is actually true. The chance of a Type I error

Significant

A result that is unlikely to occur by random chance, as determined by an observed p value less than the predetermined significance level

Standard error of the mean

The estimated standard deviation of sample means repeatedly drawn from the same population

Test statistic value

The value that results from the application of a statistical test

Type I error

Rejecting the null hypothesis when it is actually true

Type II error

Failing to reject the null hypothesis when it is actually false