PSYCH 110 Terms

Variable

numeric/ categorial representations of the object of interest that can take on different values.

Random variable

a property that can take on a different value. (at least 2 or <1)

discrete variable

a type of random variable that can take on values that are made up of disjointed categories

continuous variable

a type of random variable that can take on any value within a given range or interval, representing measurements or quantities.

Empirical distribution

a set of scores derived from observed data, showing the frequency of various outcomes in a sample.

Theoretical distribution

a probability distribution constructed by mathematicians/ statisicians based on assumptions and mathematical principles, providing a model for expected outcomes.

data

information that has been collected by the researcher

data matrix

a structured arrangement of data in rows and columns, often used in statistical analysis to organize variables and observations.

univariate

analysis involving a single variable

bivariate

analysis involving two variables

multivariate

analysis involving multiple variables

census population

all the individuals or objects of interest to a researcher

statistical populations

the entire set of possible outcomes on the variable(s) of interest and thier associated frequencies or probabilities.

sample

a subset or portion of scores or measurements taken from a population

parameters

numerical properties that describe statistical populations

statistic

real-valued quantity that describe various features of data sets and are used to summarize and analyze the data in a meaningful way.

Data analysis/ descriptive statistic

provides a non-inferential description of an empirical distribution.

Quantification

the process of defining non-numerical concepts in numerical terms.

measurement

the assignment of numerical values to objects or events for the purpose of comparison or analysis.

constant

A fixed value that does not change or vary in an experiment or analysis.

population

the entire set of individuals or items that are of interest in a statistical study.

nominal scale

A type of measurement scale used to categorize data without any quantitative value, primarily for labeling variables.

ordinal scale

A type of measurement scale that ranks data in a specific order, indicating relative positions but not the magnitude of differences between them.

interval scale

A measurement scale that not only orders data but also specifies the exact differences between values.

ratio scale

A type of measurement scale that has all the properties of an interval scale, with the addition of a true zero point, allowing for the comparison of absolute magnitudes.

nominal variable

A type of variable that categorizes data without a defined order or ranking, often labeled or named for identification. Examples include gender, race, or types of cars.

dichotomous variable

A type of nominal variable that has only two categories or levels, such as yes/no or true/false.

ordered categorial variable

A type of variable that categorizes data into distinct groups with a specific order or ranking, allowing for meaningful comparisons in terms of sequences.

pseudo-continuous variable

A type of variable that is treated as continuous, though it is derived from discrete categories.

proportion

A statistical measure that expresses the relationship between a part and the whole

frequency

the number of times a particular value or category occurs within a dataset, often expressed as a count or in relation to the total number of observations.

frequency distribution

A representation of the number of observations within each category or interval in a dataset. It summarizes how often each value or range of values occurs.

relative frequency

the proportion of the total count represented by each category in a frequency distribution, calculated by dividing the frequency of each category by the total number of observations.

percentage frequency

the relative frequency expressed as a percentage of the total number of observations in a dataset.

cumulative frequency

The total number of observations accumulated up to a certain point in a frequency distribution, showing how many data points fall below or at a specific value.

cumulative relative frequency

the cumulative frequency expressed as a proportion of the total number of observations, showing the accumulation of frequencies up to a certain point in the distribution.

cumulative percentage frequency

a frequency distribution that shows the accumulation of percentages of observations up to a certain point in a dataset.

histogram

A graphical representation of the distribution of numerical data, with bars representing the frequency of data points within specified ranges (bins).

bar graph

a graphical representation of data using rectangular bars, where the height of each bar represents the frequency of the corresponding category.

line graph

A type of chart that displays information as a series of data points connected by straight line segments, often used to show trends over time.

symmetry

A property of a distribution where the left and right sides are mirror images of each other, indicating that data points are evenly distributed around the center.

skewness (postive/negative)

A measure of the asymmetry of the probability distribution of a real-valued random variable, indicating whether the data is skewed to the left (negative skewness) or right (positive skewness).

kurtosis (leptokurtic, platykurtic, mesokurtic)

A statistical measure that describes the distribution's tails' heaviness relative to a normal distribution, indicating whether data points are concentrated around the mean (leptokurtic) or dispersed (platykurtic).

outlier

A data point that significantly deviates from the other observations in a dataset

measure of location

describes the central tendency of a dataset, such as the mean, median, or mode.

measure of central tendency

A statistical value that represents a typical or central value of a dataset, commonly including the mean, median, and mode.

mean

a measure of central tendency calculated by adding all values in a dataset and dividing by the number of values.

median

the middle value of a dataset when it is ordered from least to greatest, effectively dividing the dataset into two equal halves.

mode (bimodal, unimodal, multimodal)

a measure of central tendency that indicates the most frequently occurring value(s) in a dataset. Bimodal refers to two modes, unimodal to one mode, and multimodal to multiple modes.

dispersion

a statistical measure that describes the spread of a dataset

minimum and maximum

the smallest and largest values in a dataset, respectively; they define the range of the dataset.

range

the difference between the maximum and minimum values in a dataset, providing a measure of dispersion.

interquartile range

the difference between the third quartile (Q3) and the first quartile (Q1) in a dataset. It measures the middle 50% of values.

deviation score

the difference between a data point and the mean of the dataset, indicating how far away the point is from the average.

sum of deviation scores

is the total of all differences between individual data points and the mean of the dataset. It indicates the overall balance of data points above and below the mean.

average absolute deviation

is the average of the absolute differences between each data point and the mean. It measures the dispersion of data points in a dataset.

variance

a measure of the dispersion of a set of data points around their mean, calculated as the average of the squared differences from the mean.

standard deviation

is a measure of the amount of variation or dispersion of a set of values. It quantifies how much individual data points differ from the mean of the dataset.

box plot (hinges, whiskers)

A graphical representation of data that displays the median, quartiles, and potential outliers. The "hinges" represent the quartiles, while "whiskers" indicate the range of the data.

bivariate distribution

a probability distribution that describes the relationship between two random variables, depicting how their values co-vary.

scatterplot

A graphical representation of two-dimensional data points on a Cartesian plane, used to visualize the relationship or correlation between two quantitative variables.

observed values

the values obtained from experiments or observations that represent the data collected during a study or analysis.

statistical relationship

a correlation or association between two or more variables that can be analyzed to determine how one variable may affect or relate to another.

form of a statistical relationship

refers to the specific pattern or shape that describes how variables are related, such as linear, curvilinear, or non-linear.

regression

a statistical method used to model and analyze the relationship between a dependent variable and one or more independent variables,

conditional mean

the expected value of a random variable given that another variable takes a specific value, often used in regression analysis.

conditional mean function

describes the expected value of a dependent variable given specific values of one or more independent variables, providing insights into the relationship between those variables.

strength of a linear relationship

the degree to which a linear model can predict the dependent variable from the independent variable, often measured by correlation coefficients.

covariance

a measure of the degree to which two random variables change together, indicating the direction of their linear relationship.

correlation

a statistical measure that indicates the extent to which two variables fluctuate together, quantified by a correlation coefficient ranging from -1 to 1.

PPMC

a method for calculating the correlation coefficient that assesses the strength and direction of the linear relationship between two continuous variables, also known as Pearson's correlation.

general-type proposition

a type of statement that makes a general claim about a relationship between two or more variables, often used in hypothesis testing.

aggregate-type proposition

a statement that asserts a characteristic of a group, rather than of individual members, often used in statistics for generalizations about populations.

linear transformation

a mathematical operation that transforms a vector space into another by applying a function, such as scaling or rotating, while preserving linearity.