Psychological Statistics Exam 1 (Chapters 1-4)

Statistics

a branch of mathematics used to summarize, analyze, and interpret a group of numbers or observations

Data

(plural) are measurements or observations that are typically numeric; a datum (singular) is a single measurement or observation, usually referred to as a score or raw score

Descriptive Statistics

are procedures used to summarize, organize, and make sense of a set of scores or observations

- typically presented graphically, in tables, or a summary

Inferential Statistics

are procedures used that allow researchers to infer or generalize observations made with samples to the larger population from which they were selected

Population

the set of all individuals, items, or data of interest; this is the group scientists will generalize

Population Parameter

a characteristic (usually numeric) that describes a population

Sample

a set of individuals, items, or data selected from a population of interest

Sample Statistic

a characteristic that describes a sample

Science

study of phenomena, such as behavior, through strict observation, evaluation, interpretation, and theoretical explanation

Research Method/ Scientific Method

a set of systematic techniques used to acquire. modify, and integrate knowledge concerning observable and measurable phenomena

Experiment

use of methods and procedures to make observations in which the researcher fully controls the conditions and experiences of participants by applying three required elements of control (manipulation, randomization, and comparison/control) to isolate cause-and-effect relationships between variables

Random Assignment

a random procedure used to ensure that participants in a study have an equal chance of being assigned to a particular group or condition

Independent Variable

variable that is manipulated in an experiment; remains unchanged between conditions being observed in an experiment

Dependent Variable

variable that is measured in each group of a study, and is believed to change in the presence of the independent variable

Operational Definition

description of some observable event in terms of the specific process or manner by which it was observed or measured

Quasi-Independent Variable

a preexisting variable that is often a characteristic inherent to an individual, which differentiates the groups or conditions being compared in research study

are rules for how the properties of numbers can change with different uses

Scales of Measurement

Nominal Scales

are measurements in which a number is assigned to represent something or someone

Ordinal Scales

are measurements that convey order or rank alone

Interval Scales

are measurements that have no true zero and are distributed in equal units

True Zero

when the value 0 truly indicates nothing on a scale of measurement; interval scales do not have a true zero

Continuous Variable

measured along a continuum at any place beyond the decimal point; can be measured in fractional units

Discrete Variable

measured in whole units or categories that are not distributed along a continuum

Quantitative Variable

varies by amount; this variable is measured numerically and is often collected by measuring or counting

Qualitative Variable

varies by class; this variable is often represented as a label and describes nonnumeric aspects of phenomena

Frequency

number of times or how often a category, score, or range of scores occurs

Frequency Distribution

a summary display for a distribution of data organized or summarized in terms of how often a category, score, or range of scores occurs

Simple Frequency Distribution

a summary display 1) the frequency of each individual score or category (ungrouped data) in a distribution or 2) the frequency of scores falling within defined groups or intervals (grouped data) in a distribution

Grouped Data

a set of scores distributed into intervals, where the frequency of each score can fall into any given interval

Interval

a discrete range of values within which the frequency of a subset of scores is contained

Real Range

one more than the difference between the largest and smallest value in a data set

Interval Width/ Class Width

range of values contained in each interval of a grouped frequency distribution

Interval Boundaries

upper and lower limits for each interval in a grouped frequency distribution

Lower Boundary

smallest value in each interval of a frequency distribution

Upper Boundary

largest value in each interval of a frequency distribution

Open Interval/ Open Class

an interval with no defined upper or lower boundary

Outliers

are extreme scores that fall substantially above or below most of the scores in a particular data set

Cumulative Frequency Distribution

a summary display that distributes the sum of frequencies across a series of intervals

Relative Frequency Distribution

a summary display that distributes the proportion of scores in each interval; it is computed as the frequency in each interval divided by the total number of frequencies recorded

Proportion

a part or portion of all measured data; sum of all proportions for a distribution of scores is 1.0

Relative Percent Distribution

a summary display that distributes the percentage of scores occurring in each interval relative to all scores distributed

Cumulative Relative Frequency Distribution

a summary display that distributes the sum of relative frequencies across a series of intervals

Cumulative Percent Distribution

a summary display that distributes the sum of relative percents across a series of intervals

Percentile Point

value of a score on a measurement scale below which a specified percentage of scores in a distribution fall

Percentile Rank

of a score is the percentage of scores with values that fall below a specified score in a distribution

Ungrouped Data

a set of scores or categories distributed individually, where the frequency for each individual score or category is counted

Histogram

a graphical display used to summarize the frequency of continuous data that are distributed in numeric intervals (grouped)

Frequency Polygon

a dot-and-line graph used to summarize the frequency of continuous data at the midpoint of each interval

Ogive

a dot-and-line graph used to summarize the cumulative percent of continuous data at the upper boundary of each interval

Bar Chart or Bar Graph

a graphical display used to summarize the frequency of discrete and categorical data that are distributed in whole units or classes

Pie Chart

a graphical display in the shape of a circle that is used to summarize the relative percent of discrete and categorical data and into sectors

Sector

particular portion of a pie chart that represents the relative percent of a particular class or category

Central Tendency

statistical measures for locating a single score that is most representative or descriptive of all scores in a distribution

Population Size

number of individuals who constitute an entire group or population; population size is represented by a capital N

Sample Size

number of individuals who constitute a subset of those selected from a larger population; sample size is represented by a lowercase n

Mean (arithmetic mean or average)

sum of a set of scores in a distribution, divided by the total number of scores summed

Population Mean

mean for a set of scores in an entire population

Sample Mean

mean for a sample

Weighted Mean

combined mean of two or more groups of scores in which the number of scores in each group is disproportionate or unequal

Median

middle value in a distribution of data listed in numeric order

Mode

value in a data set that occurs most often or most frequently

Normal Distribution (symmetrical, Gaussian, or bell-shaped distribution)

a theoretical distribution in which scores are symmetrically distributed above and below the mean, the median, and the mode at the center of the distribution

Skewed Distribution

a distribution of scores that includes outliers or scores that fall substantially above or below most other scores in a data set

Positively Skewed Distribution

a distribution of scores in which outliers are substantially larger (toward the right tail in a graph) than most other scores

Negatively Skewed Distribution

a distribution of scores in which outliers are substantially smaller (toward the left tail in a graph) than most other scores

Modal Distribution

a distribution of scores in which one or more scores occur most often or most frequently

Unimodal Distribution

a distribution of scores in which one score occurs most often or most frequently; has one mode

Bimodal Distribution

a distribution of scores in which two scores occur most often or most frequently; has two modes

Multimodal Distribution

a distribution of scores where more than two scores occur most often or most frequently; more than two modes

Nonmodal Distribution (Rectangular Distribution)

a distribution of scores where all scores occur at the same frequency; no mode

Variability

a measure of the dispersion or spread of scores in a distribution and ranges from 0 to +infinity

Range

difference between the largest value (L) and smallest value (S) in a data set

Interquartile Range (IQR)

range of values between the upper (Q3) and lower (Q1) quartiles of a data set

Semi-Interquartile Range (SIQR)

a measure of half the distance between the upper quartile (Q3) and lower quartile (Q1) of a data set, and is computed by dividing the IQR in half

Variance

a measure of variability for the average squared distance that scores deviate from their mean

Population Variance

a measure of variability for the average squared distance that scores in a population deviate from the mean; it is computed only when all scores in a given population are recorded

Deviation

difference of each score from its mean

Sum of Squares (SS)

sum of the squared deviations of scores from their mean; SS is the numerator in the variance formula

Sample Variance

a measure of variability for the average squared distance that scores in a sample deviate from the mean; it is computed when only a portion or sample of data is measured in a population

Biased Estimator

any sample statistic, such as the sample variance when we divide SS by n, obtained from a randomly selected sample that does not equal the value of its respective population parameter, such as a population mean, on average

Unbiased Estimator

any sample statistic; such as the sample variance when we divide SS by n-1; obtained from a randomly selected sample that equals the value of its respective population parameter, such as a population variance, on average

Degrees of Freedom (df) for Sample Variance

are the number of scores in a sample that are free to vary; all scores except one are free to vary in a sample: n-1

Definitional Formula for Variance

a way to calculate the population variance and sample variance that requires summing the squared differences of scores from their mean to compute the SS in the numerator

Computational Formula for Variance or Raw Scores Method for Variance

a way to calculate the population variance and sample variance without needing to sum the squared differences of scores from their mean to compute the SS in the numerator

Standard Deviation (Root Mean Square Deviation)

a measure of variability for the average distance that scores deviate from their mean; calculated by taking the square root of the variance

Population Standard Deviation

a measure of variability for the average distance that scores in a population deviate from their mean; calculated by taking the square root of the population variance

Sample Standard Deviation

a measure of variability for the average distance that scores in a sample deviate from their mean; calculated by taking the square root of the sample variance

Empirical Rule

states that for data that are normally distributed, at least 99.7% of data lie within three standard deviations of the mean, at least 95% of data lie within two standard deviations of the mean, and at least 68% of data lie within one standard deviation of the mean

Chebyshev's Theorem

defines the percentage of data from any distribution that will be contained within any number of standard deviations (where SD>1)