MSAV 662 Exam 1 (Chapters 1, 2, 3, 4, 6, 7) Terms & Concepts

Descriptive Statistics

applying statistics to organize and summarize information

Inferential Statistics

applying statistics to interpret the meaning of information

Population

• entire set of individuals or items of interest

• data termed parameters

• generalized inferential statistics

Sample

• representative subset of a population

• data determined statistics

• most of behavioral research

Variables

any characteristic, behavior, observation that can be measured and has different values

Score

numerical value associated with the variable

Value

number of levels or scores a variable can have

Nominal scale of measurement

• uniquely classifies

e.g., Zip codes, telephone numbers, gender (coded as 1/2/3)

Ordinal scale of measurement

• uniquely classifies

• order matters

e.g., finishing order in a competition, education level, rankings

Interval scale of measurement

• uniquely classifies

• order matters

• equal intervals

e.g., temperature, latitude and longitude, satisfaction rating scales

Ratio scale of measurement

• uniquely classifies

• order matters

• equal intervals

• natural zero

e.g., length, height, weight, time

Continuous Data

measured along a continuum at any place beyond the decimal point

e.g., Olympic sprinter’s run time

Discrete Data

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

e.g., number of students in a class

Three common research methods

• Experimental

• Quasi-experimental

• Correlational

Experimental method

applied to make observations in which a 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

Quasi-experimental method

applied to make observations in a study that is structured like an experiment but has conditions and experiences of participants that lack some control because the study lacks random assignment, includes a preexisting variable, and may not include a comparison/control group

e.g. value of education of students who went to college vs. who didn’t go to college after high school

Correlational method

the measurement of two or more factors, whose variables are not manipulated, to determine or estimate the extent to which the values for the factors are related or change in an identifiable pattern, though lacking the appropriate controls to demonstrate cause and effect

e.g. students’ hours of computer use vs. exercise minutes per week

frequency

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

frequency distribution

a summary of data in terms of how often a category, score, or range of scores occurs

(useful when researchers measure counts of behavior)

real range

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

interval width

the range of values contained in each interval of a frequency distribution with grouped data

= real range / number of intervals chosen

outlier

an extreme score that falls substantially above or below most other scores in a data set

relative frequency

a summary display that distributes the proportion of scores in each interval of a frequency distribution

= observed frequency / total frequency count

also converted to relative percentage by multiplying X 100

percentile point

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

Calculate value of a specific percentile

= (distance of percentile from top of interval cumulative value / range of width from percentages) X width of real range

Ungrouped data

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

pictogram

a summary display that uses symbols or illustrations to represent a concept

histogram

a graphical display used to summarize the frequency of continuous data that are distributed in numeric intervals, represented by a vertical rectangle for each interval frequency

frequency polygon

a dot-and-line graph used to summarize the frequency of continuous data at the midpoint of each interval, which is distributed along the x-axis and is calculated by adding the upper and lower boundary of an interval and then dividing by 2

interval boundaries

mark the cutoffs for a given interval with the upper and lower limits for each interval, with the lower being the smallest value and the upper being the largest value in each interval of the frequency distribution

ogive

a dot-and-line graph used to summarize the cumulative percentages or cumulative frequencies of data at the upper boundary of each interval, with the y-axis always ranging from 0% to 100%

stem-and-leaf display

a graphic method of displaying data that can be used for discrete or continuous data, in which each original score from an individual data set is listed

bar chart

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 a circle that depicts the relative percentage of discrete and categorical data as segments of the circle

central tendency

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

arithmetic mean

the sum of a set of scores in a distribution, divided by the total number of scores summed; conceptually the ‘balance point’ of a distribution

weighted mean

the average for a set of values in which some data points contribute more than others

= sum of weighted products / sum of weights

median

the middle value in a distribution of data listed in numeric order

mode

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

Add a score above the mean and the mean will…

increase

Add a score below the mean and the mean will…

decrease

Delete a score below the mean and the mean will…

increase

Delete a score above the mean and the mean will…

decrease

Add or delete a score equal to the mean and the mean will…

not change

normal distribution

a theoretical distribution in which scores are symetrically 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 those that fall substantially above (positively) or substantially below (negatively) most other scores in a distribution

positively skewed distribution

a distribution of scores that includes scores that are substantially larger (toward the right tail in a graph) than most other scores, where the mean is located above or to the right of the median

negatively skewed distribution

a distribution of scores that includes scores that are substantially smaller (toward the left tail in a graph) than most other scores, where the mean is located below or to the left of the median

modal distribution

a distribution of scores in which one or more scores occur most often or most frequently, which come in a variety of shapes and sizes

unimodal distribution

a distribution of scores in which one mode 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)

nonmodal (rectangular) distribution

a distribution of scores in which all scores occur at the same frequency (has no mode)

variability

statistical measures for locating a single score used to determine the dispersion or spread of scores in a distribution

range

the difference between the largest and smallest value in a data set

fractiles

measures that split a data set into two or more equal parts (e.g., quartiles, deciles, and percentiles)

the four quartiles

the 25th percentile (Q1), the 50th percentile (Q2), the 75th percentile (Q3), and the 100th percentile (Q4)

interquartile range

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

semi-interquartile range (quartile deviation)

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

variance

a measure of variability for the average squared distance that scores deviate from their mean, where the larger the value, the more dispersed or spread out scores are from their mean

population variance (σ²)

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

deviation

the difference of each score from its mean, denoted x − µ when computed for a population

sum of squares (SS)

the numerator for the variance formula, which is the sum of the squared deviations of scores from their mean

sample variance (s²)

a measure of variablity for the average squared distance that scores in a sample deviate from a mean

definitional formula for variance

calculates the population and sample variance that requires summing the squared differences of scores from their mean to compute the sum of squares (SS) in the numerator

computational formula for variance (raw scores method for variance)

a formula to compute population and sample variance that does not require summing the squared differences of scores from their mean to compute the SS in the numerator

biased estimator

any sample statistic obtained from a randomly selected sample that does not equal the value of its respective population parameter, on average

unbiased estimator

any sample statistic obtained from a randomly selected sample that equals the value of its respective population parameter

degrees of freedom (df) for sample variance

the number of scores that are free to vary in a sample

standard deviation (root mean square deviation)

a measure of variability for the average distance that scores deviate from their mean (square root of the variance)

population standard deviation (σ)

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 (s / SD)

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

1. Approximately 68% of all scores lie within one standard deviation of the mean

2. Approximately 95% of all scores lie within two standard deviations of the mean

3. Approximately 99.7% of all scores lie within three standard deviations 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