Statistics

All vocab (finish this week)

Statistics

Data, functions of data (mean and range), techniques for collecting, analyzing, and interpreting data for subsequent decision making, the science of creating and applying such techniques

Population

Collection of ALL people, objects, or events having one or more specified characteristics.

Element

A SINGLE person, object, or event of a population

Observation/Datum

Number used to represent an element in the population (measurable characteristic of the popualtion)

Sample

Proper subset of the population

Descriptive Stats

Tools for depicting or summarizing data so that they can be more readily comprehended

Inferential Statistics

procedures for using sample data to make inferences about one or more population parameters

Sampling Fluctuation/Chance Variability

Elements obtained differ from sample to sample

Range

Set of elements for which the variable stands

Value

Each element of the range

Variable

A characteristic that can take on different values (sometimes denoted as X or Y)

Constant

A characteristic that does not vary (pi)

Qualitative Variable

Symbol whose range consists of attributes or non quantitative characteristics of people, objects, or events (hair color, men, women, etc.)

Quantitative Variable

A symbol whose range consists of a count or a numerical measurement of a characteristic

Discrete

Range can assume only a finite number of values or an infinite number of values that are countable (gap in between numbers)

Continuous

Variables range is uncountable infinite (always approximate because of earth limitations)

Unordered Qual Variable

Categories do not suggest an order or rank

Ordered Qual Variable

Categories suggest order or rank

Measurement

Process of assigning numbers or labels to characteristics of people, objects, or events according to a set of rules

Nominal Measurement

Assigning elements to mutually exclusive/exhaustive equivalence classes so that those in the same class are considered to be equivalent to one another. The classes are then denoted by a set of distinct labels, which make a nominal scale

Ordinal Measurement

Consists of assigning elements to mutually exclusive or exhaustive equivalence classes that are ranked or ordered with respect to one another, The classes are then denoted by numbers or other ordered symbols (i.e. letters in the alphabet), that reflect the rank of the classes. The labels assigned to equivalence classes in ordinal measurement have the properties of distinctness and order, which make the ordinal scale

Interval Measurement

The numbers assigned to EC have distinctness, order, AND equal differences between numbers reflect equal magnitude differences between the corresponding classes. The measurement procedure consists of defining a unit of measurement and determining the number of units required to represent the difference between equivalence classes, and these numbers make the interval scale.

Ratio Measurement

The numbers assigned to an EC are distinct, ordered, equivalent in intervals, and the origin of the scale represents the absence of the measured characteristic (true 0). Set of numbers makes a ratio scale.

Equivalence Classes

A single score value, a collection of score values, a qualitative category (all can be a type of equivalence class)

Frequency Distributions

A table showing the equivalence classes and the frequency with which their score values occur (does not show distinct original information though)

Class Intervals

Equivalence classes (where everything is equal in one) of frequency distributions (so a range of numbers)

Real Limits

Extend 0.5 below the nominal lower limit and approximately 0.5 above the nominal upper limit

Class Interval Size (i)

Constructed using Real Limits (i = Real upper limint - Real lower limit)

Relative frequency distribution

A distribution that shows the prop f and %f for each class interval (which express each frequency as either a proportion or percentage of the total number of scores)

Cumulative Frequency Distribution (Cum f)

Shows the number, proportion, or percentage of scores that occur below the real upper limit of each class interval

Kurtosis

Property of being peaked, flat, or somewhere in between (for graphs)

Mesokurtic

Normal distribution (normal kurtosis level)

Platykurtic

Flatter distribution

Leptokurtic

Slender, narrower, more peaked distribution

Dispersion

Extent to which scores are spread out around a central point

Bimodal

Two humps, same maximum frequency

Uniform Distribution

Rectangle, each class interval has the same frequency (percentiles)

Mode (Mo)

The score or qualitative category that occurs at the greatest frequency

Mean (x bar)

Sum of scores divided by the number of scores (average)

Statistic -

Descriptive measure of a sample

Parameter -

Descriptive measure of a population

Median (Mdn)

Point a distribution that divides the data into two groups having equal frequency

Interpolating

Dividing the class interval containing the median into subintervals and finding the point that represents the (n + 1)/2th score or the point that was midway between the (n/2)th and the (n2)/1th scores

Weighted Means

Finding the means from two means (class averages, etc.)

Terminal Statistics

Usefulness in advanced statistics procedures is limited (Mode and Median)

Range

The distance between the largest and smallest scores

Semi-Interquartile Range (Q)

One half of the distance between the first quartile point, Q1, and the third quartile point, Q3, with Q2 being the midpoint of the data.

Standard Deviation (S for a sample and sigma for a pop)

Distances from midpoint

Index of Dispersion

DP/DPmax = number of distinguishable pairs to the maximum possible number of distinguishable pairs (instead of representing distance)

Inflection Points

Points where the curve changes from convex to concave and reverse (on a distribution)

Outliers

Scores that are unusually large or small relative to other scores

Whiskers

Extend from either side of IQR to the outermost data points that fall within the distance computed (do not contain the outliers, if any)

Measures of Dispersion

Summarize the extent to which scores differ from one another (IQR, Rande, Index of D, etc.)

Independent Variable

Variable controlled or manipulated by a researcher

Dependent Variable

Effected by independent variable

(Pearson product-moment) Correlation Coefficient (rxy or r for sample, ppop is rho)

Measure of the linear relationship (degree of association) between two quantitative variables, X and Y

Cross Product (Xi - X bar)(Yi - Y bar)

Product of the two variations, shows which quadrant the point is located on

Covariance (Sxy)

The directional relationship between two variables (direction of line of best fit)

Coefficient of Determination (r^2)

Ranges from 0 to 1 that examines how the differences in one variable can be explained by the differences in the second variable, hwne predicting the outcome of a given event

Coefficient of nondetermination (K^2 = 1 – r^2)

Shows the amount of variation in a dependent variable that is not explained by a regression model (extraneous factors)

Correlation Ration or Eta Squared (n with a squiggle ^2)

Used to determine strenght of association between nonlinearly related variables

Truncated

Restricted

Heterogeneity of Array/Heteroscedasticity

Presence of skewed X any Y distributions is often accompanied by an unequal dispersion of Y scores for different values of X and vice versa

Homogeneity of Array Variances/Homoscedasticity

Dispersions of X and Y are uniform

Spearman rank correlation coefficient (rs)

Describes the degree of agreement between paired data that are in the form of ranks

Tied Ranks

Two individuals assigned the same rank

Concomitance -

state of existing or happening at the same time

Regression Analysis

A relationship used to estimate a relationship between a dependent outcome (Y) and an independent outcome (X)

Multiple Regression

Simultaneous use of two or more independent variables in predicting a dependent variable (exercise AND diet to predict future weight) (predicted on a regression plane)

Prediction Error/Residual

The difference between the actual score and a persons predicted score

Line of Best Fit -

a line that minimizes the sum of the squared prediction errors

Standard Error of Estimate (Sy.x)

Statistical measure that shows how much actual data points stray from predicted regression line (assumes values between 0 and Sy)

Coefficient of Multiple Correlation (R²)

Measures the strongest linear relationship between one dependent variable and a group of two or more independent variables (extension of r²)

Multicollinearity

When two or more input variables in a regression model are closely tied together/presence of nonzero correlations among the independent variables (can be bad)

Subjective Personalistic View of Probability

Probability is a measure of the strength of one’s expectations that an event will occur

Classical/Logical View of Probability

The probability of an event, A, is given by the number of events favoring A (priori knowledge of previous events)

Empirical Relative-Frequency View of Probability

Defines the chance of an event as the ratio of the number of times the event occurs to the total number of experimental trials or observations (infinity)

Event

An observable happening

Mutually Exclusive Events

When two events contain NO sample points in common

Exhaustive Events

Events for which the probability of their union equals 1 (one of the events must occur)

Random Variable

a numerical outcome of an experiment

Probability Distribution

A table showing the possible values of a random variable and the associated probaabilities

Sampling Distribution

Probability distribution of a statistic (shown as a random variable) which is based on the results of more than one trial

Random Sampling

Drawing samples form a population so every possible sample of a particular size has the same probability of being selected

Random Variables

A mathematical function that assigns a real number to each possible outcome of a random event or experience

Expected Value

Average outcome you expect to see if you repeat a random event many times

Bernoulli Trials

1) only one of two outcomes, 2) prob of success remains constant from trial to trial, 3) The outcomes of successive trials are independent

Multinomial Distribution

extension of binomial distribution: k > equal to 2 classes and probabilities associated with the classes remain constant (sampling with replacement or iinfinite pop) (3+)

Hypergeometric Distribution

Outcome of k > or equal to 2 BUT the probabilities DO NOT remain constant (sampling without replacement from finite pop)

Standard Score

A number that expresses the value of a score relative to the mean and the standard deviation of its distribution

Percentile Rank of a Score -

Indicates the percentage of the scores of the distribution that falls below the score

Point Estimate (Estimation [inferential stat procedure])

One number representing the estimate is associated with a point on a real number line

Interval Estimate (Type of estimate, 2 numbers)

2 numbers and associated points define an interval on the real number line

Estimator

A rule that tells you how to calculate an estimate of a population parameter using sample information

Law of Large Numbers

The larger the sample size, the more probable it is that the sample mean comes arbitrarily close to the population mean

Standard Error of a Statistics (sigma with subscript of statistic to which it applies)

Sampling distributions standard deviation

Unbiased Estimator

Statistic whose long-term expected value equals the true population parameter it estimates

Minimum Variance Estimator

Unbiased estimator with the smallest variance (thus highest precision) of any unbiased estimator for all possible values of a population parameter

Test Stat

A statistic that is used to test hypotheses about the values of population parameters

Statistical Inference

Making decisions abut the population by using samples that contain only a small portion of the population