Psych Stats

Key Words for Midterm 1

Population

Collection of ALL people, objects, or events having one or more SPECIFIED characteristic(s)

Element (of pop.)

A single person, object, or event you are receiving data from

Conrete (pop.)

The number of elements is finite and the population is well defined (can record everything)

Conceptual (pop.)

Population exists as an idea rather than a material object

Observation/Datum

Number of label used to represent an element of the population, the OUTCOME of observing properties of objects

Property

Feature (characteristic, quality of object), represented by attributes

Attributes

Concept ascribed to an object

Variables

The characteristic, number, or quality that is being counted. Represent aspects of property

Sample

Proper subset of a population (studying sample assumes something about the pop)

Descriptive Statistics

(Describe something) Tools for depicting or summarizing data so that they can be more readily comprehended

Inferential Statistics

(Make inferences about something) Tool for inferring the properties (features) of a population(s) by inspecting samples drawn from the pops

Induction

Using data from a small specific sample to make generalizations about a population

Chang Variability/Sampling Fluctuation

Elements (single person object or event) obtained differ from sample to sample

Range

Set of elements for which the variable stands (from ___ to ___, variable could be ___ or between __)

Value

Any or each element on a range

Constant

Characteristic that DOES NOT VARY (range usually consists of a single element)

Qualitative Variables (characteristic that can take on diff values)

Ordered or unordered. Symbol who’s range consist of attributes or non-quantitative characteristics of people, objects, or events (eye color, gender, etc.)

Quantitative Variable

ORDERED: Symbol who’s range consists of a count or a numerical measurement of a characteristic (weight, height, etc.)

Discrete

Counting

Continuous

Measured

Measurement

Process of assigning numbers/labels to characteristics of people, objects, or events according to a set of rules created by researchers (4 TYPES)

Nominal Measurement

Assigning things to mutually exclusive equivalence classes (all elements equal each other in these classes)

• Classes sorted by disting labels (“male” and “female”)

Nominal: One-to-one transformation

Every distinct class must be preserved if transforming values (ex. 1 = red, 2 = blue, etc. or A = male, B = Female, Each label/symbol = one distinct category)

Ordinal Measurement

Assigning elements to equivalence classes that are ranked/ORDERED with respect to one another (denoted as numbers or ordered symbols)

• Ordinal Scales: labels given to equivalence classes to make distinct/ordered

Ordinal: Strictly Increasing Monotonic Transformation

Old set of numbers/symbols can replace new set of numbers/symbols as long as they have the same order (no decreasing values)

Interval Measurement

Ordinal measurement but ALSO equal differences between numbers reflect equal magnitude differences between corresponding classes (ex. temperature)

• 0 DOESN’T ALWAYS MEAN NOTHING, STARTING POINT = ARBITRARY

Interval: Positive Linear Transformation

Specific equation, where b > 0, changes measurement while keeping scale the same

Ratio Measurement

Ordered scale, equal and measurable intervals, and an ABSOLUTE ZERO POINT (height in inches, weight in lbs, etc.)

Ratio: Multiplication by a Positive Constant

Transformation of a ration scale that preserves all properties (equation, 0 DOES HAVE MEANING)

Class Intervals

Equivalence classes of frequency distributions (28-30, 31-33, etc.)

Grouped

Class interval spans 2+ scores (28-30)

Ungrouped

Class intervals are a single score (30)

(For Grouped Quantitative Dist.) Nominal Lower Limit and Nominal Upper Limit

Ex. if class interval is 66-68, the NLL = 66 and the NUL = 68

Real Limits

Grouped class intervals (ex. 66-68) actually also contain number 0.5 above and below both nominal limits (ex. real limits for 66-68 are 65.5-68.5).

Class Interval Size (i)

Computed by Real Limits

Relative Frequency Distributions

Show prop f and %f for EACH class interval (shows which # are “relatively large” compared to other numbers)

Cumulative Frequency Distribution

Shows the # of proportions of percentage of scores that occur below the RUL of each class interval

Kurtosis

Property of being peaked, flat, or in between

Mesokurtic

Meso = Intermediate

Platykurtic

Flatter

Leptokurtic

Slender of narrower

Central Tendency (AVERAGE)

Score value in which a distribution centers (Mean, Median, Mode)

Dispersion

Extent to which scores differ from one another

Mode

(Qualitative) Score or category that occurs with the greatest frequency

• CANNOT use if bimodal

• CANNOT use if no most typical score

Mean

Sum of scores divided by # of scores

Median

Point in a distribution that divides the data into 2 groups having equal frequency

• Odd = middle number of scores, even = midway point of 2 middle numbers (add then divide by two)

Interpolating

Estimates unknown values that fall between existing values

Statistical Stability

How Consistently a stats result holds up when different samples are drawn from the same population

Mathematically Tractable

Problem/equation/situation can be solved or handled with ease

Measures of Dispersion

Represent the spread or scatter of scores around a central point or the distinguishability of scores

Range (MoD) (Mode)

Distance between largest and smallest scores

Semi-Interquartile Range (MoD) (Median)

First half of the distance between Q1 and Q3

Percentile Point

Point on x-axis BELOW which a specified percentage of scores falls

Percentile Rank

Refers to percentage of scores that falls below the percentile point

Standard Deviation (Mean)

Most important and most widely used measure of dispersion (quantifies amount of variation or dispersion between a dataset relative to its mean)

Index of Dispersion (Mode)

Ratio DP/DPmax — number of distinguishable pairs to the maximum possible number of distinguishable pairs — denoted as D

Independent Variable

Controlled/manipulated by researcher

Dependent Variable

Outcome dependent on independent variable

Correlation

Knowing if and how variables are related

Regression

Predicting Y from knowledge of X and vice versa (I and D variables)

Bivariate Frequency Distribution

Scatter plot

Correlation Coefficient

Degree of association or strength between two variables

Truncated

Restricted Range (reduced size of r if range of X or Y is truncated)

Heteroscedasticity (Heterogeneity of array vairances)

(spread or scatter of data is unequal) Presence of skewed X or Y distribution meaning the distribution is accompanied by an unequal dispersion of Y scores for diff values of X and vice versa

Homoscedasticity

Spread or scatter of data is equal (good)

Spearmen Rank Correlation Coefficient

Describes the degree of agreement between paired data that are in the form of ranks (measures monotonic relationship between 2 ranks)

Monotonic Relationship

As one variable goes up, so does the other variable

Tied Ranks

When two or more individuals/objects are assigned the same rank

Regression Analysis

Prediction Data where X = IV and Y = DV

Multiple Regression

Simultaneous use of 2+ predictors for predicting a dependent variable

Line of Best-Fit (Regression Line)

Line that minimizes some error when predicting Yi and Xi

Prediction error/residual

Difference between the ith persons actual score (Yi) and the score PREDICTED for that person (Y’i)

Standard Error of Estimate

Measures the size of prediction errors

Regression Plane

Used when tgere are 2 independent variables present (3 planes, surface rather than a regression line)

Coefficient of Multiple Correlation

(used when 2+ IV) Correlation between Y and the combined predictions X1, X2….Xn

Coefficient of Multiple Determination

Extension of r², how well multiple variables work together to predict an outcome

Multicollinearity

Presence of nonzero correlations among the independent variables (when IV in regression model are highly correlated)