Behavioral Statistics Midterm

• Numerical Summarize measure computed on data from a sample
• Numerical Characteristics of a Sample
• Ex: Mean, T-Test, Z-Score

• A target group of participants about which the researcher will make decisions
• Ex: OU Students, Am Citizens, 1999 Honda Civics

• 1. Large
• 2. Unobtainable-never can collect all data (CENSUS)
• 3. Hypothetical-we make assumptions because 1 &2 are as well as people are always changing

Subgroup of Population

Small group of participants from which the researcher makes decisions about the population

Random Sampling eliminates biases

• Quantity or property that takes on different values
• Continuous-infinite # of values
• Discrete-finite # of values

variables manipulated by researchers

behavior observed and measured

• Not IV or DV but might effect the study
• a variable we need to control
• Ex: Gender

• 1 Randomize participants into groups
• 2 Keep all participants constantion EV
• 3 include EV in the design of experiment

• True Experiment
• Observational Research
• Quasi-Experiemtn

• Manipulation of Independent Variable
• Randomization of Group
• Optional methods to control Extraneous variables
• Causal relationship between IV and EV

Problems:Taking it to the streets

• Predictive relationships
• Observation of prediction and criterion variable
• No Manipulation
• Minimal control of EV
• Predictive relationship btwn prediction of variable and criterion variable

• Manipulation of IV
• No Randomization
• Some control of EV
• degree to which we can attribulte a causal relationship depends on consideration of possible outcomes

• 1)internal validity-applies outside the lab
• 2)External validity-applies in the lab only

• Nominal
• Ordinal
• Internal
• Ratio

• Data with identity only
• Qualitative in nature
• Ex: Gender, religion

• N+O
• Identity
• Order
• Ex:Ranking, Year in School, Scales!!!

• N+O+I
• Identity
• Order
• Equal Distance on # Scale
• Ex: Temperature, Not Scales!

• N+O+I+R
• Identify
• Order
• Equal Distance
• True point 0
• Ex:Kelvin Temp, Height, Weight

• If Both halves of the distribution is said to be Normal Distributed
• Departure from Symmetry is defined as Skewness

• A typical or Representative score
• Scores that represents the middle of the distribution
• Ex:Test scores in class, Average age

• Mode:Most frequestn score
• Median-Middle valuse in distribution-50% below/above
• Mean-arithmetic average= Sum X/N
• Parameter Mean µ
• Statistic Mean= X_bar

• Spread
• Dispersion of the Scores
• EX: Variance, Standard Deviation,Range, Biased Sampled Variance

• Variance
• Parameter = σ²
• Statistic= S*² and S²

• Standard Deviation
• Parameter= σ
• Statistic= S* & S

• Range
• Maximize mean
• *Point of the class*
• Stat= obtain from sample
• Parameter= Exists in Population

• Biased Sample Variance
• Bias to small on average
• Bias sample variance (s*²) average² Deviation from mean

Z=SOMETHING minus MEAN divided by STANDARD DEVIATION

• Each X to a Z
• Mean= Z_bar=0
• Variance= s_z^*2=1
• Standard Deviation= s_z*=1
• Transformation to Z-Score does not change the shape of the distribution

• 1 Symmetric-same on both sides
• 2 Smooth-1 hump
• 3 Unimodal-1 mode
• 4 Bell Shaped
• -Tails of distrubution-never touch X-axis
• -Mode = Median=Mean
• -Infinite # of score values (continuous variable)

• The degree of linear relationship between two variables
• ↑↑ ↑↓ ↓↓

• r = I 1 I
• Closer to 0= Weak
• Closer to 1 or -1 = Strong

• The area of statistics where a researcher is concerned with predicting one variable from another
• -Describing data for two variables

• Y'= predicted score of criteron variable
• b=slope of the line= Rise/run (Rise over Run)
• X=score of the predictor variable
• a= Y-intercept of the line
• (Y=observed point, Y' what come out of formula)

• Group of data points representing all possible outsomes of an experiment
• Ex: A population of a deck of Cards

• Single member in a sample space
• (Ace of Diamonds in a deck of cards)

• Any group of elementary events
• Ex: Kings

# in the event divided by total # of possible outcomes

• A probabilit of one event that is dependent of another event
• P(A/B)

One event occuring does not change the probability of another event occuring

• INDEPENDENT
• P(A&B)= P(A) X P(B)
• NOT INDEPENDENT
• P(A&B)= P(A/B)*P(B)=P(A)*P(B/A)

• When A & B do not have an elementary event in common
• P(A&B)=0

P(A or B)= P(A) + P(B)- [P(A&B)]

Distribution of all possible values of a statistic, sample mean, st devi, or variance

sahpe of the mean is approximated by normal distribution

Every statistic has a sampling distribution

• 1 Pop and Param are typically unknow-we want to make decision about them
• 2 Sample and Stats are know and stats are estimates of parameter can't say stats is = to param and make decisions directly b/c stats have variability
• 3 Samp dis of stats is used to quantify into probability the info about variability of the stat

as N (Sample size) approaches infinity, the sampling distribution of X_Bar approches normality

N=30 is best (closest to infinity)

• Stats are used to estimate Parameter
• Stats- does vary
• Param-does not vary

• Descriptive Statistic
• Stat procedures used to describe a sample
• Ex: Mean, St Devi

• Inferential Statistic
• Statistic procedure used to make decisions about a population based upon result from a sample
• Ex: T-Score, ANOVA, Z-Score

• Indepentdent Variables-One manipulated by researcher
• Dependent Variables-Changes observed
• Extraneous Varibles- something that effects the experiment