Building Statistical Models Lesson 4

Theories & Models n Theories l Describe, explain, & predict real-world events/objects n Models l Replicas of real-world events/objects l Can test predictions ~

Models & Fit n Model not exact replica l Smaller, simulated n Sample l Model of population l Introduces error n Fit l How well does model represent population? l Good fit  more useful ~

Models in Psychology n My research model l Domestic chicks l Effects of pre-/postnatal drug use l Addiction & its consequences n Who/What do most psychologists study? l Rats, pigeons, intro. psych. students n External validity l Good fit with real-world populations? ~

The General Linear Model n Relationship b/n predictor & outcome variables form straight line l Correlation, regression, analysis of variance l Other more complex models ~

The Mean as a Statistical Model n Very simple model l 1 number represents all the observations l Often hypothetical value e.g., mean # friends = 2.6 n Error introduced l Actual # friends = mean + error n Deviation (deviance) l ~

Assessing the Fit of the Mean n How well does it represent all observations? l On average near or far from mean? Distance from mean l Or width of distribution

  For which group is the mean a better fit for the data? Mean Daily Temperature

Measures of Variability n Deviation: for a single score n Range l Highest value – lowest value + 1 n Standard deviation l Conceptually: mean of all deviation scores l average distance of scores from mean n Variance l Used to calculate standard deviation l Also used in analysis of variance ~

Calculating the Standard Deviation n Why only conceptually mean of deviation scores? n If n What is mean deviation?  (X i –  ) = 0 ~ XiXi X i - 

Variability: Notation & Formulas n 3 steps to standard deviation n Sums of squares (squared deviations) SS =  (X i –  ) 2 n Variance = mean of squared deviations (MS) l n square root of variance = standard deviation ~

Standard Deviation (SD) n Conceptually mean deviation score for all data l Gives width (dispersion) of distribution n Describing a distribution l Report mean & standard deviation  ~

Samples & Variability n Usually study samples u to learn about populations l Sampling introduces error l Change symbols & formula

Samples: Degrees of Freedom (df) n df = N – 1 l For a single sample (or group) s tends to underestimate  l Fewer X i used to calculate l Dividing by N-1 boosts value of s n Also used for l Confidence intervals for sample means l Critical values in hypothesis testing ~

Degrees of Freedom: Extra Don’t lose any sleep over this n df theory l If n= 4 & sample mean = 10 l 3 of X i can be any value, 4 th can be only one value See Jane Superbrain 2.2 (pg 37) ~

Level Of Measurement & Variability n Which can be used? n nominal l none n ordinal l range only n interval/ratio l all 3 OK l range, standard deviation, & variance ~

Statistical Models n Representation of the population l We will focus on linear models n Mean is a simple model l One number represents all data l Both n Standard deviation l measures fit of model l Better fit  more useful l Smaller ~