Lecture 5 Psyc 300A

Agenda Return quizzes & homework Descriptive statistics review New –Types of distributions –Z-scores –Area under the normal curve Discussion

Formulas to Calculate the SD

Group Exercise Calculate SD for the following data: 10, 20, 30, 40, 50, 60, 70, 80, 90 Calculate SD for the sample and for a sample which you wish to generalize to a population.

Normal (Bell-shaped)Curve From: Salkind, N.J. (2007). Statistics for people who (think they) hate statistics (3 rd ed.). Thousand Oaks, CA: Sage

Normal Curve Characteristics –Mean, mode, median are equal –Curve is symmetrical –Tails of the curve are asymptotic

Distributions : Skewness From: Salkind, N.J. (2007). Statistics for people who (think they) hate statistics (3 rd ed.). Thousand Oaks, CA: Sage

Distributions : Kurtosis From: Salkind, N.J. (2007). Statistics for people who (think they) hate statistics (3 rd ed.). Thousand Oaks, CA: Sage

Normal curve and probabilities, Part 1 A visual representation of a distribution of scores.

Z-Scores If we want to know where a raw score falls along the normal curve, we can use z-scores. _ z-score = (X – X) / s IQ examples: z = (110 – 100) / 15 =.667 z = (70 – 100) / 15 = -2.0

Group Exercise: z-scores Calculate z–scores: –Mean=2, score=3, SD=2 –Mean=2, score=1, SD=2 –Mean=10, score=8, SD=5 –Mean=10, score=11, SD=5 What is the raw score if, –Z=1.5, mean=10, SD=5

Normal curve and probabilities, Part 2 From: Jackson, S.L. (2011). Sresearch methods: A modular approach (2nd ed.). Belmont, CA: Wadsworth/Centgage

Score Transformations New score = z*NewSD + NewMean Examples: T = 10z + 50 IQ = 15z + 100