Statistical Analysis of Data

What is a Statistic???? Population Sample Parameter: value that describes a population Statistic: a value that describes a sample PSYCH  always using samples!!!

Descriptive & Inferential Statistics Descriptive Statistics OrganizeOrganize SummarizeSummarize SimplifySimplify Presentation of dataPresentation of data Inferential Statistics Generalize from samples to pops Generalize from samples to pops Hypothesis testing Hypothesis testing Relationships among variables Relationships among variables Describing data Make predictions

Descriptive Statistics 3 Types 1. Frequency Distributions 3. Summary Stats 2. Graphical Representations # of Ss that fall in a particular category Describe data in just one number Graphs & Tables

1. Frequency Distributions # of Ss that fall in a particular category How many males and how many females are in our class? Frequency (%) ? ?/tot x % % total scale of measurement? nominal

1. Frequency Distributions # of Ss that fall in a particular category Categorize on the basis of more that one variable at same time CROSS-TABULATION Democrats Republican total Total

1. Frequency Distributions How many brothers & sisters do you have? # of bros & sis Frequency 7? 6? 5? 4? 3? 2? 1? 0?

Histogram of the categorical variables 2. Graphical Representations

Polygon - Line Graph 2. Graphical Representations

Summary Statistics describe data in just 2 numbers Measures of central tendency typical average score Measures of dispersion typical average variation

Measures of Central Tendency Quantitative data: –Mode – the most frequently occurring observation –Median – the middle value in the data (50 50 ) –Mean – arithmetic average Qualitative data: –Mode – always appropriate –Mean – never appropriate

Mean The most common and most useful average Mean = sum of all observations number of all observations Observations can be added in any order. Sample vs population Sample mean = X Population mean =  Summation sign = Sample size = n Population size = N Notation

Special Property of the Mean Balance Point The sum of all observations expressed as positive and negative deviations from the mean always equals zero!!!! –The mean is the single point of equilibrium (balance) in a data set The mean is affected by all values in the data set –If you change a single value, the mean changes.

Summary Statistics describe data in just 2 numbers Measures of central tendency typical average score Measures of dispersion typical average variation 1.range: distance from the lowest to the highest (use 2 data points) 2. Variance: (use all data points) 3. Standard Deviation 4. Standard Error of the Mean

Measures of Variability 2. Variance: (use all data points): average of the distance that each score is from the mean (Squared deviation from the mean)  otation for variance s 2 3. Standard Deviation= SD= s 2 4. Standard Error of the mean = SEM = SD/ n