Describing Data Lesson 3

Psychology & Statistics n Goals of Psychology l Describe, predict, influence behavior & cognitive processes n Role of statistics l Descriptive statistics u Describe, organize & summarize data u Efficient communication l Inferential statistics u Draw conclusions about data u Aid decision making ~

Organizing Data n Describing distribution of variables l enumeration: list raw data n Frequency distributions l organize  tables or graphs l highlight important characteristics u range, most frequent value ~

Distributions as Tables n f = Frequency l # of times a value of variable occurs  f = n l calculate proportions & percentages n Tabular frequency distributions l ordered list of all values of variable & their frequencies l logical order (usually descending) ~

Tabular Frequency Distribution X f # of presentations to be able to recall 100% Enumeration

Grouped Frequency Distribution n Group by class intervals l report f for intervals l Lose information: exact values n General rules l each interval same width l consecutive & do not overlap ~

Grouped Frequency Distribution X f Tabular Frequency Distribution X f

Distributions as graphs n Summarizes data l focus on clear communication n Bar Graphs l nominal or ordinal data n Histograms & Frequency Polygons l Interval/ratio data u continuous & discrete variables ~

Bar Graphs f Political affiliation Rep Dem Ind OrdinalNominal f Exam Grades A B C D F

Histograms n X-axis l Class intervals of variables n Y-axis l Frequencies vertical bars ~ f # of presentations

Frequency polygons n Frequency represented as points l Contains same info as histogram ~ f # of presentations # of presentations f Relative Frequency

Distributions: 3 useful features n Summarizes important characteristics of data 1. What is shape of the distribution? 2. Where is middle of distribution? 3. How wide is distribution?

Shapes of distributions n Unimodal distribution l single value is most frequent n Bimodal (or multimodal ) l 2 most frequently occurring values l May indicate relevant subgroups ~ X f X f

Symmetry of distributions n Symmetric l if right side mirror- image of left n Skewed - asymmetric l a few extreme values l Positively skewed: right tail longer l Negatively skewed: left tail longer ~ X f X f f

The Normal Distribution n Bell-shaped n 3 characteristics l Unimodal l symmetric l asymptotic n Many naturally-occurring variables approximately normally distributed l Makes statistics useful ~ f

Central Tendency n Describes most typical values l Depends on level of measurement n Mode (all levels) l Most frequently occurring value n Median (only ordinal & interval/ratio) l value where ½ observations above & ½ below n Mean (only interval/ratio) l Arithmetic average ~

f Political affiliation Rep DemInd f # of presentations f # of presentations f exam grades A B C D F Mode n Most frequently occurring value ~

Median n Midpoint of a data set values ½ smaller, ½ larger ~

Finding the Median 1. List all values from largest  smallest if f=3, then list 3 times 2. Odd # entries median = middle value 3. Even # entries = half way b/n middle 2 values ~

Mean n Summarizes quantitative data l May not be actual value in data set l Introduces error l Most commonly used n Computing the mean Sum of all observations Number of observations Mean =

Statistical Notation n Formula for mean: n Σ: summate l add all that follows n X: observation l value of an observation n N: number of observations l Or data points ~

Populations & Samples n Population: all individuals of interest l Depends on goal of researchers n Parameter: value describing population l all observations used in calculation l an exact value – no error n Sample: a portion of group of interest l represents the whole population n Statistic: value describing sample l Estimate of parameter l Error introduced ~

Populations & Samples: Notation n Different symbols l Often different formulas for calculation n Population: Greek letters l Population mean = μ n Sample: Roman letters l Sample mean = l APA style: M ~

Formulas for Mean n Population mean l Parameter n Sample mean l Statistic l Estimate / error l Sometimes n used for sample ~