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McGill University
PSYC 204
Heungsun Hwang

Psyc 204 Midterm I study guide Topic 1: A. What are statistics? 1. Applications: political polls, weather, drug trials 2. Statistics are tools: a) describe populations, samples b) decision making in uncertain cases based on samples B. Population vs. Sample 1. Population – all instances on some quantitative dimension. Refers to a defined group or aggregate 2. Sample- a subset of all instances on some quantitative dimension. Refers to subgroups or sub aggregates drawn by some appropriate method from a population. C. Two Areas of Statistics 1. Descriptive statistics: Parameter (a property descriptive of a population) and Estimate (to a property of a sample drawn at random from a population). Statistical procedures used in describing the properties of samples, or of populations where complete population data are available. Do not allow us to make conclusions beyond the data we have analyzed or reach conclusions regarding any hypotheses we might have made. Just a way to describe data 2. Inferential statistics: Draw conclusions about populations based on information from samples. Statistical procedures used in the drawing of inferences about the properties of populations from sample data. D. Variables (X, Y): Represent measurements in samples and populations 1. Differences vs. Similarities A) Variables (x, y) assume a range of values B) Constant, (c = 5)- a property whereby the members of a group do not differ. 2. Dependent (Y) vs. Independent (X): measurement versus manipulations 3. Discrete (takes specific values only, finite set of values) vs. Continuous (any value within a defined range of values, infinite number) 4. Types of variables: Qualitative: Nominal (a property of the members of a group defined by an operation which permits the making of statements only of equality or difference, e.g eye color, political parties) and Ordinal ( a property defined by an operation which permits the rank ordering of the members of a group; statements of greater than or less than e.g. letter grades) Quantitative: Interval ( a property defined by an operation which permits the making of statements of equality of intervals, in addition to statements of sameness or difference or greater than or less than, arbitrary 0, e.g. temperature, calendar time)and Ratio (a property defined by an operation which permits the making of statements of equality of ratios in addition to all other kinds of statements, meaningful 0, e.g. weight, length) E. Summation Notation 1. Definition of Symbols a) Variables: attributes take a range of values designated by a capital letter, specific value along dimensions of interest designated by subscripted capital letter Topic II II. Descriptive Statistics A. Frequency Distributions: Raw data unwieldy and uninterpretable - organize and display 1. Nominal or Ordinal Data: Constructing a Frequency Distribution. a) Collect data ( e.g. what religion?) b) Classify c) Count and Tabulate 2. Interval or Ratio Data: Constructing a Frequency Distribution. a) Collect data (absolute frequency distribution) b) Classify( note: interval information is meaningful) c) Count and Tabulate Guidelines for constructing a frequency distribution based on class interval: 1. Divide data into equal but arbitrary intervals, use 5-20 2. Choose class intervals (interval width) of 1, 3, 5, 10 or 20 3. Appropriate interval size reflects distributional nature of data d) Relative frequency (proportion) or % frequency (percent) Relative: Express each frequency as a proportion Percent: Express each frequency out of 100 3. Types of Frequency Distributions a) Cumulative frequency: total number/proportion below a certain value b) Bivariate frequency distribution: 2 measures per observation 4. Class Intervals a) Conventions → manageable number and equal size b) Exact limits for discrete variables c) Exact limits for continuous variables → + or – reported interval width 5. Graphical Representation a) Histogram (Bar chart) : frequency is represented by area, more area means greater frequency b) Relative Frequency (% frequency) histogram: area is the relative or percent frequency, total area = 1.00 or 100% c) Frequency Polygon- Definition: The line joining the midpoints of the class intervals in a histogram Topic III II. Descriptive Statistics (continued) B. Averages 1. Intro a) Central Tendency: what value best represent distribution? I. Average: Total number of cases / N II. Most common (Mode) III. Midway through data, midpoint in rank order (median) 2. Arithmetic Mean: numerical average - If class interval is not 1, use the interval midpoint / N 3. Properties of the Arithmetic Mean a) Sum of deviations from the mean equals zero. Deviation score: x = observation – me
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