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WSU PSYCH 311 - Scales of Measurement

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StatsPopulationSampleXfLecture 3Outline of Last LectureI. Intro to StatisticsII. Population and samplesIII. Types of StatisticsIV. Defining and Measuring Variables V. Constructs and Operational DefinitionsOutline of Current Lecture I. Scales of MeasurementII. Review of Mathematical OperationsIII. Symbols IV. Descriptive Statistics V. Frequency DistributionsCurrent Lecture I. Scales of Measurement Psych 311 1nd Edition• allows us to quantify constructDiscrete (Categorical) Variable: separate categories are used to quantify-->HOW MANY• Continuous Variables: variables with the property that between any two values, there are an infinite number of other values-used to quantify: HOW MUCH• Four Scales of Measurement: Normal, Ordinal, Interval, Ratio (least-->most sophisticated)-more sophisticated gives more info• Nominal: categorical variable; set of categories with different names; none are better or worse than another-measurement doesn’t make any quantitative distinction; ex. gender, major, etc.-only receivable info: how many are in each category; can’t organize or make calculations• Ordinal: continuous variable (sometimes categorical)-has same qualities as nominal scale but with added dimension of ordering-measurements are ranked observations in terms of size or magnitude-->ranked order-intervals between categories are uneven or unequal These notes represent a detailed interpretation of the professor’s lecture. GradeBuddy is best-ex. olympic metals are listed 1st, 2nd, 3rd, but you don’t know by how much-continuous because can rank variables• Interval: continuous variable-has same qualities as ordinal scale but with added dimension of same size intervals-equal differences between the numbers on of this scale reflect equal differences in magnitude-zero doesn’t equal absence of variables; ex. 1 2 3 4 5 vs -2 -1 0 1 2-most psychological characteristics measured by this interval scale-temperature measured on interval scale--> 0 degrees is still a temp• Ratio: continuous variable -has same qualities as interval scale but with added dimension of true zero-0=absence of variableex. recording number of absences per student within a semester-most observable behaviors can be measured on ratio scaleII. Review of Mathematical Operations• PEMDAS-Calculations within Parentheses-Exponenets (e.g. squaring)-Multiplying/Dividing from left to right-Addition/Subtraction is last from left to right• Summation (∑): sum all the numbers-Data (X): 5, 8, 3, 9-∑X= sum of all X’s= 5+8+3+9=25-∑X²=sum of all X²=5²+8²+3²+9²=179-(∑X)²= sum all X’s then square it= 5+8+3+9=25-->25²=625III. Symbols• symbols should tell you something•different sets of symbols for population and samplesStats Population SampleSize�nMean μ MVariance ơ² s²Standard Deviation (SD) ơ sIV. Descriptive Statistics• statistical procedures used to summarize, organize, and simplify data• should be able to look at descriptive stats and get general idea of whole set-averages are descriptive stats: gives sense about population• ways of describing data: graphs; measures of central tendency; measures of variability V. Frequency Distributions• graphs or organized tabulation of number of individuals located in each category on scale or measure-tallying up numbers within category•frequency table: shows how often each value of variable occurs ∑f=NX fa 5b 3c 7• Finding ∑X: (Xf)+(Xf)+...∑fX• Proportions and Percentages: p=f/N %=p(100)• Frequency Distribution Graphs-y axis is the frequency; you can have a frequency of zero-x axis is the


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