# Chapter 10 Descriptive Statistics

Numbers One tool for collecting data about communication phenomena Capture quality, intensity, value, or degree Only meaningful if they are interpreted Operationalizations specify how data are collected and become numerical

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Chapter 10 Descriptive StatisticsNumbers One tool for collecting data about communication phenomenaCapture quality, intensity, value, or degreeOnly meaningful if they are interpretedOperationalizations specify how data are collected and become numerical1Copyright c 2001 The McGraw-Hill Companies, Inc.Looking at a Data Set2Copyright c 2001 The McGraw-Hill Companies, Inc.Normal CurveAlso known as bell curveA theoretical distribution of scoresMajority of cases distributed around the peak in the middle Progressively fewer cases moving away form the middleSymmetrical – one side mirrors the otherMean, median, and mode have the same value3Copyright c 2001 The McGraw-Hill Companies, Inc.Normal Curve4Copyright c 2001 The McGraw-Hill Companies, Inc.Skewed DistributionsCurve is asymmetricalPositively skewed curve – very few high scoresNegatively skewed curve – very few low scores5Copyright c 2001 The McGraw-Hill Companies, Inc.Descriptive StatisticsSummary information for each variableNumber of casesCentral tendencyDispersionHelps researcher describe variables in research reportUsed in statistical tests to analyze differences and relationships between variables6Copyright c 2001 The McGraw-Hill Companies, Inc.Number of CasesNumber of cases for which data are reportedRepresented by n or Nn = 231Cases may be people, speaking turns, episodes – any phenomenon studied7Copyright c 2001 The McGraw-Hill Companies, Inc.Measures of Central TendencyMeanArithmetic mean or averageMost sensitive to extreme scoresMedianMiddle of all scores on one variableModeScore or scores that appear most often8Copyright c 2001 The McGraw-Hill Companies, Inc.Measures of DispersionDescribes the variability or spread of scoresShould be reported with meanRangeHighest to lowest scoreStandard deviation or sdIf sd = 0, all scores are the sameLarger the sd, the more the scores differ from the mean9Copyright c 2001 The McGraw-Hill Companies, Inc.Standard Deviation10Copyright c 2001 The McGraw-Hill Companies, Inc.Standard DeviationsTheoretical normal curve is divided into equal standardsThe more normal a distribution of scores, the more this theoretical property applies68.26% of scores fall within +1 to –1 standards11Copyright c 2001 The McGraw-Hill Companies, Inc.Application of Descriptive StatisticsReported in methods section of research reportMean, sd, range, and n should be reported for each variableFrequencies – the number of times a particular value of a variable occursPercentages – often used to describe characteristics or attributes of participants12Copyright c 2001 The McGraw-Hill Companies, Inc.Crunching NumbersNeed calculator with square root key, spreadsheet program, or statistics programResearcher must select appropriate descriptive statistic and testResearcher must indicate which data are to be calculated or testedWrong input = error in results13Copyright c 2001 The McGraw-Hill Companies, Inc.