Chapter 09 Descriptive statistics, significance levels, and hypothesis testing

Descriptive statistics, significance levels, and hypothesis testingChapter 9 Looking at datasetNormal 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 valueNormal curvePositively skewed distributionNegatively skewed distributionDescriptive statisticsSummary information for each variableNumber of casesCentral tendencyDispersionUsed by researcher to describe variables Used in statistical tests to analyze differences and relationships between variablesNumber of casesNumber of cases for which data are reportedRepresented by n or Nn = 231Cases may be people, speaking turns, episodes – any phenomenon studiedMeasures of central tendencyMean or M or Arithmetic mean or averageMost sensitive to extreme scoresMedian or MdnMiddle of all scores on one variableMode or MoScore or scores that appear most oftenMeasures 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 meanStandard deviationStandard 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 standardsUsing Descriptive statisticsReported in methods section of research reportMean, sd, range, and n should be reported for each variableFrequencies or f the number of times a particular value of a variable occursPercentages or %often used to describe characteristics or attributes of participantsCalculating -- Need 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 resultsSignificance levelsThe researcher sets the significance level, or p, for each statistical testA criterion for accepting or rejecting hypothesesThe degree of error the researcher finds acceptable in a statistical testAn estimate of what would happen if the study were actually repeated many timesGenerally .05 is accepted levelSignificance levels.05 significance level5 out of 100 findings that appear to be valid will be due to chanceAlso known as the alpha level or pIf p > .05, the finding is nonsignificantIf p is  .05, the finding is significant or realHypothesis testingHypothesis states the expected relationship or difference between two or more variablesFindings for alternative hypothesis is reportedNull is statistically testedAct of decision making based on the significance levelDecision based on comparison between p set before study to p produced by statistical testType I and type ii errorsIn reality, the null hypothesis is trueIn reality, the null hypothesis is falseUse level of significance to reject nullType I error – Null is rejected even though it is trueDecision 1 – Null is rejected when it is falseUse level of significance to retain the nullDecision 2 – Null is retained when it is trueType II error – Null is retained even though it is false