# statistical analysis of data. what is a statistic???? population sample parameter: value that...

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• Statistical Analysis of Data

• What is a Statistic???? PopulationSampleSampleSampleSampleParameter: value that describes a population

Statistic: a value that describes a sample PSYCH always using samples!!!

• Descriptive & Inferential StatisticsDescriptive Statistics OrganizeSummarizeSimplifyPresentation of dataInferential Statistics Generalize from samples to popsHypothesis testingRelationships among variables

Describing dataMake predictions

• Descriptive Statistics3 Types1. Frequency Distributions3. Summary Stats2. Graphical Representations# of Ss that fallin a particular categoryDescribe data in just one numberGraphs & Tables

• 1. Frequency Distributions# of Ss that fallin a particular categoryHow many males and how many females are in our class?Frequency(%)? ??/tot x 100 ?/tot x 100

-----% ------%totalscale of measurement?nominal

• 1. Frequency Distributions# of Ss that fallin a particular categoryCategorize on the basis of more that one variable at same timeCROSS-TABULATION Democrats

Republican

total24 1 25

19 6 25

Total 43 7 50

• 1. Frequency Distributions How many brothers & sisters do you have?# of bros & sis Frequency7?6?5?4?3?2?1?0?

• Histogram of the categorical variables 2. Graphical Representations

• Polygon - Line Graph

2. Graphical Representations

• Summary Statisticsdescribe data in just 2 numbersMeasures of central tendency typical average scoreMeasures of dispersion typical average variation

• Measures of Central TendencyQuantitative data:Mode the most frequently occurring observationMedian the middle value in the data (50 50 ) Mean arithmetic averageQualitative data:Mode always appropriateMean never appropriate

• MeanThe most common and most useful averageMean = sum of all observations number of all observationsObservations can be added in any order.Sample vs populationSample mean = XPopulation mean =mSummation sign = Sample size = nPopulation size = NNotation

• Special Property of the MeanBalance PointThe sum of all observations expressed as positive and negative deviations from the mean always equals zero!!!!The mean is the single point of equilibrium (balance) in a data setThe mean is affected by all values in the data setIf you change a single value, the mean changes.

• Summary Statisticsdescribe data in just 2 numbersMeasures of central tendency typical average scoreMeasures of dispersion typical average variation range: distance from the lowest to the highest (use 2 data points)2. Variance: (use all data points)3. Standard Deviation4. Standard Error of the Mean

• Measures of Variability 2. Variance: (use all data points):

average of the distance that each score is from the mean (Squared deviation from the mean)

Notation for variances23. Standard Deviation= SD= s24. Standard Error of the mean = SEM = SD/ n