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Data Analysis Statistics

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OVERVIEW Getting Ready for Data Collection The Data Collection Process Getting Ready for Data Analysis Descriptive Statistics

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GETTING READY FOR DATA COLLECTION Four steps Constructing a data collection form Establishing a coding strategy Collecting the data Entering data onto the collection form

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THE DATA COLLECTION PROCESS Begins with raw data Raw data are unorganized data

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CONSTRUCTING DATA COLLECTION FORMS IDGenderGradeBuildingReading Score Mathematics Score 1234512345 2212222122 8 2 8 4 10 1666616666 55 41 46 56 45 60 44 37 59 32 One column for each variable One row for each subject

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CODING DATA Use single digits when possible Use codes that are simple and unambiguous Use codes that are explicit and discrete VariableRange of Data PossibleExample ID Number001 through 200 138 Gender1 or 2 2 Grade1, 2, 4, 6, 8, or 10 4 Building1 through 6 1 Reading Score1 through 100 78 Mathematics Score1 through 100 69

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Interpretation The process of making pertinent inferences and drawing conclusions concerning the meaning and implications of a research investigation

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The Basics Descriptive statistics Inferential statistics Sample statistics Population parameters

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Sample--------------population

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Sample statistics Variables in a sample or measures computed from sample data Population parameters The variables in a population or measured characteristics of the population

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Making Data Usable …Or what to do with all those numbers

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Descriptive Statistics Frequency Distributions Organizing a set of data by summarizing the number of times a particular value of a variable occurs Frequency distribution of ice cream consumption AgeFrequency (number in range) 0 1-5 6-10 11-15 TOTAL 25 15 8 2 50

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Percentage Distributions Organizing the frequency distribution into a chart or graph that summarizes percentage values associated with particular values of a variable Proportion The percentage of elements that meet some criterion (percentage, fraction or decimal) Frequency distribution of ice cream consumption by age AgePercent (of people who consumed ice cream in range) 0 1-5 6-10 11-15 TOTAL 50 30 16 4 100%

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Graphic Representations of Data Pie Chart: Ice cream consumption

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Bar Chart: Frequency of Seasonal Ice Cream consumption

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Cross tabulation Cross tabulation: a technique for organizing data by groups, categories or classes, thus facilitating comparisons; a joint frequency distribution of observations on two or more sets of variables

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Types of Cross tabs Contingency table: the results of a cross tabulation of two variables, such as survey questions Cross tab of question: Do you have children under the age of six currently living with you? This is a 2X2 table, why YesNoTotal Males51520 Females102030 Total153550

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Types of Cross tabs Percentage cross-tab. Using percentages helps us make relative comparisons. The total number of respondents/observations may be used as a base for computing the percentage in each cell Percentage Cross tab : Do you have children under the age of six currently living with you? YesNoTotal Males20%80% 100% (20) Females33.33%66.66%100% (30) Total30%70%100% (50)

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Bar Chart: Frequency of Seasonal Ice Cream consumption Shown By Gender Graphical representation of results from cross tab

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Elaboration Analysis of Cross tabs Analysis of the basic cross-tab for each level of another variable, such as subgroups of the same sample Percentage Cross tab : Do you have children under the age of six currently living with you? Moderator Variable; Spurious relationship Aged 17-25 Aged 25 and up MaleFemale Yes02 No1020 MaleFemale 58 00

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Calculating Rank Data Please place in rank order the following varieties of cookies (1= most preferred to 4=least preferred) __ Chocolate chip __ Marshmallow __ Oatmeal __ Oreo

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Choco chipMarshmOatmealOreo 11243 21342 32134 42431 52134 63412 72314 81423 94321 102134 Chocolate chip: (3X1) +(4X2) + (2X3) +(1X4) = 21 ******** Marshmallow: (3X1) +(1X2) + (3X3) +(3X4) = 26 Oatmeal: (2X1) +(2X2) + (4X3) +(3X4) = 26 Oreo: (2X1) +(2X2) + (2X3) +(4X4) = 28

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Measures of central tendency Mode: the value that occurs most often Median: the midpoint; the value below which half the values in a distribution fall Mean: the arithmetic average Remember: what type of scale you use determines the type of statistic you may calculate

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WHEN TO USE WHICH MEASURE Measure of Central Tendency Level of Measurement Use WhenExamples ModeNominalData are categoricalEye color, party affiliation MedianOrdinalData include extreme scores Rank in class, birth order MeanInterval and ratioYou can, and the data fitSpeed of response, age in years

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Measures of dispersion What is the tendency for measures to depart from the central tendency? Range: simplest measure of dispersion Deviation scores- quantitative index of dispersion Average deviation: never used Variance: the sum of squared deviation scores divided by sample size minus 1- often used. (variance is in squared units, eg squared dollars) Standard Deviation: square root of variance

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MEASURES OF VARIABILITY Variability is the degree of spread or dispersion in a set of scores Range—difference between highest and lowest score Standard deviation—average difference of each score from mean

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THE MEAN AND THE STANDARD DEVIATION

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STANDARD DEVIATIONS AND % OF CASES The normal curve is symmetrical One standard deviation to either side of the mean contains 34% of area under curve 68% of scores lie within ± 1 standard deviation of mean

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