# Data Analysis Statistics. OVERVIEW Getting Ready for Data Collection Getting Ready for Data Collection The Data Collection Process The Data Collection.

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Data Analysis Statistics

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

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

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

CONSTRUCTING DATA COLLECTION FORMS IDGenderGradeBuilding Reading Score Mathematics Score 12345221228284101666655414656456044375932 One column for each variable One row for each subject

CODING DATA Use single digits when possible Use single digits when possible Use codes that are simple and unambiguous Use codes that are simple and unambiguous Use codes that are explicit and discrete Use codes that are explicit and discrete Variable Range of Data Possible Example ID Number 001 through 200 138 Gender 1 or 2 2 Grade 1, 2, 4, 6, 8, or 10 4 Building 1 through 6 1 Reading Score 1 through 100 78 78 Mathematics Score 1 through 100 69 69

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

The Basics Descriptive statistics Descriptive statistics Inferential statistics Inferential statistics Sample statistics Sample statistics Population parameters Population parameters

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

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

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

Descriptive Statistics Frequency Distributions Organizing a set of data by summarizing the number of times a particular value of a variable occurs Organizing a set of data by summarizing the number of times a particular value of a variable occurs Frequency distribution of ice cream consumption Age Frequency (number in range) 01-56-1011-15TOTAL25158250

Percentage Distributions Organizing the frequency distribution into a chart or graph that summarizes percentage values associated with particular values of a variable Organizing the frequency distribution into a chart or graph that summarizes percentage values associated with particular values of a variableProportion The percentage of elements that meet some criterion (percentage, fraction or decimal) The percentage of elements that meet some criterion (percentage, fraction or decimal) Frequency distribution of ice cream consumption by age Age Percent (of people who consumed ice cream in range) 01-56-1011-15TOTAL5030164100%

Graphic Representations of Data Pie Chart: Ice cream consumption

Bar Chart: Frequency of Seasonal Ice Cream consumption

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

Cross tabulation 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

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

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. 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? 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)

Elaboration Analysis of Cross tabs Analysis of the basic cross-tab for each level of another variable, such as subgroups of the same sample 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? Percentage Cross tab : Do you have children under the age of six currently living with you? Aged 17-25 Aged 25 and up Aged 17-25 Aged 25 and up MaleFemale Yes02 No1020MaleFemale58 00

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

Choco chip MarshmOatmealOreo 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

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

WHEN TO USE WHICH MEASURE Measure of Central Tendency Level of Measurement Use When Examples ModeNominal Data are categorical Eye color, party affiliation MedianOrdinal Data include extreme scores Rank in class, birth order Mean Interval and ratio You can, and the data fit Speed of response, age in years

Measures of dispersion What is the tendency for measures to depart from the central tendency? Range: simplest measure of dispersion Range: simplest measure of dispersion Deviation scores- quantitative index of dispersion Deviation scores- quantitative index of dispersion –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

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

THE MEAN AND THE STANDARD DEVIATION

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

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