1QuestionWhat are data and what do they mean to a scientist?Dinner at the Urquhart HouseBrought to you by the Briggs Multiracial AllianceSunday nightAll food provided (probably Chinese)Contact Mimi Reddy, [email protected] detailsData, Statistics, and SpreadsheetsWhat are data?What are statistics?What are spreadsheets?How can you analyze data with spreadsheets?Data Data are pieces of information Data can be numbers, words, descriptions Data have UNITS The word data is PLURAL, datum is singular Data about Willoughby: • Age: 5 (years)• Height: 47 (inches)• Weight: 66 (pounds)• Eyes: Blue• Favorite word: Wrestle• Favorite letter: WTypes of DataNumbers – two types– Real #s – rational numbers – 28.75 lbs– Integers – whole numbers – 18 monthsLetters – called characters in programming– W is a characterWords – called strings in programming– “No thanks” is a strings, can be individual words or phrasesStatistics and Data Test Scores: – Jeff: 88– Mollie: 92– Marcie: 88– Dave: 47– Karim: 99– Willoughby: 42– Benjamin: 0 What statistics can you calculate to describe these data?– Try to think of four things to describe the data stop2StatisticsStatistics are derived from the data Statistics are descriptions of dataStatistics are meant to simplify the dataStatistics can be misleadingTypical Statistics Sample Size - number of individuals measured = n Sum = Σ Average or Mean = Σ/n Median – Value of 50th percentile, half of values fall above, half below Maximum, Minimum, Range (Max-Min) Mode - most common value Standard deviation Variance (SD2)Analyze these data... Mean, max, min, range, median, mode• 18• 33• 4• 47• 49• 38• 29• 4• 55 sample size (n) Sum Σ mean=average=Σ/n• denoted x median = halfway mode = most commonSpreadsheetsSpreadsheets are tables Spreadsheets allow calculations and manipulations of data• Calculations: mean, standard deviation• Manipulations: sort, CostaRica NicaraguaRainforest 625,000 3,712,000Dry Forest 50,000 300,000Total 675,000 4,012,000Make a data table: Fly 1, length 13.4 mm, velocity 27 Kph, age 21 days Fly 2, length 9.4 mm, velocity 0 Kph, age 220 days Fly 3, length 9.3 mm, velocity 44 Kph, age 1 days Fly 4, length 13.4 mm, velocity 17 Kph, age 32 days Fly 5, length 17.4 mm, velocity 33 Kph, age 11 days How many columns? How many rows?  #s go down or across?Data TableAgeVelocityLengthFly #543213Microsoft ExcelTypical spreadsheet program– Lotus 1-2-3 is original commercial spreadsheetHas similar controls to MS WordNow allows graphing (charts)• very restricted formats, hard to get exactly what you wantExcel tables and graphs can be copied into MS WordFriday’s AssignmentWe will work with Microsoft Excel to analyze some dataGroups of two will submit one finished spreadsheet for the assignmentGraphsMany different types of graphs– Points– Lines– Bars– PiesPoint GraphsCalled X-Y Scatter in MS ExcelPlot points based on X and Y valueCan fit a “REGRESSION LINE” to the data– Line that best fits the dataX-Y Scatter Bar GraphsCategorize data into counts or percentsCategories can be descriptive categories (Windows 98, Windows 2000, …)Can also be numeric categories – Height: 60-63, 63-66, etc. or just 61, 62, 63…– Count up number of people in each groupHistograms are a particular type of bar graph4Bar GraphStarting Salary$0$10,000$20,000$30,000$40,000$50,0001988 1989 1990 1991 1992 1993 1994Starting SalaryHistogramX axis is categoriesY axis is a number or proportion of observations in that categoryHistogram Bar GraphNumber of CrashesRegular Bar Graph vs. Histogram Bar GraphStarting Salary$0$10,000$20,000$30,000$40,000$50,0001988 1989 1990 1991 1992 1993 1994Starting SalaryDistributionsSpecial type of histogram with continuous numeric scale at bottomNormal distribution is a key concept in statisticsSkewed distribution is one that is unbalancedSample distribution histogramsDanyoungyoo, Katanchalee, and Srichawla, www.s-t.au.ac.th/handout/st2204/week5-Univariate-Des.pptRobert D. Duval, PS 400 Lecture, www.polsci.wvu.edu/duval/ps400/Notes/400Notes.ppt5The NORMAL Distribution A NORMAL DISTRIBUTIONis the theoretical distribution of values given natural variation around a MEAN It is balanced, humped distributionDistributionsSkew is an imbalance in the distributionDanyoungyoo, Katanchalee, and Srichawla, www.s-t.au.ac.th/handout/st2204/week5-Univariate-Des.pptHypothesis TestingStatistical Tests are how scientists decide if data support their hypothesis (NOT PROVE their hypothesis)Four major statistical tests: T-test, X2 Test, Regression, ANOVAHypothesisProcessor speed has an effect on the performance of the computer.Null Hypothesis– H0: Processor speed has NO EFFECT on the performance of a computer.Statistical Tests and ProbabilityStatistical tests give a valueThat value can be related to a probabilityProbability is likelihood that NULL hypothesis is correct given the data you haveIf P < 0.05 (1/20), then you conclude NULL hypothesis is FALSET-TestCompares differences between two meansFormula: T = (x1-x2)/SEM– SEM is Standard Error of Mean [SD/(N-1)]T Values: Difference between mean in comparison to the amount of spread in your data6T-ValuesIf T > 2.5 or 3.0, difference is usually significant (this depends on your sample