1. CHAPTER OVERVIEW Getting Ready for Data Collection The Data Collection Process Getting Ready for Data Analysis Understanding Distributions

2. 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

3. GRADE 2.004.006.0010.00Total gendermale2016231995 female19211816105 Total 39374135200

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

5. 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

6. ADVANTAGES OF OPTICAL SCORING SHEETS If subjects choose from several responses, optical scoring sheets might be used –Advantages Scoring is fast Scoring is accurate Additional analyses are easily done –Disadvantages Expense

7. 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

8. TEN COMMANDMENTS OF DATA COLLECTION 1.Think about what data are needed to answer the question 2.Think about where the data will come from 3.Be sure the data collection form is clear and easy to use 4.Make a duplicate of the original data 5.Ensure that your assistants are well trained 6.Schedule your data collection efforts 7.Cultivate sources for finding participants 8.Follow up on participants that you originally missed 9.Don’t throw away original data 10.Follow these guidelines

9. GETTING READY FOR DATA ANALYSIS Descriptive statistics—Basic measures –Average scores on a variable –How different scores are from one another Inferential statistics—Help make decisions about –Null and research hypotheses –Generalizing from sample to population

10. DESCRIPTIVE STATISTICS Distributions of Scores Comparing Distributions of Scores

11. MEASURES OF CENTRAL TENDENCY Mean—”average” Median—midpoint in a distribution Mode—most frequent score

12. How to compute it – =  X n  = summation sign X = each score n = size of sample 1.Add up all of the scores 2.Divide the total by the number of scores X MEAN What it is –Arithmetic average –Sum of scores/number of scores

13. How to compute it when n is odd 1.Order scores from lowest to highest 2.Count number of scores 3.Select middle score How to compute it when n is even 1.Order scores from lowest to highest 2.Count number of scores 3.Compute X of two middle scores MEDIAN What it is –Midpoint of distribution –Half of scores above & half of scores below

14. MODE What it is –Most frequently occurring score What it is not! –How often the most frequent score occurs

15. 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

16. 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

17. COMPUTING THE STANDARD DEVIATION s –  = summation sign –X = each score –X = mean –n = size of sample =  (X – X) 2 n - 1

18. COMPUTING THE STANDARD DEVIATION 1.List scores and compute mean X 13 14 15 12 13 14 13 16 15 9 X = 13.4

19. COMPUTING THE STANDARD DEVIATION 1.List scores and compute mean 2.Subtract mean from each score X(X-X) 13-0.4 140.6 151.6 12-1.4 13-0.4 140.6 13-0.4 162.6 151.6 9-4.4  X = 0 X = 13.4

20. X 13-0.40.16 140.60.36 151.62.56 12-1.41.96 13-0.40.16 140.60.36 13-0.40.16 162.66.76 151.62.56 9-4.419.36 X =13.4  X = 0 COMPUTING THE STANDARD DEVIATION 1.List scores and compute mean 2.Subtract mean from each score 3.Square each deviation (X – X) 2 (X – X)

21. COMPUTING THE STANDARD DEVIATION 1.List scores and compute mean 2.Subtract mean from each score 3.Square each deviation 4.Sum squared deviations X 13-0.40.16 140.60.36 151.62.56 12-1.41.96 13-0.40.16 140.60.36 13-0.40.16 162.66.76 151.62.56 9-4.419.36 X =13.4  X = 0  X 2 = 34.4 (X – X)(X – X) 2

22. COMPUTING THE STANDARD DEVIATION 1.List scores and compute mean 2.Subtract mean from each score 3.Square each deviation 4.Sum squared deviations 5.Divide sum of squared deviation by n – 1 34.4/9 = 3.82 (= s 2 ) 6.Compute square root of step 5  3.82 = 1.95 X 13-0.40.16 140.60.36 151.62.56 12-1.41.96 13-0.40.16 140.60.36 13-0.40.16 162.66.76 151.62.56 9-4.419.36 X =13.4  X = 0  X 2 = 34.4 (X – X)(X – X) 2

23. THE NORMAL (BELL SHAPED) CURVE Mean = median = mode Symmetrical about midpoint Tails approach X axis, but do not touch

24. THE MEAN AND THE STANDARD DEVIATION

25. 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

26. STANDARD SCORES: COMPUTING z SCORES Standard scores have been “standardized” SO THAT Scores from different distributions have –The same reference point –The same standard deviation Computation Z = (X – X) s –Z = standard score –X = individual score –X = mean –s = standard deviation

27. STANDARD SCORES: USING z SCORES Standard scores are used to compare scores from different distributions Class Mean Class Standard Deviation Student’s Raw Score Student’s z Score Sara Micah 90 2424 92 1.5

28. WHAT z SCORES REALLY, REALLY MEAN Because –Different z scores represent different locations on the x-axis, and –Location on the x-axis is associated with a particular percentage of the distribution z scores can be used to predict –The percentage of scores both above and below a particular score, and –The probability that a particular score will occur in a distribution