1. 2011 Pearson Prentice Hall, Salkind. Chapter 7 Data Collection and Descriptive Statistics

2. 2011 Pearson Prentice Hall, Salkind.  Explain the steps in the data collection process.  Construct a data collection form and code data collected.  Identify 10 “commandments” of data collection.  Define the difference between inferential and descriptive statistics.  Compute the different measures of central tendency from a set of scores.  Explain measures of central tendency and when each one should be used.

3. 2011 Pearson Prentice Hall, Salkind.  Compute the range, standard deviation, and variance from a set of scores.  Explain measures of variability and when each one should be used.  Discuss why the normal curve is important to the research process.  Compute a z-score from a set of scores.  Explain what a z-score means.

4. 2011 Pearson Prentice Hall, Salkind. CHAPTER OVERVIEW  Getting Ready for Data Collection  The Data Collection Process  Getting Ready for Data Analysis  Descriptive Statistics ◦ Measures of Central Tendency ◦ Measures of Variability  Understanding Distributions

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6. 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

7. 2011 Pearson Prentice Hall, Salkind. GRADE 2.004.006.0010.00Total gendermale2016231995 female19211816105 Total 39374135200

8. 2011 Pearson Prentice Hall, Salkind.

9. THE DATA COLLECTION PROCESS  Begins with raw data ◦ Raw data are unorganized data

10. 2011 Pearson Prentice Hall, Salkind. 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

11. 2011 Pearson Prentice Hall, Salkind. 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

12. 2011 Pearson Prentice Hall, Salkind. 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

13. 2011 Pearson Prentice Hall, Salkind. TEN COMMANDMENTS OF DATA COLLECTION 1. Get permission from your institutional review board to collect the data 2. Think about the type of data you will have to collect 3. Think about where the data will come from 4. Be sure the data collection form is clear and easy to use 5. Make a duplicate of the original data and keep it in a separate location 6. Ensure that those collecting data are well-trained 7. Schedule your data collection efforts 8. Cultivate sources for finding participants 9. Follow up on participants that you originally missed 10. Don’t throw away original data

14. 2011 Pearson Prentice Hall, Salkind. 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

15. 2011 Pearson Prentice Hall, Salkind. DESCRIPTIVE STATISTICS

16. 2011 Pearson Prentice Hall, Salkind. DESCRIPTIVE STATISTICS  Distributions of Scores Comparing Distributions of Scores

17. 2011 Pearson Prentice Hall, Salkind. MEASURES OF CENTRAL TENDENCY  Mean—arithmetic average  Median—midpoint in a distribution  Mode—most frequent score

18. 2011 Pearson Prentice Hall, Salkind.  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 scoresMEAN  What it is ◦ Arithmetic average ◦ Sum of scores/number of scores X

19. 2011 Pearson Prentice Hall, Salkind.  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 scoresMEDIAN  What it is ◦ Midpoint of distribution ◦ Half of scores above and half of scores below

20. 2011 Pearson Prentice Hall, Salkind.MODE  What it is ◦ Most frequently occurring score  What it is not! ◦ How often the most frequent score occurs

21. 2011 Pearson Prentice Hall, Salkind. WHEN TO USE WHICH MEASURE Measure of Central Tendency Level of Measurement Use WhenExamples ModeNominalData are categorical Eye color, party affiliation MedianOrdinalData include extreme scores Rank in class, birth order, income MeanInterval and ratio You can, and the data fit Speed of response, age in years

22. 2011 Pearson Prentice Hall, Salkind. 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

23. 2011 Pearson Prentice Hall, Salkind. COMPUTING THE STANDARD DEVIATION  s ◦ = summation sign ◦ X = each score ◦ X = mean ◦ n = size of sample =  (X – X) 2 n - 1 

24. 2011 Pearson Prentice Hall, Salkind. COMPUTING THE STANDARD DEVIATION 1. List scores and compute mean X 13 14 15 12 13 14 13 16 15 9 X = 13.4

25. 2011 Pearson Prentice Hall, Salkind. 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

26. 2011 Pearson Prentice Hall, Salkind. 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)

27. 2011 Pearson Prentice Hall, Salkind. 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 COMPUTING THE STANDARD DEVIATION 1. List scores and compute mean 2. Subtract mean from each score 3. Square each deviation 4. Sum squared deviations

28. 2011 Pearson Prentice Hall, Salkind. 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

29. 2011 Pearson Prentice Hall, Salkind.

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

31. 2011 Pearson Prentice Hall, Salkind. THE MEAN AND THE STANDARD DEVIATION

32. 2011 Pearson Prentice Hall, Salkind. 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

33. 2011 Pearson Prentice Hall, Salkind. 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

34. 2011 Pearson Prentice Hall, Salkind. 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

35. 2011 Pearson Prentice Hall, Salkind. WHAT z SCORES 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

36. 2011 Pearson Prentice Hall, Salkind.  Explain the steps in the data collection process?  Construct a data collection form and code data collected?  Identify 10 “commandments” of data collection?  Define the difference between inferential and descriptive statistics?  Compute the different measures of central tendency from a set of scores?  Explain measures of central tendency and when each one should be used?  Compute the range, standard deviation, and variance from a set of scores?  Explain measures of variability and when each one should be used?  Discuss why the normal curve is important to the research process?  Compute a z-score from a set of scores?  Explain what a z-score means?