Chapter 7 Data Collection and Descriptive Statistics 2009 Pearson Prentice Hall, Salkind. 1
CHAPTER OBJECTIVES - STUDENTS SHOULD BE ABLE TO: 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. 2009 Pearson Prentice Hall, Salkind. 2
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 2009 Pearson Prentice Hall, Salkind. 3
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 2009 Pearson Prentice Hall, Salkind. 4
GRADE 2.00 4.00 6.00 10.00 Total gender male 20 16 23 19 95 female 19 21 18 16 105 Total 39 37 41 35 200 2009 Pearson Prentice Hall, Salkind. 5
THE DATA COLLECTION PROCESS Begins with raw data Raw data are unorganized data 2009 Pearson Prentice Hall, Salkind. 6
CONSTRUCTING DATA COLLECTION FORMS One column for each variable ID Gender Grade Building Reading Score 1 2 3 4 5 2 2 1 2 2 8 2 8 4 10 1 6 6 6 6 55 41 46 56 45 Mathematics Score 60 44 37 59 32 One row for each subject 2009 Pearson Prentice Hall, Salkind. 7
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 2009 Pearson Prentice Hall, Salkind. 8
CODING DATA 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 Mathematics Score 1 through 100 69 Use single digits when possible Use codes that are simple and unambiguous Use codes that are explicit and discrete 2009 Pearson Prentice Hall, Salkind. 9
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 2009 Pearson Prentice Hall, Salkind. 10
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 2009 Pearson Prentice Hall, Salkind. 11
DESCRIPTIVE STATISTICS Distributions of Scores Comparing Distributions of Scores 2009 Pearson Prentice Hall, Salkind. 12
MEASURES OF CENTRAL TENDENCY Mean arithmetic average Median midpoint in a distribution Mode most frequent score 2009 Pearson Prentice Hall, Salkind. 13
MEAN What it is Arithmetic average Sum of scores/number of scores How to compute it X = ΣX n Σ = 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 2009 Pearson Prentice Hall, Salkind. 14
MEDIAN What it is Midpoint of distribution Half of scores above and half of scores below 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 2009 Pearson Prentice Hall, Salkind. 15
MODE What it is Most frequently occurring score What it is not! How often the most frequent score occurs 2009 Pearson Prentice Hall, Salkind. 16
WHEN TO USE WHICH MEASURE Measure of Central Tendency Level of Measurement Use When Mode Nominal Data are categorical Median Ordinal Data include extreme scores Mean Interval and ratio You can, and the data fit Examples Eye color, party affiliation Rank in class, birth order, income Speed of response, age in years 2009 Pearson Prentice Hall, Salkind. 17
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 2009 Pearson Prentice Hall, Salkind. 18
COMPUTING THE STANDARD DEVIATION s = (X X) 2 n - 1 Σ = summation sign X = each score X = mean n = size of sample 2009 Pearson Prentice Hall, Salkind. 19
COMPUTING THE STANDARD DEVIATION X 13 14 1. List scores and compute mean 15 12 13 14 13 16 15 9 X = 13.4 2009 Pearson Prentice Hall, Salkind. 20
COMPUTING THE STANDARD DEVIATION X (X-X) 13-0.4 14 0.6 15 1.6 12-1.4 13-0.4 1. List scores and compute mean 2. Subtract mean from each score 14 0.6 13-0.4 16 2.6 15 1.6 9-4.4 X = 13.4 X = 0 2009 Pearson Prentice Hall, Salkind. 21
COMPUTING THE STANDARD DEVIATION X (X X) (X X) 2 13-0.4 0.16 14 0.6 0.36 15 1.6 2.56 12-1.4 1.96 13-0.4 0.16 14 0.6 0.36 13-0.4 0.16 1. List scores and compute mean 2. Subtract mean from each score 3. Square each deviation 16 2.6 6.76 15 1.6 2.56 9-4.4 19.36 X =13.4 X = 0 2009 Pearson Prentice Hall, Salkind. 22
COMPUTING THE STANDARD DEVIATION X (X X) (X X) 2 13-0.4 0.16 14 0.6 0.36 15 1.6 2.56 12-1.4 1.96 13-0.4 0.16 14 0.6 0.36 13-0.4 0.16 16 2.6 6.76 15 1.6 2.56 9-4.4 19.36 1. List scores and compute mean 2. Subtract mean from each score 3. Square each deviation 4. Sum squared deviations X =13.4 X = 0 X 2 = 34.4 2009 Pearson Prentice Hall, Salkind. 23
COMPUTING THE STANDARD DEVIATION X (X X) (X X) 2 13-0.4 0.16 14 0.6 0.36 15 1.6 2.56 12-1.4 1.96 13-0.4 0.16 14 0.6 0.36 13-0.4 0.16 16 2.6 6.76 15 1.6 2.56 9-4.4 19.36 X =13.4 X = 0 X 2 = 34.4 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 2009 Pearson Prentice Hall, Salkind. 24
THE NORMAL (BELL SHAPED) CURVE Mean = median = mode Symmetrical about midpoint Tails approach X axis, but do not touch 2009 Pearson Prentice Hall, Salkind. 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 2009 Pearson Prentice Hall, Salkind. 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 2009 Pearson Prentice Hall, Salkind. 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 90 2 92 1 Micah 90 4 92.5 2009 Pearson Prentice Hall, Salkind. 28
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 2009 Pearson Prentice Hall, Salkind. 29
HAVE WE MET OUR OBJECTIVES? CAN YOU: 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? 2009 Pearson Prentice Hall, Salkind. 30