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Data Collection and Descriptive Statistics 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. 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. 2011 Pearson Prentice Hall, Salkind. 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 2011 Pearson Prentice Hall, Salkind. 2011 Pearson Prentice Hall, Salkind. Constructing a data collection form Establishing a coding strategy Collecting the data Entering data onto the collection form 2011 Pearson Prentice Hall, Salkind. GRADE 2.00 gender Total 4.00 6.00 10.00 Total male 20 16 23 19 95 female 19 21 18 16 105 39 37 41 35 200 2011 Pearson Prentice Hall, Salkind. 2011 Pearson Prentice Hall, Salkind. Begins with raw data ◦ Raw data are unorganized data 2011 Pearson Prentice Hall, Salkind. One column for each variable ID Gender Grade Building Reading Score Mathematics 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 60 44 37 59 32 One row for each subject 2011 Pearson Prentice Hall, Salkind. 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 2011 Pearson Prentice Hall, Salkind. Variable Range of Data Possible Example ID Number 001 through 200 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 69 138 Use single digits when possible Use codes that are simple and unambiguous Use codes that are explicit and discrete 2011 Pearson Prentice Hall, Salkind. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. Get permission from your institutional review board to collect the data Think about the type of data you will have to collect Think about where the data will come from Be sure the data collection form is clear and easy to use Make a duplicate of the original data and keep it in a separate location Ensure that those collecting data are well-trained Schedule your data collection efforts Cultivate sources for finding participants Follow up on participants that you originally missed Don’t throw away original data 2011 Pearson Prentice Hall, Salkind. 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 2011 Pearson Prentice Hall, Salkind. 2011 Pearson Prentice Hall, Salkind. Distributions of Scores • Comparing Distributions of Scores 2011 Pearson Prentice Hall, Salkind. Mean—arithmetic average Median—midpoint in a distribution Mode—most frequent score 2011 Pearson Prentice Hall, Salkind. What it is ◦ Arithmetic average ◦ Sum of scores/number of scores How to compute it ◦ X = X n 1. 2. = summation sign X = each score n = size of sample Add up all of the scores Divide the total by the number of scores 2011 Pearson Prentice Hall, Salkind. What it is ◦ Midpoint of distribution ◦ Half of scores above and half of scores below How to compute it when n is odd 1. 2. 3. Order scores from lowest to highest Count number of scores Select middle score How to compute it when n is even 1. 2. 3. Order scores from lowest to highest Count number of scores Compute X of two middle scores 2011 Pearson Prentice Hall, Salkind. What it is ◦ Most frequently occurring score What it is not! ◦ How often the most frequent score occurs 2011 Pearson Prentice Hall, Salkind. Measure of Central Tendency Level of Measurement Use When Examples Mode Nominal Data are categorical Eye color, party affiliation Median Ordinal Data include extreme scores Rank in class, birth order, income Mean Interval and ratio You can, and the data fit Speed of response, age in years 2011 Pearson Prentice Hall, Salkind. 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 2011 Pearson Prentice Hall, Salkind. s ◦ ◦ ◦ ◦ = (X – X)2 n-1 = summation sign X = each score X = mean n = size of sample 2011 Pearson Prentice Hall, Salkind. X 13 14 1. List scores and compute mean 15 12 13 14 13 16 15 9 X = 13.4 2011 Pearson Prentice Hall, Salkind. X (X-X) 13 -0.4 14 0.6 15 1.6 12 -1.4 13 -0.4 14 0.6 13 -0.4 16 2.6 15 1.6 9 -4.4 X = 13.4 1. 2. List scores and compute mean Subtract mean from each score X = 0 2011 Pearson Prentice Hall, Salkind. (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 1. 2. 3. List scores and compute mean Subtract mean from each score Square each deviation 2011 Pearson Prentice Hall, Salkind. (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 X2 = 34.4 1. 2. 3. 4. List scores and compute mean Subtract mean from each score Square each deviation Sum squared deviations 2011 Pearson Prentice Hall, Salkind. (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 X2 = 34.4 1. 2. 3. 4. 5. 6. List scores and compute mean Subtract mean from each score Square each deviation Sum squared deviations Divide sum of squared deviation by n – 1 • 34.4/9 = 3.82 (= s2) Compute square root of step 5 • 3.82 = 1.95 2011 Pearson Prentice Hall, Salkind. 2011 Pearson Prentice Hall, Salkind. Mean = median = mode Symmetrical about midpoint Tails approach X axis, but do not touch 2011 Pearson Prentice Hall, Salkind. 2011 Pearson Prentice Hall, Salkind. 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 2011 Pearson Prentice Hall, Salkind. 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 2011 Pearson Prentice Hall, Salkind. Standard scores are used to compare scores from different distributions Class Mean Sara Micah 90 90 Class Standard Deviation 2 4 Student’s Student’s Raw z Score Score 92 1 92 .5 2011 Pearson Prentice Hall, Salkind. 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 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? 2011 Pearson Prentice Hall, Salkind.