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m m m m m Data Collection & Descriptive Statistics Kate Cerri Lynn Robinson Julie Thompson 6/13/2006 Practical Research for Learning Communities m Steps for data collection • Create a data collection form to organize the data collected. • Create a coding strategy to represent data on the form. • Collect the actual data. • Enter the data on the form. The ten commandments of data collection • Consider the type of data to be collected. • Determine where data will be collected. • Design a data collection form that is clear & easy to use. • Copy the data file & keep it in a separate location. • Be certain that any other people who collect or transfer the data are trained & understand the data collection process. The ten commandments of data collection • Plan a detailed schedule of when & where the data will be collected. • Cultivate possible sources for the participant pool. • Follow up on participants who missed their testing session or interview. • Never discard original data. • Follow the previous nine rules! Measures of Central Tendency • Mean • Median • Mode The Mean • The sum of a set of scores divided by the number of scores. If you have a number set of the following: 88 76 52 34 26 Find the mean The mean is 55.2 The Median • The score or the point in a distribution above which one-half of the scores lie. If you have a number set of the following: 88 76 52 47 34 26 Find the median The median is 49.5 The Mode • The score that occurs most frequently. If you have a number set of the following: 26 89 76 34 88 76 84 83 76 76 88 84 52 88 26 95 34 Find the mode The mode is 76 Now that you have reviewed measurements of central tendency, calculate the mean, median, and mode using the data from your group’s bag of M & M® chocolates. Record them on your worksheet. Measures of Variability • Range • Standard Deviation • Variance The Range • The difference between the highest & lowest scores in a distribution. If you have a number set of the following: 88 76 52 34 26 Find the range The range is 62 Calculate the range using the data from your group’s bag of M & M® candies and record it on your worksheet. The Standard Deviation • The average amount that each of the individual scores varies from the mean of the set scores. Your group will find the standard deviation with the data from your bag of M & M®s. Don’t panic!! We’ll guide you step by step! Calculating the Standard Deviation • Step 1: List the original color totals, then list the mean computed for the bag. Standard Deviation Calculation Table Raw number in bag Deviation from the mean (X - X) X Squared deviations (X - X)2 31 17 COLORS 9 17 13 18 Mean X = 17.5 (mean for bag) ∑ (X - X) = 0 ∑ (X - X)2 =________ Calculating the Standard Deviation •Step 2: Subtract the bag’s mean from each color total and list it in the middle column. Standard Deviation Calculation Table Example: Raw number in bag Deviation from the mean (X - X) X 31 13.5 31 – 17.5 = 17 - 0.5 13.5 9 - 8.5 17 - 0.5 13 - 4.5 18 0.5 X = 17.5 (mean for bag) ∑ (X - X) = 0 Squared deviations (X - X)2 ∑ (X - X)2 =________ Calculating the Standard Deviation •Steps 3 & 4: Square each deviation, & list it in the last column. Find the sum of the deviations and list it in the bottom box. Standard Deviation Calculation Table Example: Raw number in bag Deviation from the mean (X - X) X Squared deviations (X - X)2 31 13.5 182.25 (13.5)2 = 17 - 0.5 0.25 182.25 9 - 8.5 72.25 17 - 0.5 0.25 13 - 4.5 20.25 18 0.5 0.25 X = 17.5 (mean for bag) ∑ (X - X) = 0 ∑ (X - X)2 = 275.5 SUM And the Standard Deviation is... n Calculation Table om the mean - X) Squared deviations (X - X)2 3.5 182.25 4.5 20.25 0.5 0.25 • Step 5: Divide the sum in the bottom right 0.5 0.25 box by 5 (the # of colors – 1). 8.5 72.25 • Step 0.25 6: Take the square root of the answer 0.5 in step 5, and Voilà! X) = 0 ∑ (X - X)2 = 275.5 In the example, divide 275.5 by 5 to get 55.1, then take the square root to get 7.42 Variance • The square of the standard deviation. • It represents everything in the formula for the standard deviation except the square root, and is often cited in research reports. For the set of M& M®s, the variance is 55.1 M & M® Single Bag Distribution 35 Green 31 Mean = 17.5 25 Brown Orange Blue 18 17 15 17 Yellow 13 Red 9 5 M&M Colors The Normal (Bell-Shaped) Curve • The mean, median and mode are all the same value, represented by the red line. • The two halves of the curve mirror one another. • The tails of the curve get closer and closer to the X axis, but never touch it. • Mean and standard deviation define characteristics of the normal curve. Characteristics of a Normal Distribution • The distance between the mean of the distribution and either ±1s (standard deviation) covers 34% of the area beneath the normal curve. • Because the curve is symmetrical, 68% of the distribution falls between +1s and -1s around the mean. • Scores are more likely to fall toward the middle than toward the extremes. -1s +1s Standard Scores • Standard scores have the same reference point and the same standard deviation. • Are useful for accurate comparison of scores from different distributions. • Z scores are the most frequent type of standard score. The formula: z = (X - X) s Z scores and their implications Remember: s = 7.42 Raw scores (X - X) z score 31 13.5 1.82 17 - 0.5 - .06 9 - 8.5 - 1.14 17 - 0.5 - .06 13 - 4.5 - .61 18 0.5 .06 Example: 13.5 ÷ 7.42 = •Z scores are associated with the likelihood or probability that a certain raw score will appear in a distribution. Check it out online!! Introduction to descriptive statistics: http://www.mste.uiuc.edu/hill/dstat/dstat.html Statistics tutorial & links elsewhere: http://www.meandeviation.com/tutorials/stats/notes/ outline.html m 6/13/2006 m m m m Practical Research for Learning Communities m