6/13/2006Practical Research for Learning Communities Data Collection & Descriptive Statistics Kate Cerri Lynn Robinson Julie Thompson mmmmmm

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: The mean is 55.2 Find the mean

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: The median is 49.5 Find the median

The Mode The score that occurs most frequently. If you have a number set of the following: The mode is 76 Find the mode

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: The range is 62 Find the range

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. Mean COLORS

Calculating the Standard Deviation Step 2: Subtract the bag’s mean from each color total and list it in the middle column. Example: 31 – 17.5 = 13.5

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. Example: (13.5) 2 = SUM

And the Standard Deviation is... Step 5: Divide the sum in the bottom right box by 5 (the # of colors – 1). Step 6: Take the square root of the answer in step 5, and Voilà! In the example, divide 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 Mean = 17.5

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 Example: 13.5 ÷ 7.42 = 1.82 Z scores are associated with the likeli- hood or probability that a certain raw score will appear in a distribution.

6/13/2006Practical Research for Learning Communities Introduction to descriptive statistics: Statistics tutorial & links elsewhere: outline.html outline.html Check it out online!! mmmmmm