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# Unit 1 lesson 4

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### Unit 1 lesson 4

1. 1. Unit 1: Background to Inferential Statistics Lesson 4: Measures of Spreadoutness EDER 6010: Statistics for Educational Research Dr. J. Kyle Roberts University of North Texas Next Slide
2. 2. Measures of Spreadoutness <ul><li>Range </li></ul><ul><li>Standard Deviation </li></ul><ul><li>Z-scores </li></ul><ul><li>Standard Error of the Mean </li></ul>Next Slide
3. 3. Range “ The simplest measure of spreadoutness” The number of units on the scale of measurement that include the highest and lowest values Range = (X Highest – X Lowest ) + 1 X = 1,2,3,4,5 Range = (5 – 1) +1 = 5 X = -1,-2,-3,-4,-5 Range = ((-1) – (-5)) +1 = 4 + 1 = 5 Next Slide
4. 4. Problems with Range It only considers two scores: Study 2: X = 1, 2, 3, 4, 5 Range = 5 Study 3: X = 1,1,1,1,1,5,5,5,5,5 Range = 5 Study 4: X = 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,5 Range = 5 Study 1: X = 1, 5 Range = 5 Next Slide
5. 5. Standard Deviation “ A measure of spreadoutness in the data’s own metric” Next Slide where: is each person’s individual score is the mean of all scores n is the number of people in the study
6. 6. Computing the SD X = 1, 2, 3, 4 SD = 1.29 Next Slide
7. 7. “ Average Distance From the Mean” SD = 1.29 SD = 1.29 SD = 1.73 Next Slide 1 2 3 4 8 9 10 11 1 2 3 4
8. 8. Quiz Time Which of the following datasets will have the largest standard deviation? <ul><li>1, 2, 3, 4, 5, 6 </li></ul><ul><li>2, 2, 3, 4, 5, 5 </li></ul><ul><li>1, 1, 1, 6, 6, 6 </li></ul><ul><li>3.5, 3.5, 3.5, 3.5, 3.5, 3.5 </li></ul><ul><li>1, 2, 3, 4, 5, 6 </li></ul><ul><li>2, 2, 3, 4, 5, 5 </li></ul><ul><li>1, 1, 1, 6, 6, 6 </li></ul><ul><li>3.5, 3.5, 3.5, 3.5, 3.5, 3.5 </li></ul>Next Slide a. b. c. d.
9. 9. Z-Scores A measure of spreadoutness for individuals. 2 Studies Study 1 Study 2 Johnny scored 5 points above the mean Susan scored 9 points above the mean Who did better in relationship to their fellow classmates? Next Slide
10. 10. Computing Z-Scores How far that person is from the mean Relative to the standard deviation Next Slide
11. 11. The 2 Studies Mean = 10 SD = 2 Mean = 10 SD = 9 Z Johnny = +2.5 Z Susan = +1.0 Next Slide Study 1 Study 2 Johnny scored 5 points above the mean Susan scored 9 points above the mean Who did better in relationship to their fellow classmates?
12. 12. Relative Rules for Z-Scores 1. Typically ranges from -3.0 to +3.0 2. All Z-scores have a mean of 0 and a SD of 1 Next Slide X 2 3 3 4 5 5 6 Z -1.42 -.71 -.71 .00 .71 .71 1.42
13. 13. Standard Error of the Mean “The Standard Deviation of the Sampling Distribution” Standard Deviation of X Number of people in the study Used in the construction of “Confidence Intervals” Next Slide
14. 14. Unit 1: Background to Inferential Statistics Lesson 4: Measures of Spreadoutness EDER 6010: Statistics for Educational Research Dr. J. Kyle Roberts University of North Texas