Unit 3: Basic Test Statistics and Correlation Lesson 3: Measures of Spreadoutness Next Slide EDER 5350: Educational Evaluation and Assessment Dr. J. Kyle Roberts University of North Texas

Measures of Spreadoutness:

Measures of Spreadoutness Range Standard Deviation Z-scores Standard Error of the Mean Next Slide

Range:

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

Problems with Range:

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

Standard Deviation:

Standard Deviation “A measure of spreadoutness in the data’s own metric” where: is each person’s individual score is the mean of all scores n is the number of people in the study Next Slide

Computing the SD:

Computing the SD X = 1, 2, 3, 4 SD = 1.29 Next Slide

“Average Distance From the Mean”:

“Average Distance From the Mean” 1 2 3 4 8 9 10 11 1 2 3 4 SD = 1.29 SD = 1.29 SD = 1.73 Next Slide

Quiz Time:

Quiz Time Which of the following datasets will have the largest standard deviation? 1, 2, 3, 4, 5, 6 2, 2, 3, 4, 5, 5 1, 1, 1, 6, 6, 6 3.5, 3.5, 3.5, 3.5, 3.5, 3.5 1, 2, 3, 4, 5, 6 2, 2, 3, 4, 5, 5 1, 1, 1, 6, 6, 6 3.5, 3.5, 3.5, 3.5, 3.5, 3.5 Next Slide a. b. c. d.

Z-Scores:

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

Computing Z-Scores:

Computing Z-Scores How far that person is from the mean Relative to the standard deviation Next Slide

The 2 Studies:

The 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? Mean = 10 SD = 2 Mean = 10 SD = 9 Z Johnny = +2.5 Z Susan = +1.0 Next Slide

Relative Rules for Z-Scores:

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 X 2 3 3 4 5 5 6 Z -1.42 -.71 -.71 .00 .71 .71 1.42 Next Slide

Standard Error of the Mean:

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

Unit 3: Basic Test Statistics and Correlation:

Unit 3: Basic Test Statistics and Correlation Lesson 3: Measures of Spreadoutness EDER 5350: Educational Evaluation and Assessment Dr. J. Kyle Roberts University of North Texas The End

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