Unit_1_lesson_4_redone

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Slide 1: 

University of North Texas Unit 1: Understanding and Representing DataLesson 4:Distributions and Graphing EDER 5210 – Educational Statistics Dr. Robin K. Henson University of North Texas © 2002 Dr. Robin K. Henson © 2002 Next Slide

A set of continuous scores is called a distribution. : 

A set of continuous scores is called a distribution. To understand a variable, we must understand the variable’s distribution. Tables and graphs are often the best place to start. (Wilkinson & APA Task Force on Statistical Inference, 1999) University of North Texas Dr. Robin K. Henson © 2002 Next Slide

X f cum. f cum. % 75 4 4 22.2 76 2 6 33.3 77 1 7 38.9 78 4 11 61.1 79 3 14 77.8 80 2 16 88.9 81 0 16 88.9 82 2 18 100.0 n=18 : 

X f cum. f cum. % 75 4 4 22.2 76 2 6 33.3 77 1 7 38.9 78 4 11 61.1 79 3 14 77.8 80 2 16 88.9 81 0 16 88.9 82 2 18 100.0 n=18 X 76 79 75 79 80 79 77 82 78 80 82 78 75 78 75 75 78 76 Frequency Table University of North Texas Dr. Robin K. Henson © 2002 Next Slide

Interval Frequency Table : 

Interval Frequency Table Interval 75-76 77-78 79-80 81-82 f 6 5 5 2 cum. f 6 11 16 18 cum. % 33.3 61.1 88.9 100.0 University of North Texas Dr. Robin K. Henson © 2002 Next Slide

Grouping sometimes helps us make sense of large amounts of data. : 

Grouping sometimes helps us make sense of large amounts of data. Grouping inherently loses information. Larger the group, larger the loss of detail. University of North Texas Dr. Robin K. Henson © 2002 Next Slide

Histogram Raw score based … : 

Histogram Raw score based … 4 3 2 1 f 75 76 77 78 79 80 81 82 * * * * * * * * * * * * * * * University of North Texas Dr. Robin K. Henson © 2002 Next Slide

Slide 7: 

University of North Texas Dr. Robin K. Henson © 2002 Q: How would you characterize how the class did based on the score distribution? Describe the performance of the class. Go to next slide for answer. Click mouse to continue

Answer : 

Answer A: There are many ways to describe the distribution depending on how much detail you want to include. However, I would say that there are two general patterns: (a) the class tended to score in the upper 70s and (b) only a couple of persons scored better than the bulk of the other students. Click mouse to go to next slide.

Histogram Interval based … : 

Histogram Interval based … Loss of detail Different picture - More #s, more needed. 6 5 4 3 2 1 75-76 77-78 79-80 81-82 * * * * * * * * * * * * f * * * * * * University of North Texas Dr. Robin K. Henson © 2002 Next Slide

Slide 10: 

Go to next slide for answer. University of North Texas Dr. Robin K. Henson © 2002 Q: How would you characterize how the class did based only on the interval distribution? How is this the same or different from the raw score distribution? Click mouse to continue

Answer : 

Answer A: You still can note that most student scored in the upper 70s. I would say that you loose two pieces of important information: (a) the couple of students that scored better than the others do not appear to be as far from the bulk of the other scores and (b) the lack of 76 and 77 scores is hidden by the intervals. These are not major issues, but they do illustrate the loss of information sometimes inherent in grouping data. The trade-off is an easier interpretation for grouped data. Click mouse to go to next slide.

Frequency distributions are very important in helping us visually understand our data. : 

Frequency distributions are very important in helping us visually understand our data. They tell us … a) The shape of the distribution. b) How people (or other cases) scored. University of North Texas Dr. Robin K. Henson © 2002 Next Slide

What about categorical data?Bar Graph : 

What about categorical data?Bar Graph Non-continuous - Bars don’t touch. 10 8 6 4 2 * ** * * * Male Female * * * * * * * University of North Texas Dr. Robin K. Henson © 2002 Next Slide

Cumulative Percentage Curve(AKA: Ogive) : 

Cumulative Percentage Curve(AKA: Ogive) 75 76 77 78 79 80 81 82 100 80 60 40 20 % University of North Texas Dr. Robin K. Henson © 2002 Next Slide

Scatterplot- Represent relationship between two continuous variables.- “Crossing” two distributions. : 

Scatterplot- Represent relationship between two continuous variables.- “Crossing” two distributions. X 1 3 3 4 5 5 Y 1 1 2 2 2 3 X 1 2 3 4 5 Y 1 2 3 4 5 * * * * * * * * * * * * University of North Texas Dr. Robin K. Henson © 2002 Next Slide

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X 1 3 3 4 5 5 Y 1 1 2 2 2 3 * 2 4 -2 -2 2 4 5 University of North Texas Dr. Robin K. Henson © 2002 Next Slide

Slide 17: 

University of North Texas Dr. Robin K. Henson © 2002 Go to next slide for answer. Q: Which of the following best explains the “relationship” between the two variables X and Y in the current example? a. As X increases, Y tends to decrease. b. As X decreases, Y tends to decrease. c. As X decreases, Y tends to increase. d. As X increases, Y tends to increase. e. None of the above. Click mouse to continue

Answer : 

Answer a. No, X and Y tend to increase and decrease together. b. Yes, smaller X values tend to be related to smaller Y values. (d) is also correct. c. No, same reason as (a) above. d. Yes, larger X values tend to be related to larger Y values. (b) is also correct. e. No, both (b) and (d) are correct. Click mouse to go to next slide.

Slide 19: 

University of North Texas Unit 1: Understanding and Representing DataLesson 4:Distributions and Graphing EDER 5210 – Educational Statistics Dr. Robin K. Henson University of North Texas © 2002 Dr. Robin K. Henson © 2002 End

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