# Unit_5_lesson_4_redone

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### Unit 5: Distributional ShapeLesson 4:Normal Distributions :

Unit 5: Distributional ShapeLesson 4:Normal Distributions EDER 5210 – Educational Statistics Dr. Robin K. Henson University of North Texas © 2002 University of North Texas Dr. Robin K. Henson © 2002 Next Slide

### Infinite number of normal distributions. :

Infinite number of normal distributions. But there is only one… Standard normal distribution (of Z scores) Dr. Robin K. Henson © 2002 University of North Texas Next Slide

### 34.13% :

34.13% 13.59% 2.14% -3 -2 -1 1 2 3 Dr. Robin K. Henson © 2002 University of North Texas Next Slide

### To be more precise … :

To be more precise … 95% +/- 1.96 SD 99% +/- 2.58 SD Dr. Robin K. Henson © 2002 University of North Texas Next Slide

### Z=1.00 :

Z=1.00 Z=-1.00 Better than 84.13% Worse than 84.13% Dr. Robin K. Henson © 2002 University of North Texas Next Slide

### Slide 6:

Dr. Robin K. Henson © 2002 University of North Texas Go to next slide for answer. Q: As a parent you received your child’s results from a recent standardized test he took at school. The report said that your child’s Z score was 2.00. Because you are knowledgeable of Z scores and normal distributions, you know that your child’s percentile rank was approximately (assume the distribution was normal): a. 50 b. 84 c. 98 d. 14 e. 34 Click mouse to continue

Answer a. No, see (c). 50 would be just half of the distribution. b. No, see (c). 84 would be about 1 standard deviation above the mean. c. Yes, a Z = 2.00 is 2 standard deviations above the mean. In a normal distribution, this means the score is better than about 98% of the distribution (other scores). See the distribution with the percentages under the curve in the PP presentation for where this number comes from. Remembering that a percentile rank is the percentage of scores at or below the score in question, you then know that the percentile rank of Z = 2.00 is about 98. d. No, see (c). 14 would be about the area under the curve between 1 and 2 standard deviations. e. No, see (c). 34 would be about the area under the curve between the mean and 1 standard deviation. Click mouse to go to next slide.

### Asymptotic – the distribution curves never touch the line in the tails.*Allows for extreme scores on a continuous scale. :

Asymptotic – the distribution curves never touch the line in the tails.*Allows for extreme scores on a continuous scale. Dr. Robin K. Henson © 2002 University of North Texas Next Slide

### Slide 9:

Dr. Robin K. Henson © 2002 University of North Texas Used with permission. www.jasonlove.com Extreme case are sometimes called “outliers”. A score beyond +/- 3 SDs above and below the mean has less than a 1% chance of occurring. Unlikely, but possible on a continuous scale in an asymptotic distribution. Next Slide

### Unit 5: Distributional ShapeLesson 4:Normal Distributions :

Unit 5: Distributional ShapeLesson 4:Normal Distributions EDER 5210 – Educational Statistics Dr. Robin K. Henson University of North Texas © 2002 University of North Texas Dr. Robin K. Henson © 2002 End