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# Descriptive Statistics Introduction

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### Descriptive Statistics Introduction

1. 1. Presented by:
2. 2. Common Errors Not using as intended Scoring errors Poor interpretation Not following rules No rapport Poor Documentation during test Using the quickest test Because we have to
3. 3. Raw Score • First Score • Number Correct Presented by: Brent Daigle, Ph.D. (ABD)
4. 4. Norm Referenced Test Compares with national average Presented by: Brent Daigle, Ph.D. (ABD)
5. 5. Scales of Measurement Nominal Number used for category : no value Presented by: Brent Daigle, Ph.D. (ABD)
6. 6. Scales of Measurement Ordinal No True Zero. Categories / Rank Presented by: Brent Daigle, Ph.D. (ABD)
7. 7. Scales of Measurement No True Zero. Equal Distance between each point Interval Presented by: Brent Daigle, Ph.D. (ABD)
8. 8. Scales of Measurement Ratio True Zero Equal Distance between each point
9. 9. Frequency Distribution
10. 10. Normal Distribution Normal Distribution: Symmetrical , single # for Mean/Med/Mode Measures of Central tendency : How # cluster around the mean Presented by: Brent Daigle, Ph.D. (ABD)
11. 11. Median Middle value in distribution 1) Arrange data in order 2) Find the middle value Presented by: Brent Daigle, Ph.D. (ABD)
12. 12. Calculating the Median (High Temperatures) High Date Temperature 42 43 7-Jan 32 median 42.5 8-Jan 32 2 6-Jan 35 10-Jan 41 5-Jan 42 <===Middle values 4-Jan 43 <===Middle values 9-Jan 46 11-Jan 52 2-Jan 59 3-Jan 60 Presented by: Brent Daigle, Ph.D. (ABD)
13. 13. Mean X X n Add up, divide by number of values The average Presented by: Brent Daigle, Ph.D. (ABD)
14. 14. Mode Not useful with several = values Does not take into account exact scores Most frequent value
15. 15. Notice how there are more people (n=6) with a 10 inch right foot than any other length. Notice also how as the length becomes larger or smaller, there are fewer and fewer people with that measurement. This is a characteristics of many variables that we measure. There is a tendency to have most measurements in the middle, and fewer as we approach the high and low extremes. If we were to connect the top of each bar, we would create a 8 frequency polygon. 7 6 5 Number of People with 4 3 that Shoe Size 2 1 4 5 6 7 8 9 10 11 12 13 14 Length of Right Foot
16. 16. Presented by: Brent Daigle, Ph.D. (ABD) You will notice that if we smooth the lines, our data almost creates a bell shaped curve. 8 7 6 5 Number of People with 4 3 that Shoe Size 2 1 4 5 6 7 8 9 10 11 12 13 14 Length of Right Foot
17. 17. Presented by: Brent Daigle, Ph.D. (ABD) You will notice that if we smooth the lines, our data almost creates a bell shaped curve. This bell shaped curve is known as the “Bell Curve” or the “Normal Curve.” 8 7 6 5 Number of People with 4 3 that Shoe Size 2 1 4 5 6 7 8 9 10 11 12 13 14 Length of Right Foot
18. 18. Whenever you see a normal curve, you should imagine the bar graph within it. 9 8 Number of Students 7 6 5 4 3 2 1 12 13 14 15 16 17 18 19 20 21 22 Points on a Quiz Presented by: Brent Daigle, Ph.D. (ABD)
19. 19. The mean, mode, will all fall on the same value in a normal distribution. and median Now lets look at quiz scores for 51 students. 12 13 13 12+13+13+14+14+14+14+15+15+15+15+15+15+16+16+16+16+16+16+16+16+ 12, 13, 13, 14, 14, 14, 14, 15, 15, 15, 15, 15, 15, 16, 16, 16, 16, 16, 16, 16, 16, 17, 17, 17, 17, 17, 17, 17, 17, 17, 18, 18, 18, 18, 18, 18, 18, 18, 19, 19, 19, 19, 19, 19, 20, 20, 20, 20, 21, 21, 22 17+17+17+17+17+17+17+17+17+18+18+18+18+18+18+18+18+19+19+19+19+ 19+ 14 14 14 14 19+20+20+20+20+ 21+21+22 = 867 15 15 15 15 15 15 867 / 51 = 17 16 16 16 16 16 16 16 16 17 17 17 17 17 17 17 17 17 18 18 18 18 18 18 18 18 19 19 19 19 19 19 20 20 20 20 9 21 21 8 22 Number of Students 7 6 5 4 3 2 1 12 13 14 15 16 17 18 19 20 21 22 Points on a Quiz Presented by: Brent Daigle, Ph.D. (ABD)
20. 20. Normal distributions (bell shaped) are a family of distributions that have the same general shape. They are symmetric (the left side is an exact mirror of the right side) with scores more concentrated in the middle than in the tails. Examples of normal distributions are shown to the right. Notice that they differ in how spread out they are. The area under each curve is the same. Presented by: Brent Daigle, Ph.D. (ABD)
21. 21. If your data fits a normal distribution, approximately 68% of your subjects will fall within one standard deviation of the mean. Approximately 95% of your subjects will fall within two standard deviations of the mean. Over 99% of your subjects will fall within three standard deviations of the mean. Presented by: Brent Daigle, Ph.D. (ABD)
22. 22. The mean and standard deviation are useful ways to describe a set of scores. If the scores are grouped closely together, they will have a smaller standard deviation than if they are spread farther apart. Small Standard Deviation Large Standard Deviation Click the mouse to view a variety of pairs of normal distributions below. Same Means Different Means Different Means Different Standard Deviations Same Standard Deviations Different Standard Deviations Presented by: Brent Daigle, Ph.D. (ABD)
23. 23. Presented by: Brent Daigle, Ph.D. (ABD)