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Presented by:
Common Errors
Because we have to
Not using as intended
Using the quickest test
Poor Documentation during test
No rapport
Not following rules
Scoring errorsPoor interpretation
Raw Score• First Score
• Number Correct
Presented by: Brent Daigle, Ph.D. (ABD)
Norm Referenced Test
Compares with national average
Presented by: Brent Daigle, Ph.D. (ABD)
Scales of MeasurementNominal
Number used for category : no value
Presented by: Brent Daigle, Ph.D. (ABD)
Scales of Measurement
Ordinal
No True Zero.
Categories / Rank
Presented by: Brent Daigle, Ph.D. (ABD)
Scales of Measurement
Interval
No True Zero.
Equal Distance between each point
Presented by: Brent Daigle, Ph.D. (ABD)
Scales of Measurement
Ratio
True Zero
Equal Distance between each point
Frequency Distribution
Normal Distribution
Measures of Central tendency : How # cluster around the mean
Normal Distribution: Symmetrical , single # for
Mean/Med/Mode
Presented by: Brent Daigle, Ph.D. (ABD)
Median
1) Arrange data in order
Middle value in distribution
2) Find the middle valuePresented by: Brent Daigle, Ph.D. (ABD)
Calculating the Median(High Temperatures)
5.422
4342median
High
Date Temperature
7-Jan 32
8-Jan 32
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)
Mean
Add up, divide by number of values
n
XX
The averagePresented by: Brent Daigle, Ph.D. (ABD)
Mode
Most frequent valueDoes not take into account exact scores
Not useful with several = values
Length of Right Foot
87654321
4 5 6 7 8 9 10 11 12 13 14
If we were to connect the top of each bar, we would create a frequency polygon.
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.
Nu
mb
er
of
Pe
op
le w
ith
that
Sh
oe
Siz
e
Length of Right Foot
87654321
4 5 6 7 8 9 10 11 12 13 14
Nu
mb
er
of
Pe
op
le w
ith
that
Sh
oe
Siz
e
You will notice that if we smooth the lines, our data almost creates a bell shaped curve.
Presented by: Brent Daigle, Ph.D. (ABD)
87654321
4 5 6 7 8 9 10 11 12 13 14
Length of Right Foot
Nu
mb
er
of
Pe
op
le w
ith
that
Sh
oe
Siz
e
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.”
Presented by: Brent Daigle, Ph.D. (ABD)
Whenever you see a normal curve, you should imagine the bar graph within it.
12 13 14 15 16 17 18 19 20 21 22
Points on a Quiz
Nu
mb
er o
f St
ud
ents
987654321
Presented by: Brent Daigle, Ph.D. (ABD)
The mean, mode, and median
12 13 14 15 16 17 18 19 20 21 22
Points on a Quiz
Nu
mb
er o
f St
ud
ents
987654321
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 = 867
867 / 51 = 17
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
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
will all fall on the same value in a normal distribution.
Now lets look at quiz scores for 51 students.
Presented by: Brent Daigle, Ph.D. (ABD)
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)
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)
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.
Different MeansDifferent Standard Deviations
Different Means Same Standard Deviations
Same Means Different Standard Deviations
Presented by: Brent Daigle, Ph.D. (ABD)
Presented by: Brent Daigle, Ph.D. (ABD)