Today's Objectives. Determine why properties of scales are important in the field of measurement.Relate the concepts of mean, standard deviation, and z score to the concept of a standard normal distribution.Define quartiles and deciles and explain how they are used.Explain how norms are created.Relate the notion of tracking to the establishment of norms..
1. Norms and Basic Statistics for Testing
2. Today’s Objectives Determine why properties of scales are important in the field of measurement.
Relate the concepts of mean, standard deviation, and z score to the concept of a standard normal distribution.
Define quartiles and deciles and explain how they are used.
Explain how norms are created.
Relate the notion of tracking to the establishment of norms.
3. Why we need statistics First, statistics are used for purposes of description.
From the UC Undergraduate Student Experiences Survey, 2003:
“Approximately 57% of the UCSD sample, and 55% of the UC Norm group report that English was the language first learned in the home while approximately 43% and 45%, respectively, learned some other language first, or both languages together.”
From Beloit College’s Class of 2010’s mindset list:
“This year’s entering students form "a generation that has always been ‘connected’ and is used to things happening in ‘real time,’ like live satellite coverage of revolutions and wars, instant messaging and movies on demand.”
4. Why we need statistics Second, we can use statistics to make inferences. Inferential statistics enable us to test hypotheses.
Can children learn second languages more easily than adults? (critical period hypothesis)
Are there differences in ability to delay gratification between the class of 2010 and the class of 2007?
5. Scales of Measurement Measurement is the application of rules for assigning numbers to objects.
3 properties make scales of measurement different from one another:
6. Magnitude Scale has the property of magnitude if we can say that a particular instance of the attribute represents more, less, or equal amounts of the given quality than does another instance.
Given this definition, does height have the property of magnitude? How about assigning numbers to football jerseys to identify players?
7. Equal Intervals Scale has the property of equal intervals if the difference between two points at any place on the scale has the same meaning as the difference between two other points that differ by the same number of scale units.
Difference between 4 and 6 on a ruler equals the difference between 10 and 12.
8. Equal Intervals When a scale has the property of equal intervals, the relationship between the measured units and some outcome can be described by a straight line, or by a linear equation.
9. Absolute Zero An absolute zero is obtained when nothing of the property being measured exists.
E.g., heart rate equals zero
10. Scales of Measurement
11. Frequency Histogram interval or ratio data
12. Normal Distribution (Frequency Polygon example)
13. A raw score by itself cannot give us information about its position within the distribution
20. Transforming raw scores You can use z scores to transform raw scores to give them more intuitive meaning.
In his system of measuring mental qualities, he wanted the mean to be 50 (like the 50th percentile) and the standard deviation to be 10
Thus, T Scores were born:
21. Transforming raw scores You can use z scores to transform raw scores to give them more intuitive meaning.
Developers decided to make the mean 500 and the standard deviation 100.
Thus, they multiplied the Z scores for those who took the test by 100 and added 500:
22. Quartiles Quartiles divide scores into quarters (or 25% intervals)
– first quartile = divide lower 25% from upper 75%
– second quartile = divide lower 50% from upper 50%
– third quartile = divide lower 75% from upper 25%
Deciles use points that mark 10% intervals
– the top decile is D9, and it is the point below which 90% of the scores fall
– the next decile is D8, and it is the point below which 80% of the scores fall
– and so forth.
Percentiles use points that mark 1% intervals
– the 99th percentile means that you scored better than approximately 99 out of 100 students (Way to go!)
23. Z scores and percentiles
24. Norms Norms refer to the performances by defined groups on particular tests.
There are many ways to express norms (means, z scores, percentiles)
The norms for a test are based on the distribution of scores obtained by some defined sample of individuals
Norms give information about performance relative to what has been observed in a standardization sample
25. Norms SAT norms:
1941 national sample, a person with a 650 verbal score was at the 93rd percentile of high school seniors
In 1980, a score of 650 indicates that you would have been in the 93rd percentile had you been in the group the test had been standardized on
If the normative group was a representative sample of the group to which you belonged, then you could reasonable assume that you were in the 93rd percentile of your own group
26. Age-Related Norms Some tests have different normative groups for particular age groups
Most IQ tests are of this sort
27. Tracking For a variety of physical characteristics, children tend to stay at about their same percentile level as they age, relative to other children in their age group.
28. The reference group problem To what reference group should we compare ourselves?
For example, should a person’s profile on the General Aptitude Test Battery (GATB) be measured against norms specific to their racial/ethnic group?
National Academy of Sciences says “yes”, the Civil Rights Act of 1991 says “no”.