achievement and intelligence tests? ... content unique to a particular class or .... z
-score. -3 -2 -1 0 1 2 3. T-score. 20 30 40 50 60 70 80. IQ-score. 65 70 85 100 ...
Standardized Tests!
Testing Controversies! n n n
If you lived in Scarsdale would you have been protesting?! Do we test too much?! What did you think about what the woman said about the tests driving the curriculum?!
Thought Questions! What is the primary difference between achievement and intelligence tests?! n There are different purposes for giving achievement and intelligence tests. What are they?! n What is the best description of psychometric intelligence ?! n
Functions of Standardized Tests! Student Assessment! n Diagnosis! n Placement and Selection! n Accountability! n Predictive Validity! n
What is a standardized test?! n
A test that has standard procedures for administration, scoring, and interpretation.!
Advantages of Standardized Tests! Evaluating students general educational development in the basic skills & in learning outcomes common to many courses of study! n Evaluating student progress during the school year or over a period of years! n Determining strengths & weaknesses! n
Weaknesses of Standardized Tests! Evaluating the learning outcomes and content unique to a particular class or school! n Evaluating students day-to-day progress! n Evaluating knowledge of current developments in rapidly changing content areas such as science and social studies! n
Types of Achievement Tests! State Developed Tests! ! !N.C. EOG s, FL FCAT s, VA s SOL s! n Publisher-Developed Norm-referenced batteries! ! !ITBS, CAT, GRE, Stanf. Ach. Test! n Publisher-Developed Norm-referenced content area tests! n Publisher-Developed Criterion-referenced tests! ! n
No Child Left Behind
Will all students be at grade level by 2014?
Who did you identify with most in the video, anyone you did not agree with?
How has NCLB affected you?
http://www.youtube.com/watch?v=hSTzLILQx3c
http://www.youtube.com/watch? v=Ugeb_B3aJXM&feature=related
Some popular tests to be aware of:! California Achievement Test (CAT)! n Iowa Tests of Basic Skills (ITBS)! n Metropolitan Achievement Tests (MAT)! n Stanford Achievement Tests! n TerraNova! n
Why do we use these?! High technical quality! n Standard directions for administration and scoring! n Norms based upon large national samples! n Equivalent forms! n Comprehensive manuals! n
Using Achievement Tests:! Be wary of using subtests for diagnostic purposes unless enough items are included! n What is a norm group and what is the benefit of having a norm group?! n Norm groups provide a standard frame of reference! n Equivalent forms! n
Judging the Adequacy of Norms! Should be relevant (Who do you want to compare your scores to?)! n Should be representative! n Should be up to date! n Should be comparable! n Should be adequately described! n
Achievement Batteries! n
Consists of a series of individual tests all standardized on the same national sample!
Some Aptitude/Intelligence tests " to be aware of:! n n n n n n n n n
Wechsler Intelligence Tests (WISC, WAIS)! Stanford-Binet! Raven s Advanced Progressive Matrices! Cognitive Abilities Test (CogAT)! Graduate Record Examination (GRE)! Otis-Lennon School Ability Test (OLSAT)! Cattell Culture-Fair Intelligence Tests! Armed Services Vocational Aptitude Battery (ASVAB)! Differential Aptitude Test (DAT)!
Questions about Aptitude & Intelligence! What is meant by aptitude? What are aptitude tests measuring?! n How is IQ determined? - chart -! n Can IQ change over time?! n Who administers an individual intelligence test?! n
Normal Curve! 34% 13.5%
34% 13.5%
2.5%
-3
2.5%
-2
Mean +1 -1 Standard Deviations
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+3
Aptitude Tests! Do not measure fixed capacity but rather a different type of ability used to predict future performance! n Common distinction: achievement tests measure what a student has learned and that aptitude tests measure the ability to learn new tasks! n
Why use aptitude tests when you have achievement tests?! Can be administered in a relatively short time! n Can be used with students of more widely varying educational backgrounds! n Can be used before any training or instruction! n
Bell Curve for Wechsler Intelligence Test
Specific theories of importance:! Spearman vs. Thurstone! n Guilford s 120 abilities! n Crystallized & Fluid intelligence! n Gardner s multiple intelligences! n Others include David Perkins & Robert Sternberg! n
What is general intelligence?! General ability typically measured via standardized tests--symbolized as g! n Predictive power strongest when facing novel tasks or beginning competence! n Considered to be reasoning ability (typically inductive) that is highly dependent upon working memory-making transformations in your head! n
General intelligence, or g, reflected by the positive manifold between tests of cognitive ability
Suppose we measured the right foot length of 30 teachers and graphed the results. Assume the first person had a 10 inch foot. We could create a bar graph and plot that person on the graph.
Number of People with that Shoe Size
If our second subject had a 9 inch foot, we would add her to the graph. As we continued to plot foot lengths, a 8 pattern would begin to emerge. 7 6 5 4 3 2 1 4
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Length of Right Foot
Number of People with that Shoe Size
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 characteristic 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 8 would create a frequency polygon. 7 6 5 4 3 2 1 4
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Length of Right Foot
Number of People with that Shoe Size
You will notice that if we smooth the lines, our data almost creates a bell shaped curve.
8 7 6 5 4 3 2 1 4
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7
8
9 10 11 12 13 14
Length of Right Foot
You will notice that if we smooth the lines, our data almost creates a bell shaped curve.
Number of People with that Shoe Size
This bell shaped curve is known as the Bell Curve or the Normal Curve. 8 7 6 5 4 3 2 1 4
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Length of Right Foot
Number of Students
Whenever you see a normal curve, you should imagine the bar graph within it.
9 8 7 6 5 4 3 2 1 12 13 14
15 16 17 18 19 20 21 22 Points on a Quiz
The Nowmean, lets look mode, at quiz andscores median forwill 51all students. fall on the same value in a normal distribution. 12
13 13 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+ 14 14 14 14 19+ 19+20+20+20+20+ 21+21+22 = 867 15 15 15 15 15 15
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
16 16 16 16 16 16 16 16
867 / 51 = 17
17 17 17 17 17 17 17 17 17 18 18 18 18 18 18 18 18 19 19 19 19 19 19
Number of Students
20 20 20 20 21 21
9 8 7 6 5 4 3 2 1
22
12 13 14
15 16 17 18 19 20 21 22 Points on a Quiz
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.
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.
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
Same Means Different Standard Deviations
Large Standard Deviation
Different Means Same Standard Deviations
Different Means Different Standard Deviations
When you have a subject s raw score, you can use the mean and standard deviation to calculate his or her standardized score if the distribution of scores is normal. Standardized scores are useful when comparing a student s performance across different tests, or when comparing students with each other.
z-score
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IQ-score
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145
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SAT-score
The number of points that one standard deviation equals varies from distribution to distribution. On one math test, a standard deviation may be 7 points. If the mean were 45, then we would know that 68% of the students scored from 38 to 52.
24
31
38
On another test, a standard deviation may equal 5 points. If the mean were 45, then 68% of the students would score from 40 to 50 points.
45 52 59 Points on Math Test
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35
63
40 45 50 55 Points on a Different Test
60
Data do not always form a normal distribution. When most of the scores are high, the distributions is not normal, but negatively (left) skewed. Skew refers to the tail of the distribution.
Number of People with that Shoe Size
Because the tail is on the negative (left) side of the graph, the distribution has a negative (left) skew. 8 7 6 5 4 3 2 1 4
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Length of Right Foot
When most of the scores are low, the distributions is not normal, but positively (right) skewed.
Number of People with that Shoe Size
Because the tail is on the positive (right) side of the graph, the distribution has a positive (right) skew. 8 7 6 5 4 3 2 1 4
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Length of Right Foot
When data are skewed, they do not possess the characteristics of the normal curve (distribution). For example, 68% of the subjects do not fall within one standard deviation above or below the mean. The mean, mode, and median do not fall on the same score. The mode will still be represented by the highest point of the distribution, but the mean will be toward the side with the tail and the median will fall between the mode and mean.
Negative or Left Skew Distribution
Positive or Right Skew Distribution
Normal Distribution (Bell Curve) with Wechsler Intelligence Test Scores
Questions about Grade Equivalent Scores! What does it mean if a 4th grader has a grade equivalent score of 7.3?! n What is the purpose of grade equivalent scores?! n
Avoid Misconceptions with Grade Equivalent Scores! Don t confuse norms with standards of what should be! n Don t interpret a grade equivalent as an estimate of the grade where a student should be placed! n Don t expect that all students should gain 1.0 grade equivalent each year! n Don t assume that the units are equal at different parts of the scale! n
Avoid Misconceptions with Grade Equivalent Scores! Don t assume that scores on different tests are comparable! n Don t interpret extreme scores as dependable estimates of student performance level! n
Some Popular Standard Scores! Mean!
SD!
Scale Name!
500!
100!
GRE; SAT; GMAT!
100!
15!
Wechsler IQ!
20!
5!
ACT!
50!
10!
T-scale MMPI!
Standard Scores! A calculated score that enables a researcher to compare scores from different scales! n Z-score most popular (mean of zero and SD of one)! n z = (X-M)/SD! n
T Scores! Another type of standard score -sometimes preferred because all numbers are positive! n T score = 50 + 10(z)! n Example: If you scored 2 SD s above the mean on a reading test your T score would be 50 + 10(2) = 70! n
Stanines! Another type of standard score -preferred for interpretability! n Score between 1 and 9 with each stanine covering 1/2 standard deviation unit (e.g., stanine of 5 = 40%ile-59%ile)! n
A Graphic Explanation of Stanines!
Problem Solving:! You scored 107 on the WISC. What percent of people scored above you?! n What percent of people score between 100 and 125 on IQ tests?! n What percent of people score below 60 and above 130 on the WISC?! n A score of 91 on the WISC would place you in front of what percent of people?! n
http://www.webster.edu/~woolflm/zscores.html
