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Ratio
- Real measurements
- ex. height, weight, speed, velocity, mass, area, volume
- there is a true 0 point
- this means that division and multiplication are meaningful
- experimental psychology tends to use ratio measurements
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Experimental psychology ratios
- accuracy
- reaction time
- heartrate
- brain waves
- response rates of pigeon or rate in a Skinner box
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Interval
- quantitative variable
- like ratio measurement
- There is NO true 0 point
- Sums and differences are meaningful, but not multiplication and division (ratios)
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Interval examples
- temperature scales, including Celsius and FAhrenheit
- clock or calender time, because we dont know when time started
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Interval level measurements
- In testing, personality and social psychology we frequently use questionnaire and test responses such as Liket (agree-disagree) scales
- usually convert these to numbers and use math on them, so we are treating them as interval scales.
- may be considered ordinal scales
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Nominal
- categories without order
- there are no numbers
- sometimes we use numbers as categories
- ex. social security numbers
- numbers on football jersies
- telephone numbers
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how do you do statistics with nominal variables
it requires a trick, count the number of items in each category
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Ordinal
- Ordered categories
- freshman, sophomore, junior, senior
- Nominal and ordinal are similar
- the distances between each point are not neccessarily equal
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Levels of measurement have a natural order, from strong to weak
- Strong: Ratio; Interval (quantitative)
- Weak: Ordinal;Nominal (qualitative/catergorical)
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Permissible operations
all levels of measurement have certain mathematical operations that are allowed, and others that are not allowed
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Permissible operations: Ratio variables
Multiplication and division (ratio) operations ar permitted because there is a true 0 point
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Permissble operations: Interval variables
addition and subtraction ar allowed, but not division and multiplication
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Permissible operations: ordinal variables
comparison of less and more are allowed, but not the other mathematical operations
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Permissible operations: nominal variables
comparison of same or different are allowed, but not less or more, or any other mathematical operations
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Demotion
- Involves throwing away information
- ex Rank height
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Promotion
- Involves adding information that you dont have
- ex. GPA calculator
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Norm Referencing
- each score is compared to the average of a reference group
- grading on a curve is an application
- ex IQ tests
- SAT, GRE
- Personality inventories
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Criterion referencing
- each score is compared to an absolute standard
- these are generally used when absolute performance levels are set
- Ex. DMV written exams
- State K-12 testing (No Child Left Behind)
- PACT
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Percentile
it depends on how many ppl took the test to determine how good the rank is
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Standard scores
- obtained from raw scores by converting the distribution to one with a new mean and standard deviation
- Z scores are the most common
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Z scores
once z score is obtained we can convert this to a percentile by looking up the z scored on a table of the normal distibution
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grade equivalents
- publishers cheat
- based on z scores for the same school grade, not different school grades
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SEM
- standard error of measurement
- test scores vary randomly
- ppl test scores may vary from their true scores
- measures how far a test score is likely to be from the true score (it is a kind of standard deviation of measurment)
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True score
a real score that would be obtained by giving the test over and over again and averaging the results
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