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What are the 4 Scale of Measurement?
Nominal, Ordinal, Interval, Ratio
Nominal Scale of Measurement
Classify, No logical order
Ordinal Scale of Measurement
Classify and rank or order
Interval Scale of Measurement
Classify, orders, adds zero (arbitrary) and equal units
Ratio Scales of Measurement
Classify, order, equal units, true zero point
Why not use raw scores?
Lack of comparability, original score of 30 could mean several things, need to change it into something with a meaningful value such as a derived score
Examples of Derived Scores
Age/Grade equivalents, perventile ranks, standard scores
Name two types of Developmental Scores
Age Equivalent Scores
Grade Equivalent Scores
What are some problems with age and grade scores?
Different Meaning:Raw scores can mean several different things
Meaningful Difference: Most tests don't have enough items at a specific age grade level
Ordinal Scale: Can't get standard error of measurement
Imply constant rate of growth: unequal intervals
Imply false standard
Different meanings across tests
What are Percentiles?
Not percentage correct, as high or higher than xx% of children on this test (not as well or better), among easiest to interpret for parents, not useful for comparing scores (overestimate differences in center of normal curve and underestimate differences on tails)
Why are percentiles not useful in comparing scores?
They overestimate differences in the center of the normal curve and underestimate difference on the tails of the normal curve
What are standard scores?
They make use of means and standard deviations, derived from z-scores, best scores for comparing
What are z-scores? What is the formula?
Z-scores are the number of SD's from the mean, easy to convert from z-scores to others
Z scores = (Raw-Mean)/Standard Deviation
- Mean = 50
- Standard Deviation = 10
What are norm referenced tests?
Tests that compare score to a normative sampe, must control variables that are likely to affect variable meausuring.
What is a normative sample?
A representative sample that matches the population. Larger size means more stability. Relevance of Comparisons.
SEM=Standard Error of Meausrement
Mean, some include mode and median
Standard Deviation, Variance, some include Range
Name the four types of notation.
Central Tendency, Variation (Scatter), Standard Error of Measurement, Correlation =r
Name ways to summarize data for a single variable.
Charts, graphs (histograms), central tendency, variabiltiy
What is a histogram? Name its different parts.
Histogram (history of data) = Bar Graph
- Vertical Bars=data, frequency
- Baseline (horizontal axis)=observed scores on the dependent variable
What is a frequency polygon? Name its parts.
Frequency Polygon = Line Graph
Vertical lines = score intervals, individual scores
Baseline (horizontal axis) = frequencies or percentages
Positive scew: has a longer tail on the higher scores or right side
Negative scew: has a longer tail on the lower scores or left side
Playukurtic Curve (very low and wide)
Leptokutic Curve (very high and narrow)
What is a tendency
A data trend
Name two types of trends.
Measures of central Tendency, Measures of dispersion (spread or variability)
What are types of central tendency measures?
Median Mean Mode
What are measures of dispersion?
Measures of variability = range, variance, and standard deviation
What is mode?
The number that appears most often
What is the median? And how do you calculate it?
The middle score, 1/2 below and 1/2 above, put data in order and find the middle one, if you have an even number you add the middle two numbers and divide by two
How do you find the mean?
Add up all of the scores and divide by the number of scores
Differences in Distributions:
Where are the median, mode, and mean in:
a symmetrical distribution?
a positively skewed distribution?
a negatively skewed distribution?
Symmetrical Distribution: All line up in the middle
Positive Skew (Left to right): Mode, Median, Mean
Negative Skew (Left to right): Mean, Median, Mode
Measures of Variability
how spread out the scores are, measures of variability cannot be negative, suggests dispersion
What are Homogeneous Scores?
What are heterogeneous scores?
What is range?
the difference between the lowest and the highest
What is interquartile range?
Spread among middle 50% of scores
Name the measures of variability.
Range, Interquartile Range, Variance, Standard Deviation
What is variance? How do you calculate it?
Variance is how much scores deviate from the mean (used more in statistics and less in measurement), average of the squared deviation scores
What is Standard Deviation? How do you Calculate it?
- SD is another measure of dispersion
- SD=square root of variance
- SD puts scores back in original metric
- Useful for describing scores, inherent in any type of standard scores,
What is a normal curve?
A normal curve is a unimodal, symmetrical graphic depiction of scores
How do you summarize data on more than one variable?
Bivariate relations, correlations