Term
Levels of measurement and corresponding mathematical operations |
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Definition
NOIR
Nominal - John passed the test & Jean did not
Ordinal - John has more knowledge of math than Jean
Interval - John has twice the math knowledge of Jean
Ratio - John has no knowledge of math |
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Term
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Definition
- categorical
- Numbers are used to classify and identify
person
• Numbers are substituted for names and verbal
labels (e.g. uniform numbers identify football
players)
• Actual numbers not important |
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Term
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Definition
• ordering/ranking
• Assigns #s to individual so that the rank
order of the number corresponds to the
rank order of the attribute being measured
• The order does not indicate how far about
the subjects are in an absolute sense
• Ordinal information can help with decisionmaking |
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Term
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Definition
| • The size of the difference between the numbers assigned to two persons or objects corresponds to the degree to which these persons or objects differ on the attribute being measured. |
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Term
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Definition
| • Ratios between the numbers assigned to persons or objects correspond to ratios between the attributes measured in these persons or objects. |
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Term
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Definition
- yields only categorical data (data grouped according to common property)
- number has no quantitative value
- reported in the terms of the number of occurrences in each category
- reported as 1 (average), 2 (gifted)
ex - number on players' uniforms
appropriate statistics - frequency, mode |
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Term
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Definition
- Numbers rank people based on the attribute being measured
- distance between numbers vary; numbers only have meaning within the group
ex - rankings of bball players before the draft
appro stats - frequency, mode, median, percentile |
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Term
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Definition
- points on scale are equal distance apart
- scale has no absolute zero
ex - measure of player's "desire to win"
appro stats - frequency, mean, mode, median, standard deviation, correlation, f test, analysis of variance |
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Term
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Definition
- points on scale are equal distance
- there is an absolute zero
ex - players heights & game score
appro stats - frequency, mean, mode, median, standard deviation, correlation, f test, analysis of variance, proportions |
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Term
| Procedures for interpreting test scores |
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Definition
Raw scores
Frequency distributions
Normal curve
Descriptive statistics |
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Term
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Definition
- most basic scores calculated from test
- not useful without interpretation information |
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Term
Techniques to make sense of raw
scores
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Definition
Frequency Distributions
The Normal Curve
Descriptive Statistics |
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Term
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Definition
- Provide visual image of group data
- Orderly arrangement of group of scores
- Show number or percentage of
observations that fall into a category or range |
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Term
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Definition
| - distributions become more symmetrical because it is a better representation of the large population |
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Term
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Definition
- Summarize a distribution of test scores numerically
- Provide us with main points of a group of scores
- Typical descriptive statistics include:
Measures of central tendency
Measures of variability
Measures of relationship |
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Term
| Measures of central tendency |
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Definition
• Measures of central tendency provide
information about the typical score in a set of numbers.
– Median
– Mean
– Mode |
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Term
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Definition
• “Average”
• Takes into account every observation
• Appropriate for interval or ratio data
• Obtained by adding all the scores and dividing by the total # of scores |
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Term
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Definition
• Middle score of a distribution
• To find:
– 1
st Order all the scores.
– If odd number of scores it is the middle score.
– If even number of scores, average the two middle
scores.
• Appropriate for ordinal, interval, & ratio data |
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Term
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Definition
• Most frequently occurring score
• Easy to find
• A data set can have more than one mode (e.g.
bimodal distribution)
• Can be used with all measurement scales |
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Term
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Definition
- numerical tools to help understand the distribution
- range, variance, standard deviation |
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Term
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Definition
| Range = highest score – lowest score |
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Term
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Definition
• Problems with variance:
– Squared units not on the same scale as the original measurements |
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Term
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Definition
Use total deviation? – Deviation score (d)– measures the extent to which
each individual differs from the mean
• Interpret as approximately the average distance of an observation from the mean |
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Term
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Definition
- how two sets of scores are related
- correlation coefficient |
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Term
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Definition
• Standard Scores
–Universally understood units in testing
–Allow us to evaluate a person’s test
score in reference to others’ test scores |
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Term
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Definition
change unit of measurement but do not change the characteristics of raw data
• Linear transformations
– Percentages
– Standard deviation units
– Z scores
– T scores |
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Term
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Definition
• Useful for interpreting your deviation score
in comparison with other people’s
deviation scores
• Allows you to compare to test scores that
are on different scales
• Also, allows you to compare two scores on
the same exam, but from groups that have
different sample means and standard
deviations (e.g. 8 o’clock class and 9 o’clock class)
• Tells how far a score is from the mean in standard deviation units.
• Z score mean = 0, sd=1.0 |
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Term
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Definition
• Way to describe a relationship between 2
variables
• Tells:
– Magnitude of relationship
– Direction of relationship |
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Term
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Definition
- average scores of an identified group of individuals scores
• Norms provide standards for interpreting |
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Term
| Norm-based interpretation |
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Definition
- process of
comparing an individual’s test score to a norm group |
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Term
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Definition
• Types of norms
-Percentile ranks
-Age and grade norms |
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Term
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Definition
• Test publishers often publish more than
one norm group
• Must use correct norm group
• Must use up-to-date norms
• Should look at size of norm group |
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Term
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Definition
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Term
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Definition
1. administering a test to a group of
individuals,
2. re-administering that same test to the
same group at some later time, and
3. correlating the first set of scores with
the second. |
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Term
| Alternate forms reliability |
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Definition
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Term
Internal consistency
1. split-half
2. coefficient alpha |
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Definition
- how related the test items are to eachother
- how the answer on one question predicts the answer on another test item
1. dividing the test in half equally/randomly, comparing the two sides
2. |
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Term
| Scorer reliability and agreement |
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Definition
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Term
| Classical test theory view of reliability |
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Definition
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Definition
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Definition
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Term
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Definition
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Term
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Definition
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Term
| Spearman-Brown formula – when to use, why? |
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Definition
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Term
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Definition
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Term
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Definition
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Term
| Scorer reliability and agreement |
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Definition
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Term
| Standard error of measurement – interpretation and uses |
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Definition
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Term
| Factors that influence reliability (book) |
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Definition
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