DESCRIPTIVE STATISTICS - Arizona State University
[Pages:43]DESCRIPTIVE STATISTICS
The purpose of statistics is to condense raw data to make it easier to answer specific questions; test hypotheses.
DESCRIPTIVE VS. INFERENTIAL STATISTICS
? Descriptive
? To organize, summarize & describe the data
? Inferential
? To determine reliability of the data
RELATIONSHIPS ? SCALES OF MEASURMENT
? Nominal Scale
? Only use those statistical procedures that rely on counting -- the number (N) in the sample.
? Ordinal Scale
? Same as nominal scale ? Can use statistics that indicate points
below which certain percentages of the cases fall.
RELATIONSHIPS ? SCALES OF MEASURMENT
? Interval Scale
? Any of the above plus procedures that include adding.
? Ratio Scale
? Any statistical procedure is acceptable.
MEASUREMENT SUMMARY
Measurement Characteristics
Scoring
Types Examples
Nominal
Lowest level -- used to classify variables into two or more categories.
Cases placed in the same category must be equivalent.
The categories must be exhaustive -- all persons or items must fit into one of the categories.
Must also be mutually exclusive -- one person or item can't fit more than one category.
Counting "N" in sample
Labels or #'s
No relation between #'s
N of sample
Mode
Football player jerseys ? 48 not better than 36
Range Race
Gender
MEASUREMENT SUMMARY
Measurement Ordinal
Characteristics
Scoring
Types
Examples
Numbers only used to indicate the rank order of cases of a variable.
Cannot measure or evaluate the difference in value between each case.
No mathematical or statistical operations (you can't add label 1 to label 2, etc.).
Points below which certain % falls.
Size of distance between intervals unknown.
Order of objects with respect to an attribute.
Frequency distribution
Median
Quartile deviation
Spearman rho coefficient of correlation
Hardness of metal
Personnel evaluations of performance
MEASUREMENT SUMMARY
Measurement Characteristics
Scoring
Types
Examples
Interval
Has all of the above characteristics.
Added requirement of equal distances or intervals between labels -represent equal distances in the variables of your study.
= intervals w/ arbitrary origin
No true zero
Adding
Mean
Standard deviation
Variance
Pearson product moment coefficient of correlation
Temperature difference
Footcandle levels in lighting
IQ's
MEASUREMENT SUMMARY
Measurement Characteristics
Scoring
Types
Ratio
Has all of above features plus an absolute zero point.
Enables you to multiple and divide scale numbers to create ratios between labels.
Equal intervals
Multiply Divide
All types
Examples
Income ranges.
Number of years of school.
Age in years.
Yardstick or architect's scale.
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