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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