Statistics and Levels of Measurement

T/F Statistics are estimates of the parameters of the population

true

NOIR

Nominal, ordinal, interval, and ratio

Nominal

the frequency count of attributes that fall into mutually exclusive categories or named grouping

key characteristic: identity (e.g. pass/fail)

Ordinal

The arrangement of attributes in a rank order

key characteristic: Magnitude (e.g. mild, moderate)

Interval

the listing of the number of cases occurring at each value of the interval scale

key characteristic: constant distance intervals (e.g. standard scores)

Ratio

listing of number cases at each value at the ratio scale

Key characteristic: true zero (e.g. # of misarticulations or 0% intelligibility)

If the level of measurement is nominal, we should report…

the mode

If the level of measurement is ordinal or skewed we should report…

the median

If the data is symmetrical (IR), we should report…

the mean

If there is a negative skew, is the mean the smallest or highest level of central tendency?

smallest

variance

the average dispersion or scattering of the scores. Square root of this = SD

Parametric procedures assumptions

o   Level of measurements are interval and ratio

o   Sample size is large (30 is large enough in our field)

o   Scores are independent

o   Scores are normally distributed

o   Variances are about the same  (in experimental and control)

When do we use nonparametric procedures?

when the data is skewed (Nominal and Ordinal)

What do we do if interval/ratio level data violates parametric procedure assumptions?

Use nonparametric procedures OR

Transfer the data to become normally distributed