Scales of measurement and Data display

stats

What is measurement?

the assignment of numbers to attributes, objects, or events according to predetermined rules

What are the four measurement scales?

Nominal, ordinal, interval, and ratio

What is the nominal scale?

uses numbers to distinguish one type of thing from another or event; qualitative numbers

What is an example of the nominal scale?

numbers on the backs of jerseys

What is the ordinal scale?

some quantitative information; quantitative amounts between numbers is not constant; relative position

What is an example of the ordinal scale?

Ranking favorite football teams

What is the interval scale?

consists of quantitatively ordered categories for which all the intervals between the categories are held constant (conserved); no true zero point

What is an example of the interval scale?

the temperature in Celsius or Fahrenheit

What is the ratio scale?

consists of a set of quantitatively ordered categories for which all intervals are constant with a fixed zero; allows to make ratio statements

What is an example of the ratio scale?

length in meters or yards

What are discrete variables?

can be assigned only a finite number of values; but no meaningful values exist between two adjacent values

What is an example of a discrete variable?

freshmen, sophomore, junior, or senior

What are continuous variables?

has an infinite number of points between two numbers; any assigned number to a measure is an approximation

What is an example of a continuous variable?

Along a number line between 7 and 8 there is an infinite number of values like 7.3 and 7.4

What is a midpoint?

at the balance point of the interval

What are real limits?

upper and lower boundaries of the interval

What are raw (original) scores?

a list of numbers

What are the x and y axes called?

abscissa and ordinate

What is a frequency polygon?

plots the number of scores in each of the intervals in a frequency distribution (grouped or not; class intervals need to be marked by real limits

What is a histogram?

represents values with bars, not points; class intervals need to be marked by real limits

what is a bar graph?

qualitative data— space between values on abscissa

What are normal distribution graphs?

Symmetrical, normal curve, and bell-shaped; many naturally occurring phenomena are normally distributed

What are skewed distributions?

Degree to which the curve is bunched at one side and hyper extended at the other; positive/negative

What is kurtosis?

quality of peakedness (narrow; leptokurtic) or flatness (muted peak; platykurtic) of curve