Scales of Measurement and Data Display Basic Concept

Scales of Measurement and Data Display Basic Concept of Research and Descriptive Statistics Friday May 16 th 2008 Saut Sagala

Scale of Measurement SCALE Nominal DEFINITION EXAMPLES Label, replaceable with Colour – 1: Red, 2: Yellow, 3: Green Village Name: 1: Ohbaku, 2: Kohata, 3: letter Rokujizo Ordinal Ranking Show a value of more or less Earthquake is dangerous (1: Strongly disagree – 5: Strongly agree) Rank of Favorite Food (1: Ramen, 2: Tempura, 3: Sashimi) Interval Reflects a value of more or less Numerically equal distance on the scale Temperature Interval between 80 – 85 C is equal to interval between 90 – 95 C Ratio Measurement with absolute zero point Height (m), Length, Income

Scale of Measurement SCALE DEFINITION EXAMPLES Discrete Variable Gaps are found between numbers The number of people is always 1, 2, 3 (never 3. 5) Continuous Variable Infinite number of points between any two numbers Measurement of height A: 185 cm B : 184 cm, there could be C or D between those numbers Real Limits If a variable is continuous, any number along is an approximation Unit of measurement = 1 Lower real limit Upper real limit 12. 5 12. 0 13. 5 14. 0

Tables to organize data Group frequency distribution Simple frequency distribution X f 1 2 3 4 5 6 7 8 9 10 11 1 0 10 2 5 19 3 5 1 2 7 Class interval Mid point f Cum f 0– 2 1 1 1 3– 5 4 17 18 6– 8 7 27 45 9 – 11 10 10 55 Equal size range Total number of scores

Using Graphs to Display Data

Shape

Measures of Tendency Central

Population and Sample • Population: – If only consider the groups of people from which the scores are obtained • Sample – If the interest in a group of scores beyond those persons providing scores

Mean • Population Mean • Sample Mean • Deviation score (error score): distance a score from the mean

Mean • Weighted mean: • Mean of frequency distribution

Median and Mode • Median – The center of distribution in that 50 percent of the scores fall above and 50 percent of the scores below median – Example: 1, 4, 6, 8, 40, 58, 60, 62 – Solution: • Median of a frequency distribution • Mode is the most typical score in the measurement

Mean Median Mode Mean Mode Median

Conclusion Measure ment Advantage Takes into account all score in the distribution A stable measure of central tendency of distribution Thus, mean is used in many statistical formulas Median is not influenced by the value of extreme Mode Descriptive data (using frequency) Disadvantage Scale measurement Mean is not a Interval Ratio good measure of central of tendency if the distribution is skewed Nominal and Ordinal

Practice • Questions from Chapter 2 and Chapter 3