2. Sampling and Measurement

1. 2. Sampling and Measurement • Variable – a characteristic that can vary in value among subjects in a sample or a population. Two types of variables: • Categorical • Quantitative • There are different statistical methods for each type of variable

2. Categorical variable – scale for measurement is a set of categories Examples: • Vegetarian? (yes, no) • Happiness (very happy, pretty happy, not too happy) Quantitative variable – possible values differ in magnitude Examples: • Age, height, weight • Annual income • Time spent on Internet yesterday

3. Variable A characteristic that can vary in value among subjects in a sample or a population. • Categorical • Quantitative subject gen age high colltv veg party ideology abor 1 m 32 2.2 3.5 3 n r 6 n 2 f 23 2.1 3.5 15 y d 2 y 3 f 27 3.3 3.0 0 y d 2 y 4 f 35 3.5 3.2 5 n i 4 y 5 M 23 3.1 3.5 6 n i 1 y

4. Scales of measurement Two types of categorical variables: • Nominal scale – unordered categories • Race, Gender, Vegetarian (yes / no) • Ordinal scale – ordered categories • Happiness (very happy, pretty happy, not too happy) • Government spending on environment (up, same, down)

5. For quantitative variables, the set of possible values is called an interval scale. (i.e., numerical interval between each possible pair of values) Note: In practice, ordinal categorical variables often treated as interval by assigning scores Level of agreement is an ordinal scale, but treated as interval if assigned scores 4=Totally agree, 3=Agree, 2=Disagree ,1=Totally disagree. Ordering of variable types from highest to lowest level of differentiation among levels: • interval > ordinal > nominal

6. Another classification: Discrete / Continuous Discrete variable – possible values a set of separate numbers, such as 0, 1, 2, … Example: Number of … e-mail messages sent in previous day Continuous variable – infinite continuum of possible values Example: Amount of time spent on Internet in previous day (In practice, distinction often blurry)

7. What type of variable? Variable: • No. of movies seen this summer (0, 1, 2, 3, 4, …) • Favorite music type of (rock, jazz, folk, classical) • Happiness (very happy, pretty happy, not too happy) • Quantitative or categorical? • Nominal, ordinal, or interval scale? • Continuous or discrete?

8. Randomization – the mechanism for achieving reliable data by reducing potential bias • NotationN = Population sizen = sample size • Simple Random Sample, SRS: In a sample survey, each possible sample of size n has same chance of being selected. • SRS is an example of a probability samplingmethod – We can specify the probability any particular sample will be selected.

9. How to do random sampling • Establish a sampling frame (listing of all subjects in population) must exist to implement simple random sampling • Use statistical software to generaterandom numbers. • Other probabilitysampling methods:Systematic, stratifiedand cluster random sampling.

10. Sampling error • The sampling error of a statistic equals the error that occurs when we use a sample statistic to predict the value of a population parameter. • Randomization protects against bias, with sampling error tending to fluctuate around 0 with predictable size • The direction and the extent of bias is unknown for studies that cannot employ randomization.

11. Other factors besides sampling error can cause results to vary from sample to sample: • Sampling bias (e.g., nonprobability sampling) • Response bias (e.g., poorly worded questions, such as Lou Dobbs poll mentioned above and others at loudobbsradio.com/surveyarchive) • Nonresponse bias (undercoverage, missing data) Read pages 19-21 of text for examples

12. For nonprobability sampling, we cannot specify the probabilities for the possible samples. Inferences based on them are (highly) unreliable. • Example: volunteer samples, such as polls on the Internet, often are severely biased. • (But, sometimes volunteer samples are all we can get, as in most medical studies)