Sampling and levels of measurement

Data collection

Sampling terms

Population: all subjects one is interested in. Very large or very small

ElementSample: portion of populationSampling frame: list of people

(elements) in the population

Sampling

Representative sample: if the overall characteristics of the sample approximate the important characteristics of the population

Biased sample: not representativeWhy sample? time and money

Terms

Parameters and statistics

Parameters: population

Statistics: samples

Sampling in the U.S.

Literary Digest polls. Accurate until 1936, when Landon was predicted as winner of the presidential election

Reasons: (1) low return rates (2 million out of 10 million) and (2) sampling frame (telephone directories and lists of auto owners)

Poor sampling frames result in bias

Sampling in the U.S.

1948 Gallup poll predicted Dewey would win. Problems: (1) stopped polling in Oct.; (2) quota sampling

Two types of sampling: probability and non-probability sampling

Probability sampling uses the laws of probability, whereas non-probability does not

Probability

p = number of times an event could occur / total number of outcomes.

Can be expressed as a fraction, a %, as chances out of 100, or as a decimal.

P can range from 0 (no probability to 1 (certainty)

Sampling

A sample will be more likely to be representative of a population from which it is selected if all members of the population have an equal chance of being selected in the sample

Sampling

Sampling error: error due to the fact that the sample is not representative

Necessity of a complete sampling frame

Probability sampling

Simple random sampling: (out of a hat, random numbers)

Systematic random sampling: every nth element is cnosen, select first element at random (random start)

Probability sampling

Stratified random sampling 1. Divide sample into subgroups based on

important population characteristics 2. Randomly sample from those subgroups

in proportion to their percentage in the population

Probability sampling

Choice of stratification variables will often depend on what variables are available, and how much is known about the population

This technique most likely to be representative

Non-probability sampling

Probability sampling only works if there is a sampling frame of the population. Sometimes that is not possible (i.e., criminals, drug addicts, etc.)

Nonprobability sampling methods, while running the risk being unrepresentative might be the only option

Non-probability sampling

Convenience: the captive audience College students and prisoners

Purposive: researcher uses judgment For example, the mentally ill. Works best if

the criteria for inclusion are clear

Quota: like stratified random. Groups are selected on the basis of known variables

In quota sampling, subjects are not selected randomly--subjects with the desired characteristics are selected until a quota is filled for each subgroup

Non-probability sampling

Snowball: each subject is asked to suggest other subjects

Tips about sampling

Sample size: unusually the number of subjects needs to be at least 30. If several groups within the sample are to be compared, there needs to be at least 10 per group.

The larger the number of subjects (N), the less likely sampling error

Tips about sampling

There will always be “mortality”

Samples should be larger to take this into account

Tips about sampling

The greater the heterogeneity of the sample, the larger the sample must be. The less population diversity, the smaller N might be.

N is often determined by time and money factors

Levels of measurement

Nominal

And Ordinal (nonparametric) Interval And Ratio (parametric)

Nominal

Nominal: lowest level, simply classifying observations into categories

Categories should be mutually exclusive and exhaustive

Examples: gender, major, religion, state

Nominal (continued)

Numbers assigned to the categories have no numerical meaning. Assign individuals, and report the % falling into each category.

Fewer statistical techniques can be used

Ordinal measurement

Ordinal measurement: one observation represents more of a given variable than another observation

Rankings Newly developed tests

Ordinal (continued)

Ranks tell whether one observation represents more or less than another, but not how much more or less--nothing is known about the exact difference between any two ranks

Rankings of crime seriousness

Interval

Interval: like an ordinal scale, but has equal intervals between the units of measurement. Not only an ordering, but also the same distance or degree of difference between observations

For example, 81 is 1 point away from 80, etc.

Well-developed tests are interval level

With interval measurement, can do addition, subtraction, multiplication and division, more statistical tests

Ratio measurement

Ratio measurement: like interval, with the additional property of a true zero.

An individual could have two or three time as much of a trait as another with ratio measurement

Ratio

Height or weight. A 200 lb person weighs twice as much as a 100 pound person

Not true for interval. For example, no such thing as an IQ of 0, and a person with an IQ of 100 is not twice as smart as someone with an IQ of 50

Determining statistical test

1 sample 2 samples >2 samples

Nominal Chi square

Ordinal Mann-Whitney; Wilcoxin

Kruskal-Wallis

Interval or ratio

T-tests Analysis of variance