1 STAT 500 – Statistics for Managers STAT 500 Statistics for Managers

2 STAT 500 – Statistics for Managers Agenda for this Session Sampling What is Sampling? Sampling Methods –Non Probability Sampling –Probability Sampling

3 STAT 500 – Statistics for Managers Examples National level –US monthly unemployment rate (Labor) –Proportion of population with chronic disease (NCHS) –Mean age and quality of housing stock (Census) –Total # employed by US small business (Census)

4 STAT 500 – Statistics for Managers Examples (continued) State –Attitudes toward current events of Texas residents (Texas poll) –Proportion of Texas children who are uninsured

5 STAT 500 – Statistics for Managers Examples (con’t) Local (?) –# of legal UNVA parking spots available at 10:00 a.m. on a particular day –Proportion of full-time students who work at least 10 hours per week –# of students using the student union facilities during a particular week

6 STAT 500 – Statistics for Managers Nonprobability samples Nonprobability (convenience) samples – samples in which the probability of selection is not known –Inaccurate: sample may not represent the population Examples: –Call-in polls

7 STAT 500 – Statistics for Managers Nonprobability samples –Shere Hite’s best-seller Women and Love (1987) based on responses to 100,000 questionnaires distributed to women...4.5% response rate women who responded were the “angry-at- men” contingent (e.g., 91% of divorcees said THEY initiated the divorce -- much higher than actual percent)

Probability Samples Simple Random SystematicStratifiedCluster Probability of selection is known for all units that get into your sample. -- randomization used in making selection

9 STAT 500 – Statistics for Managers What you need to select a probability sample A sampling frame –List of population members (or groups) used for sampling A way of making selections “at random” –Random number table, or computer random number generator

10 STAT 500 – Statistics for Managers Simple random sample Every sample of a given size has the same chance of being chosen Can be selected sequentially, using random #’s Selection can be made with replacement or without replacement

Systematic Samples Decide on sample size: n Divide population of N individuals into groups of k individuals: k = N/n Randomly select one individual from the 1st group. Select every k-th individual thereafter. E.g., N=300, n=55, k = 300/55  5 First Group.…. Systematic Sample

Stratified Samples Population divided into 2 or more groups according to some common characteristic. Simple random sample selected from each. The two or more samples are combined into one.

13 STAT 500 – Statistics for Managers Why stratify? May want estimates for subgroups Stratification yields better estimators if it is done well

How to stratify to improve estimators Form strata so that units within same stratum are similar but… Units in different strata are as different as possible Often a good idea to sample proportionately Stratum A Stratum B Stratum C

Cluster Samples Population divided into 2 or more groups according to convenience (e.g., households). Take simple random sample of the groups. The two or more samples are combined into one.

16 STAT 500 – Statistics for Managers Cluster Sampling Advantage: May be cheaper to sample groups than individuals Disadvantage: May require a larger sample than SRS to achieve the same quality of estimation (if members of clusters are similar to each other)

Types of Survey Errors Coverage Error Nonresponse Error Sampling Error Measurement Error Excluded from sampling frame. Chance differences from sample to sample. Bad Question!

18 STAT 500 – Statistics for Managers More on Coverage Errors Coverage error occurs when......sampling frame does not contain the whole population e.g., trying to learn about unemployment by doing a telephone survey Coverage errors can lead to sample statistics that are not close to the population parameters

19 STAT 500 – Statistics for Managers Agenda for this Session Sampling What is Sampling? Sampling Methods Non Probability Sampling Probability Sampling