When we do have specific objective, and we want to collect the data and do the analysis that will help us to meet that objective, we typically get our data from two common sources: observational studies (such as polls) and experiments (such as using a treatment to improve hair growth).

In an observational study, we observe and measure specific characteristics, but we don’t attempt to modify the subjects being studied.

In an experiment, we apply some treatment and then proceed to observed its effect on the subjects.

SAMPLE SIZE

An important consideration in conducting research is the size of your sample. It must be large enough so that erratic behavior of very small samples will not produce misleading results. Repetition of a research or an experiment is called replication.

A large sample is not necessarily a good sample. Although it is important to have a sample that is sufficiently large, it is more important to have a sample in which the elements have been chosen in an appropriate way, such as random selection.

Use a sample size large enough so that we can see the true nature of any effects or phenomena, and obtain the sample using an appropriate method, such as one based on randomness.

Determining Sample Size (n)

Slovin’s Formula Lynch et. al. Formula

N N z2 p(1 – p)

n = ------------- n = ------------------------

1 + Ne2 Nd2 + Z2 p(1 – p)

n = minimum sample size n = sample size

N = population size N = population size

e = margin of error due to sampling p = 0.50 (proportion of getting a good sample)

(0.05 or 0.025 or 0.10) 1 – p = 0.50 (proportion of getting a poor sample)

d = 0.025 or 0.05 or 0.10

(your choice of sampling error)

Z = 1.96 ( 95% reliability in obtaining the sample size)

2.33 (99% reliability in obtaining the sample size)

Sample Size for Estimating Mean

Z 2

n = ----------

E

Population (N) is not known

Population (N) is known

Z or Z/2 = 1.96 (95% degree of confidence)

2.33 (99% degree of confidence)

E = desired margin of error

= population standard deviation

(In case the population standard deviation is not known, use the sample standard deviation s instead.)

Problem1:

To plan for the proper handling of household garbage, the city of Baguio must estimate the mean weight of garbage discarded by households in one week. Find the sample size necessary to estimate that mean if you want to be 95% confident that the sample mean is within 2 lb of the true population mean. For the population standard deviation , use the value 12.46 lb, which is the standard deviation of the sample of 62 households included in the Garbage Project study conducted at the University of Baguio.

Problem2:

A researcher wants to estimate the mean amount of time (in hours) that full-time college students spend watching television each weekday. Find the sample size necessary to estimate that mean with a 0.25 hr (15 minutes) margin of error. Assume that a 99% degree of confidence is desired. Also assume that a pilot study showed that the standard deviation is estimated to be 1.87 hr.

RANDOMIZATIONOne of the worst mistakes is to collect data in a way that is inappropriate. We cannot overstress this very important point:

Data carelessly collected may be so completely useless that no amount of statistical torturing can salvage them.

COMMON METHODS OF SAMPLING

In a random sample members of the population are selected in such a way that each has an equal chance of being selected.

(1) A simple random sample of size n subjects is selected in such a way that every possible sample of size n has the same chance of being chosen or selected.“Fishbowl” technique or “Lottery” techniqueTable of Random Numbers or computer-generated random numbers

(2) In a systematic sampling, we select some starting point and then select every kth (such as every 50th) element in the population.

Example: IF Coca Cola managers wanted to poll the 29,500 employees, they could begin with complete employee roster, then select every 50th person to obtain a sample of size 590. This method is simple and is often used.

(3) With (3) With convenience sampling,convenience sampling, we simply use results that are readily available. we simply use results that are readily available.

Example: In some cases, results from convenience sampling may be quite good, but in Example: In some cases, results from convenience sampling may be quite good, but in many other cases they may be seriously biased. In investigating the proportion of left-many other cases they may be seriously biased. In investigating the proportion of left-handed students, it would be convenient for a student to survey his or her handed students, it would be convenient for a student to survey his or her classmates, because they are readily available. Even though such a sample is not classmates, because they are readily available. Even though such a sample is not random, the results should be quite good. random, the results should be quite good.

(4) With (4) With stratified sampling,stratified sampling, we subdivide the population into at least two different we subdivide the population into at least two different subgroups (or strata) that share the same characteristics (such as gender or age subgroups (or strata) that share the same characteristics (such as gender or age bracket), then we draw a sample from each stratum.bracket), then we draw a sample from each stratum.

Example: Using the CAR region as strata, we might select a random sample of voters in Example: Using the CAR region as strata, we might select a random sample of voters in each province. If the different strata have sample sizes that are in the same each province. If the different strata have sample sizes that are in the same proportion as in the population, we say that we have proportion as in the population, we say that we have proportionateproportionate sampling. If it sampling. If it should happen that some strata are not represented in the proper proportion, then the should happen that some strata are not represented in the proper proportion, then the results can be adjusted or weighted accordingly. For a fixed sample size, if you results can be adjusted or weighted accordingly. For a fixed sample size, if you randomly select subjects from different strata, you are likely to get more consistent randomly select subjects from different strata, you are likely to get more consistent (and less variable) results than by simply selecting a random sample from the general (and less variable) results than by simply selecting a random sample from the general population. For that reason, stratified sampling is often used to reduce the variation in population. For that reason, stratified sampling is often used to reduce the variation in the results. the results.

(5) In cluster sampling, we first divide the population area into sections (or clusters), then randomly select some of those clusters and then choose all the members from those selected clusters

Note: In stratified sampling and cluster sampling both involve the formation of subgroups, but cluster sampling uses all members from a sample of clusters, whereas stratified sampling uses a sample of members from all strata.

Example: Cluster sampling can be found in a pre-election poll, in which we randomly select 30 election precincts and survey all the people from each of those precincts. This would be much faster and much less expensive than selecting one person from each of the many precincts in the population area. The results can be adjusted or weighted to correct for any disproportionate representations of groups. Cluster sampling is used extensively by government and private research organizations.

A sampling error is the difference between a sample result and the true population result; such an error results from chance sample fluctuations.

A nonsampling error occurs when the sample data are incorrectly collected, recorded, or analyzed (such as by selecting a biased sample, using a defective measurement instrument, or copying the data incorrectly).

Random Sampling – Each member of the population has an equal chance of being selected. Computers are often used to generate random numbers

Systematic Sampling – Select every kth member

Convenience Sampling – Use results that are readily available

Stratified Sampling – Classify the population into at least two strata, then draw a sample from each.

Cluster Sampling – Divide the population area into sections, randomly select a few of those sections, and then choose all members in them