Statistics 2 Dersi 1. Ünite Sorularla Öğrenelim

Define, describe and give examples of population.

Population is the universe to be sampled, such as all Turkish people, all universities in Turkey, all pregnant women over 40 years of age, all adult males who smoke 20 cigarettes or more daily, or all the buildings in Eskişehir, Turkey. Population can be finite or infinite. The boundaries of the population should be clearly declared. Populations can be homogenous or heterogenous. It could be consisting of any type of object. In statistics the word population is used in a broader sense.

Define and describe sample and importance of a sample in statistics. What does a good sample mean? 

The Oxford dictionary of statistical terms defines the sample as a part of a population, or a subset from
a set of units, which is provided by some process or other, usually by deliberate selection with the object of investigating the properties of the parent population or set. A good sample must represent or model the
population that the sample was taken. A representative sample includes similar distribution of important
characteristics (e.g., age, gender, marital status, health status) with the distributions of those characteristics
in the population. For example, if the population of interest includes the 10,000 workers in a factory,
where 70% of workers are male and 15% of workers are over 56 years of age. Clearly you can see that the
workers are not similar to each other, they have some distinct characteristics that define what a worker is,
in here, only two of those characteristics are shown. Therefore, if you want to take a random sample from
this population of workers, you would like to include the characteristics of the population in your sample
as much as possible. The main importance of a sample is the accuracy with which represent the target population including the people, institutions, buildings, patients, and systems to which or to whom the results obtained from
the sample are to be applied or generalized.

Why do we need sampling in statistics? List and explain the reasons?

When we try to obtain some information about the characteristics of a population there are important reasons why we use a sample instead of a census. The main reasons for sampling can be categorised by the following topics:

Cost: Every project has a limited funding. The investigator uses the funding wisely. A sampling often provides reliable and useful information at much lower cost than does a census.

Time: A sampling survey often provides more timely information than a census, because fewer data have to be collected and analysed. Thus, the required information can be achieved quickly.

Accuracy: While a census data is gathered, many unexpected problems may affect the accuracy of the results such as recording errors, copying errors, false recordings by interviewers etc. So, while working with census data, we may inadvertently come across with a figure for a population parameter being further away than the actual value. With a good sampling procedure using good sampling methods and by choosing random observations, actually we can be very close to the true value of the population parameter. Since usually the size of the sample is not very big, data errors are more controllable.

Physical Impossibility: Some populations are uncountable or infinite to conduct a census. In this situation, it is impossible to consider all the elements of a population. Thus, a sample is necessary to obtain information from a population.

Destructive Tests: If a test includes the destruction of an item or product, sampling should be used.

Why do we use probability sampling methods? Explain.

Probability sampling methods provide a statistical basis for saying that a sample is representative of
the target population. In probability sampling methods, every unit of the target population have a known
and non-zero probability of being selected for the sample. We can say that because probability sampling
methods use a random mechanism thus eliminating subjectivity in the selection of a sample, these methods
are an unbiased way of creating a sample.

What is simple random sampling?

Many types of probability samples are available for sampling from a population. The most basic sampling method is the simple random sampling. The simple random sample from a population is a sample that is selected so that each possible sample combination of the specified size has equal probability of being chosen.

A practical way of satisfying the requirements that each possible sample combination have an equal probability of being chosen is to select sample elements one at a time. 

List five types of probability sampling.

Simple random sampling

Using random numbers for sample selection

Stratified sampling

Cluster sampling

Systematic sampling

Explain using random numbers for sample selection.

Random numbers are often used to select simple random samples from a population frame. The random numbers required for this purpose can be generated by a computer program or from a table of random digits. We will first discuss the use of table of random digits. Discrete uniform probability distribution function, which has possible outcomes between 0 and 9 with equal probability, is used to generate digits in the table. Thus, for each column and row that contains digits in the table, every digit from 0 to 9 has equal probability of appearing in that column and row position. The digits in the table generally generated by a computer and tested to ensure close adherence to the required properties of equal  probability and independency among the digits.

Explain stratified sampling.

In stratified sampling method, the target population is divided into homogenous subgroups which are called strata. Each subgroup is called stratum. Then a probability sampling method such as simple random sampling method is applied for each stratum to take a sample from the population. The strata must be mutually exclusive and exhaustive. This means that each unit of the population must be assigned to only one stratum. Strata should be determined based on available characteristics that they are related to the outcome of the survey or research. When a population can be clearly divided into homogenous groups based on some characteristic, we can use stratified random sampling.

Explain cluster sampling.

A cluster is a naturally occurring group of units in the population. For example, a university which has many faculties, departments, students and lecturers can be considered as a cluster for a population consisting of universities in a country. In the cluster sampling, clusters, which are naturally occurring in the population, are randomly selected, and all units in the selected clusters are included in the sample.

Explain systematic sampling.

Another probability sampling method is systematic sampling. This method provides a means of substantially reducing the effort required for sample selection. Systematic sampling is widely used because systematic sampling is quick and convenient when you have a complete list of all the members of your population. Systematic sampling method is applied easily by taking every kth element after a random starting point. The value of k is determined by
k = Number of members in the population / Sample Size

Why do researchers use nonprobability sampling?

Researchers sometimes use nonprobability sampling methods because the members appear to be representative of the population or because they can be assembled conveniently.

List three types of nonprobability sampling methods.

Convenience sampling

Snowball sampling

Quota sampling

Explain convenience sampling. Why is this method used?

A convenience sample involves a group of individuals that is ready and available. It is also called availability sampling method. A convenience sampling is used to create sample as per ease of access, readiness to be a part of the sample, availability at a given time period or any other specifications of a particular element. The surveyors select members merely on the basis of proximity and does not consider whether they represent the entire population or not. By using this sampling techniques, we can observe habits, opinions, and viewpoints in the easiest possible manner. Many researchers prefer convenience sampling method because it is inexpensive, easy and applied quickly. Because of the potential for bias in the sampling method, the results obtained from this sampling method should be reported and used with a great caution.

Explain snowball sampling. When is this method preferred?

In snowball sampling, the members, who are identified previously, are asked to identify other members of the population. As newly identified members name others, the sample is getting larger as snowballs. Snowball sampling technique is used when listing of population is not available and cannot be compiled.

How is snowball sampling practiced? Refer to the steps, ethics and participation.

1. Two main steps are applied in snowball sampling method.
2. The potential members in the population are identified. Then, some of the members are selected initially.
The identified subjects are asked to recruit other members and then those people are asked to recruit, and so on. However, the selected participants should be made aware that they do not have to provide any other members.
The above steps are repeated until the determined sample size is achieved. Ethically, the identified members should not be forced to give other members. Rather, the previously identified members should be asked to encourage others to participate.

Explain quota sampling.

In quota sampling, the population is divided into subgroups being studied, such as male and female, younger and older, engineer, doctor and lawyer. Then, the proportion of the members who fall into each subgroup is estimated. Finally, the sample reflecting the estimated proportions is drawn from the population. It is a non-probabilistic version of stratified sampling method.

What are the advantages of quota sampling?

Quota sampling technique allows the researchers to sample a subgroup that is of great interest to the study. If a researcher aims to investigate a trait or a characteristic of a certain subgroup, quota sampling is the ideal sampling technique. Also, quota sampling allows the researchers to determine the relationships among subgroups. In some situations, traits of a certain subgroup interact with other traits of another subgroup.

While using random numbers for sample selection, what are the advantages of using computer packages?

Instead of using a table of random digits, we can use computer packages to generate random numbers directly. When the sample size is large, using computer packages is especially helpful. In some computer packages, the random numbers generated by the program are used internally to identify those elements of a computerized data base that are selected for the sample, and only the description of the sample elements are printed out.

How is simple random sampling practiced? 

The following procedure selects a simple random sample with size n without replacement from a finite population with size N.
1. Select the first sample element by giving each of the N population elements an equal probability
(1/N) of being chosen.
2. Select the second element by giving each of the remining N–1 population elements equal probability
(1/(N–1)) of being chosen.
3. Repeat this procedure until all n elements are chosen.

Why is sampling used for?

The main purpose of the inferential statistics is to generalize the information obtained from sample to the population of interest. A sample is a part of the population selected so that inferences can be drawn from it about the population. In most cases, studying on sampling is more feasible than the all elements of the population.