Probability Sampling - Multi Stage Random Sampling

The four methods we've covered so far -- simple, stratified, systematic and cluster -- are the simplest random sampling strategies. In most real applied social research, we would use sampling methods that are considerably more complex than these simple variations. The most important principle here is that we can combine the simple methods described earlier in a variety of useful ways that help us address our sampling needs in the most efficient and effective manner possible. When we combine sampling methods, we call this multi-stage sampling.

Multi-stage sampling is like cluster sampling, but involves selecting a sample within each chosen cluster, rather than including all units in the cluster. Thus, multi-stage sampling involves selecting a sample in at least two stages. In the first stage, large groups or clusters are selected. These clusters are designed to contain more population units than are required for the final sample.

In the second stage, population units are chosen from selected clusters to derive a final sample. If more than two stages are used, the process of choosing population units within clusters continues until the final sample is achieved.

An example of multi-stage sampling is where, firstly, electoral sub-divisions (clusters) are sampled from a city or state. Secondly, blocks of houses are selected from within the electoral sub-divisions and, thirdly, individual houses are selected from within the selected blocks of houses

The advantages of multi-stage sampling are convenience, economy and efficiency. Multi-stage sampling does not require a complete list of members in the target population, which greatly reduces sample preparation cost. The list of members is required only for those clusters used in the final stage. The main disadvantage of multi-stage sampling is the same as for cluster sampling: lower accuracy due to higher sampling error

Multi Stage Random Sampling is sampling technique needing minimize 2 step withdrawal of sample, which the including Multi Stage Random Sampling category is stratified random sampling, cluster random sampling and combination among both technique.

Multi Stage Random Sampling with very large populations it may be desirable to arrange the data into groups on one criterion, e.g. address by area of postcode, and to select randomly from within this group, then select from within this sample to obtain randomly a representative number of specimens, such as dogs of each age group.

A multistage random sample is constructed by taking a series of simple random samples in stages. This type of sampling is often more practical than simple random sampling for studies requiring "on location" analysis, such as door-to-door surveys. In a multistage random sample, a large area, such as a country, is first divided into smaller regions (such as states), and a random sample of these regions is collected. In the second stage, a random sample of smaller areas (such as counties) is taken from within each of the regions chosen in the first stage. Then, in the third stage, a random sample of even smaller areas (such as neighborhoods) is taken from within each of the areas chosen in the second stage. If these areas are sufficiently small for the purposes of the study, then the researcher might stop at the third stage. If not, he or she may continue to sample from the areas chosen in the third stage, etc., until appropriately small areas have been chosen.

In social research, we surely face complex problem and to solve this problem we have to use Multi Stage Random Sampling. Multi Stage Random Sampling is complex technique, which combine some technique sampling, like stratified random sampling, cluster random sampling and simple random sampling.

For example: Sample location in Jakarta, we wish to get the sample using Multi Stage Random Sample.
First, we determine cluster from Jakarta, such as south, west, north, east, and center.
Second, we determine some samples from each cluster (south, west, north, east, and center) using Simple Random Sample, we call “kelurahan”, or in other word we using Stratified Random Sampling in Jakarta area.
Third, we determine some samples from each “kelurahan” using Simple Random Sample, then we call “RW”,
Fourth, like previous step, we determine some samples from each “RW” using Simple Random Sample, then we call “RT”,
Fifth, we determine some samples from each “RT” using Simple Random Sample, then we call “starting point”
Sixth, we determine sample using Systematic Random Sampling from “starting point”. We move house to house to find chosen respondent based on interval which determined.

Scheme of Multi Stage Random Sampling
city -> kelurahan -> RW -> RT -> starting point -> unit residence -> respondent

Such an approach is called multistage sampling. It can be much more economical than trying to sample directly from the population. In this example, the multistage approach needs a list of persons in a few dwellings, a list of dwellings in a few blocks, a list of blocks in a few counties, a list of counties in a few states, and a list of states. Constructing or obtaining these lists is much easier and much less error-prone than trying to construct a list of all persons in the United States, which we would need to sample persons directly in a single stage.


Source:
-. Australian Bureau of Statistics
-. http://statistics.berkeley.edu/~stark/
-. Wikipedia.com
-. www.socialresearchmethods.net/
-. www.fao.org/

Probability Sampling - Two Stage Cluster Sampling

The concept of cluster sampling can be extended to two stage sampling by taking a simple random sampling of elements from each sampled cluster. Two satege cluster sampling is advantageous when one wishes to have sample elements in geographic proximity because of travel cost. Two stage cluster sampling eliminates the need to sample all elements in each sampled cluster. Thus the cost of sampling can often be reduced with little loss of information.

Two stage cluster sampling is an extension of the concept of cluster sampling. A cluster often contain too many elements to obtain a measurement on each, or it contains elements so nearly alike that measurement of only a few elements provides information on an entire cluster. When either situation occurs, the researcher can select a probability sample of clusters and then take a probability sample of elements within each cluster. The result is a two stage cluster sample.

A two stage cluster sample is obtained by first selecting a probability sample of clusters and then selecting a probability sample of elements from each sample cluster.

A certain similarity between cluster sampling and stratified random sampling. Think of a population being divided into nonoverlapped groups of elements. If these groups are considered to be a strata, then a simple random sample is selected from each group. If these groups are considered to be clusters, then a simple random sample of groups is selected, and the sampled groups are then subsampled. Stratified random sampling provides estimators with small variance when there is little variation among elements within each group. Cluster sampling does well when the elements within each group are highly variable, and all groups are quite similar to one another.

The advantages of two stage cluster sampling over other designs are same as cluster sampling.
First, a frame listing all elements in the population, may be impossible or costly to obtain, whereas to obtain a list of all clusters may be easy.
Second, the cost of obtaining data may be inflated by travel cost if the sampled elements are spread over a large geographic area.

How to draw a two stage random sample
The first problem in selecting a two stage cluster sample is the choice of appropriate clusters. Two conditions are desirable:
1. Geographic proximity of elements within a cluster
2. Cluster sizes that are convenient to administer

The selection of appropriate clusters also depends on whether we want to sample a few clusters and many elements from each or many clusters and few elements from each. The choice is based on costs.
-. Large clusters tend to possess heterogeneous elements, and hence a large sample is required from each in order to acquire accurate estimates of population parameters.
-. Small clusters frequently frequently contain homogenous elements, in which case accurate information on the characteristics of a cluster can be obtained by selecting a small sample from each cluster.

To select sample:
First, obtain a frame listing all clusters in the population
Second, draw a simple random sample of clusters
Third, we obtain frames that list all elements in each of the sampled clusters
Fourth, we select a simple random sample of elements from each of these frames


Source:
-. Richard L. Scheaffer, William Mendenhall, Lyman Ott; Elementary Survey Sampling, 4-th, PWS-Kent Publishing Company, 1990, Boston
-. Mugo Fridah W, Sampling in Research
-. SamplingBigSlides.pdf

Probability Sampling - Cluster sampling

A cluster sample is a probability sample in which each sampling unit is a collection, or cluster, of elements. Cluster sampling is less costly than simple or stratified random sampling if the cost of obtaining a frame that lists all population elements is very high or if the cost of obtaining observations increases as the distance separating the elements increases.

A cluster sample is obtained by selecting clusters from the population on the basis of simple random sampling. The sample comprises a census of each random cluster selected. For example, a cluster may be some thing like a village or a school, a state. So you decide all the elementary schools in Newyork State are clusters. You want 20 schools selected. You can use simple or systematic random sampling to select the schools, then every school selected becomes a cluster. If you interest is to interview teachers on thei opinion of some new program which has been introduced, then all the teachers in a cluster must be interviewed. Though very economical cluster sampling is very susceptible to sampling bias. Like for the above case, you are likely to get similar responses from teachers in one school due to the fact that they interact with one another.

In Cluster Sampling, two (or more) stage sampling of clusters of people.
Most commonly used method
Stage 1: Select sample of clusters from sampling frame of all clusters
Stage 2: Select sample of people from within each selected cluster
Probability that any member picked = Prob (Cluster picked) * Prob (Person picked from cluster)

Cluster sampling is an effective design for obtaining a specified amount of information at minimum cost under the following conditions:
1. A good frame listing population elements either is not available or is very costly to obtain, while a frame listing clusters is easily obtained.
2. The cost of obtaining observations increases as the distance separating the elements increases.
The first task in cluster sampling is to specify appropriate clusters. Elements within a cluster are often physically close together and hence tend to have similar characteristics. Stated another way, the measurement on one element in a cluster may be highly correlated with the measurement on another.
In cluster sampling each sampling unit is a group, or cluster, of elements. Cluster sampling may provide maximum information at minimum cost when a frame listing population elements is not available or when the cost of obtaining observations increasing distance between elements.

Scheme of Cluster Random Sampling

*. Blue circle show us selected sample

Summary
Cluster Sampling
• Example: A primary application is area sampling, where clusters are city blocks or other well-defined areas.
• The population is first divided into separate groups of elements called clusters. Each cluster is a representative small-scale version of the population (i.e. heterogeneous group).
• All elements within each sampled (chosen) cluster form the sample.
• Advantage: The close proximity of elements can be cost effective (i.e. many sample observations can be obtained in a short time).
• Disadvantage: This method generally requires a larger total sample size than simple or stratified random sampling.


Source:
-. Richard L. Scheaffer, William Mendenhall, Lyman Ott; Elementary Survey Sampling, 4-th, PWS-Kent Publishing Company, 1990, Boston
-. Mugo Fridah W, Sampling in Research
-. SamplingBigSlides.pdf

Probability Sampling - Systematic Sampling

A sample survey design that is widely used primarily because it simplifies the sample selection process is called systematic sampling. A sample obtained by randomly selecting one element from the first k elements in the frame and every k-th element thereafter is called a 1 – in- k systematic sample, with a random start.

A systematic random sample is obtained by selecting one unit on a random basis and choosing additional elementary units at evenly spaced intervals until the desired number of units is obtained. For example, there are 100 students in your class. You want a sample of 20 from these 100 and you have their names listed on a piece of paper may be in an alphabetical order. If you choose to use systematic random sampling, divide 100 by 20, you will get 5. Randomly select any number between 1 and five. Suppose the number you have picked is 4, that will be your starting number. So student number 4 has been selected. From there you will select every 5th name until you reach the last one, number one hundred. You will end up with 20 selected students.

Systematic sampling is presented as an alternative to simple random sampling. Systematic sampling is easier to perform and, therefore, is less subject to interviewer errors than simple random sampling. Systematic sampling often provides more information per unit cost than does simple random sampling. When N is large and variance is less than 0, the variance of systematic random sampling is smaller than simple random sampling. A systematic sample is preferable when the population is ordered and N is large. When population is random, the two sampling procedures are equivalent and either design can be used.

Systematic sampling provides a useful alternative to simple random sampling for the following reasons:
1. Systematic sampling is easier to perform in the field and hence is less subject to selection errors by field-workers than are either simple random samples or stratified random samples, especially if a good frame is not available.
2. Systematic sampling can provide greater information per unit cost than simple random sampling can provide.

In general, systematic sampling involves random selection of one element from the first k elements and then selection of every k th element thereafter. This procedure is easier to perform and usually less subject to interviewer error than is simple random sampling. The accuracy of estimates from systematic sampling depend upon the order of the sampling units in the frame. Industrial quality control sampling plans are most often systematic in structure.

How to draw a systematic sample
The methods of selecting the sample data between simple random sampling and systematic sampling are different. A simple random sample is selected by using a table of random numbers. In contrast, various methods are possible in systematic sampling. The investigator can select a 1-in-3, a1-in-5, or in general a 1-in-k systematic sample.

We cannot accurately choose k when the population size is unknown. We can determine an approximate sample size n, but we must guess the value of k needed to achieve a sample of size n.

If too large a value of k is chosen, the required sample size n will not be obtained by using a 1-in-k systematic sample from population. No problem if the user can return to population and conduct another 1-in-k systematic sample until the required sample size is obtained.

In Systematic random Sampling, easier to use for large sampling frame. Select every K-th sampling unit, K is sampling interval = 1 / desired sampling ratio = 1 / (sample size/population size) = 1/(n/N). Example: 5% sample -> K = 1/(5/100) = 20; 25% sample -> K = 1/(25/100)=4

Procedure:
a. Pick random start between 1 & K
b. Select every K-th

Scheme of Systematic Random Sampling

*. Blue circle show us selected sample

We must consider the following three types of populations
1. Random population, a population is random if the elements of the population are in random order.
2. Ordered population, a population is ordered if the elements within the population are ordered magnitude according to some scheme.
3. Periodic population, a population is periodic if the elements of the elements of the population have cyclical variation.

Summary
Systematic Sampling
• Example: Selecting every 100th listing in a telephone book after the first randomly selected listing.
• This method has the properties of a simple random sample, especially if the list of the population elements is a random ordering.
• Advantage: The sample usually will be easier to identify than it would be if simple random sampling were used.


Source:
-. Richard L. Scheaffer, William Mendenhall, Lyman Ott; Elementary Survey Sampling, 4-th, PWS-Kent Publishing Company, 1990, Boston
-. Mugo Fridah W, Sampling in Research
-. SamplingBigSlides.pdf

Probability Sampling - Stratified Random Sampling

The purpose of sample survey design is to maximize the amount of information for a given cost. Simple random sampling, the basic sampling design, often provides good estimates of population quantity at low cost. And now stratified random sampling increases the quantity of information for a given cost.

A stratified random sample is obtained by separating the population elements into group, strata, such that each elements belongs to one and only one stratum, and then independently selecting a simple random sample from each stratum. A stratified sample is obtained by independently selecting a separate simple random sample from each population stratum. A population can be divided into different groups may be based on some characteristic or variable like income of education. Like any body with ten years of education will be in group A, between 10 and 20 group B and between 20 and 30 group C. These groups are referred to as strata. You can then randomly select from each stratum a given number of units which may be based on proportion like if group A has 100 persons while group B has 50, and C has 30 you may decide you will take 10% of each. So you end up with 10 from group A, 5 from group B and 3 from group C.

The principal reasons for using stratified random sampling rather than simple random sampling are as follows:
First, the variance of the estimator of the population mean is usually reduced because the variance of observations within each stratum is usually smaller than the overall population variance.
Second, the cost of collecting an analyzing the data is often reduced by separation of large population into smaller data.
Third, separate estimates can be obtained for individual strata without selecting another sample and hence without additional cost.
Fourth, same reason with first reason, stratification may produce a smaller bound on the error of estimation than would be produced by a simple random sample of the same size. This result is particularly true if measurements within strata are homogenous.

How to draw a stratified random sample
To specify the strata, divide population into sample unit of population and placed it into its appropriate stratum. After the sampling units are divided into strata, we select a simple random sample from each stratum. We must be certain that the samples selected from strata are independent. That is, different random sampling schemes should be used within each stratum so that the observations chosen in one stratum do not depend upon those chose in another.
Stratified Sampling used to ensure representation of some group / characteristic of the population in the sample. Must know stratifying data for everyone on sampling frame. Draw a separate random sample for each category of the stratifying characteristic
a. Divide sampling frame by group
b. Use same sampling ratio to sample from within each category
Can also stratify by an interval/ordinal characteristic
a. Sort sampling frame by characteristic
b. Take a systematic sample from sorted sampling frame

Allocation of the sample
Objective of a sample survey design is to provide estimation with small variance at lowest possible cost. After the sample size n is chosen, there are many ways to divide n into individual stratum sample size, n1, n2,…, nL. Each division may result in a different variance for the sample mean. Hence our objective is to use an allocation that gives a specified amount of information at minimum cost.

Our objective the best allocation scheme is affected by three factors:
1. The total number of elements in each stratum
2. The variability of observation within each stratum
3. The cost of obtaining an observation from each stratum

We can make the following summary statement on stratified random sampling: In general, stratified random sampling with proportional allocation will produce an estimator with smaller variance than that produce by simple random sampling (with the same sample size) if there is considerable variability among the stratum means. If sampling costs are nearly equal from stratum to stratum, stratified random sampling will optimal allocation will yield estimators with smaller variance than will proportional allocation when there is variability among the stratum variances.

Estimated variance for stratified random sampling is bigger than simple random sampling. Simple random sampling may have been better than stratified random sampling for this problem.

Scheme of Stratified Random Sampling

*. Blue circle show us selected sample

All strata selected became sample and every member in strata have same chance to be selected for sample

Summary
Stratified Random Sampling
• Example: The basis for forming the strata might be department, location, age, industry type, etc.
• The population is first divided into groups of elements called strata. The elements within each stratum are as much alike as possible (i.e. homogeneous group).
• A simple random sample is taken from each stratum. Formulas are available for combining the stratum sample results into one population parameter estimate.
• Advantage: Allows for a smaller total sample size


Source:
-. Richard L. Scheaffer, William Mendenhall, Lyman Ott; Elementary Survey Sampling, 4-th, PWS-Kent Publishing Company, 1990, Boston
-. Mugo Fridah W, Sampling in Research
-. SamplingBigSlides.pdf

Probability Sampling - Simple Random Sampling

The objective of a sample survey is to make an inference about the population from information contained in a sample and to obtain a specified amount of information about a population parameter at minimum cost.

Types of Surveys
1. Cross-sectional Surveys
• surveys a specific population at a given point in time
• will have one or more of the design components example: stratification (stratified random sampling), clustering with multistage sampling (cluster random sampling)

2. Longitudinal Surveys
• surveys a specific population repeatedly over a period of time, example: panel, rotating samples

Two factors affect the quantity of information contained in the sample and hence affect the precision of our inference making-procedure. The first is the size of the sample selected from the population. The second is the amount of variation in the data; variation can frequently be controlled by the method of selecting the sample. The procedure for selecting the sample is called the sample survey design.

Type of probability sampling:
1. Simple random sampling
2. Stratified Random Sampling
3. Systematic Random Sampling
4. Cluster Random Sampling

1. Simple Random Sampling
The basic design of sampling technique is sampling random design. The procedure of simple random sampling: if a sample of size n drawn from a population of size N in such a way that every possible sample of size n has the same chance of being selected. To draw a simple random sample from the population of interest is not as trivial as it may first appear. A simple random sample is obtained by choosing elementary units in search a way that each unit in the population has an equal chance of being selected. A simple random sample is free from sampling bias. However, using a random number table to choose the elementary units can be cumbersome. If the sample is to be collected by a person untrained in statistics, then instructions may be misinterpreted and selections may be made improperly. Instead of using a least of random numbers, data collection can be simplified by selecting say every 10th or 100th unit after the first unit has been chosen randomly as discussed below. such a procedure is called systematic random sampling.

Simple random sampling is the basic sampling technique where we select a group of subjects (a sample) for study from a larger group (a population). Each individual is chosen entirely by chance and each member of the population has an equal chance of being included in the sample. Every possible sample of a given size has the same chance of selection.
(Definition taken from Valerie J. Easton and John H. McColl's Statistics Glossary v1.1)

In simple random sampling, each sampling unit has equal and known probability of being selected.

How can we draw a sample from population in simple random sampling methods ? We might use our own judgment to “randomly” select the sample. This technique called haphazard sampling. Another technique called representative sampling, involves choosing a sample that we consider to be typical or representative of the population. Both haphazard and representative sampling are subject to investigator bias and they lead to estimates who properties cannot be evaluated.

This design does not attempt to reduce the effect of variation on the error of estimation. A simple random sample of size n occurs if each sample of n elements from population has the same chance of being selected. Random number tables are quite useful in determining the elements that are to be included in a simple random sample.

Scheme of Simple Random Sampling

*. Blue circle show us selected sample


Source:
-. Richard L. Scheaffer, William Mendenhall, Lyman Ott; Elementary Survey Sampling, 4-th, PWS-Kent Publishing Company, 1990, Boston
-. Mugo Fridah W, Sampling in Research
-. SamplingBigSlides.pdf

Non Sampling Error

Seperti yang telah disebutkan dalam pembahasan mengenai Margin Error bahwa kesalahan dalam pengambilan sample terbagi menjadi dua yaitu sampling error dan non sampling error. Sampling error merupakan ketidaktepatan dari hasil sampling yang dapat diukur dan dihitung, maka dari itu sampling error ini dapat dihindari dan diminimalisasi. Berbeda dengan sampling error, non sampling error merupakan ketidaktepatan hasil sampling yang tidak dapat diukur dan dihitung, sehingga dalam pelaksaaannya non sampling error sulit dihindari dan dalam menghadapinya bersifat subyektif. Non sampling error ini cenderung terjadi akibat kesalahan manusia (human error). Non sampling error ini dapat terjadi pada setiap bagian penelitian, mulai dari penentuan masalah, desain penelitian, hingga penarikan kesimpulan. Non sampling error terjadi bukan diakibatkan dari penarikan sampel saja, namun karena error yang terjadi selama proses penelitian itu dan bersumber dari kesalahan-kesalahan yang baik disengaja maupun tidak disengaja dari peneliti itu sendiri.

Dalam http:/researchexpert.wordpress.com, non sampling error dibedakan berdasarkan sumber-sumber yang berpotensi melakukan kesalahan tersebut. Berikut ini sumber-sumber yang diambil dari blog tersebut dan beberapa tambahan dari saya.

1. Peneliti / Researcher

Pertama, surrogate information error, akibat dari adanya gap antara informasi yang dibutuhkan dengan informasi yang dikumpulkan si peneliti. Misalnya informasi yang dibutuhkan adalah preferensi bermedia cetak namun yang dikumpulkan oleh si peneliti adalah brand awareness media cetak.

Kedua, measurement error, akibat tidak validnya alat ukur yang digunakan oleh peneliti dalam mengukur subjek/objek penelitian, sehingga terjadi gap antar informasi yang telah dikumpulkan dengan informasi yang dihasilkan. Misalnya : kalau yang diukur konsep SES, maka jangan hanya mengukur pengeluaran saja, tapi ukur juga tingkat pendidikan dan jenis pekerjaaannya.

Ketiga, population defenition error, akibat dari ketidaktepatan pendefenisian populasi penelitian atau populasi target. Suatu defenisi populasi target yang benar harus mencakup 3 unsur yaitu : isi, cakupan, dan waktu.

Keempat, sampling frame error, masih terkait dengan error ketiga. Sampling frame merupakan daftar seluruh anggota populasi. Error jenis ini akan terjadi ketika ada anggota populasi yang tidak terdaftar, atau daftar yang telah kadaluwarsa. Hal ini sering terjadi di Indonesia, karena data kependudukannya masih amburadul dan instansi pemerintahan terkait yang tidak tertib administrasi.

Kelima, data analysis error, terkait dengan proses analisis data, hal ini sangat tergantung pada kompetensi si peneliti. Misalnya : peneliti menerapkan analisis parametrik terhadap data yang tidak berdistribusi normal, yang seharusnya dianalisis dengan tehnik non parametrik


2. Data Processing – Data entry

Pertama, kesalahan dalam membuat frame work entry data. Kesalahan ini dapat menyebabkan salah dalam proses entry data dan bahkan ada data yang tidak ter-entry.

Kedua, kekeliruhan dalam entry data. Kekeliruhan ini mutlak kesalahan dari manusia yang mengentry data tersebut (human error) karena kurang teliti atau yang masalah yang lain. Kekeliruhan ini bisa diminimalisasi dengan cara pengentrian dilakukan dua kali dengan orang yang berbeda, meskipun cara ini membuang waktu, biaya dan tenaga.


3. Surveyor/Interviewer/Observer/Field Unit

Pertama, questioning error, interviewer salah dalam bertanya, over interpretasi terhadap panduan pertanyaan, atau malah kebalikannya tidak menggali lebih dalam (probing) jawaban responden/informan.

Kedua, recording error, interviewer melakukan kesalahan dalam pencatatan respon yang diberikan oleh responden/informan.

Ketiga, cheating error, hal ini berkaitan dengan moralitas. Interviewer berbohong dengan “mengisi” sebagian atau seluruh kuesinoer (survei, polling).


4. Responden

Terakhir adalah error yang bersumber dari subjek/objek penelitian. Responden/informan berpartisipasi menyumbangkan tiga jenis error yaitu : inability error, unwillingness error dan no response error.

Pertama, error terjadi jika responden/informan tidak memberikan informasi yang benar atau tepat. Hal ini bisa disebabkan oleh bias memory, responden/informan sudah tidak ingat peristiwa atau pengalaman yang ditanyakan. Menurut sejumlah pakar riset pemasaran, idealnya waktu untuk wawancara dengan metode survei maksimal 20 menit, dan untuk wawancara mendalam sekitar 2 jam.

Kedua, terjadi jika responden/informan “gengsi” atau “takut” memberikan jawaban yang sebenarnya.

Ketiga, terjadi karena responden/informan menolak mentah-mentah mengikuti kegiatan riset, bisa karena masalah privacy, topik yang kurang menarik, belum lama berselang pernah menjadi responden/informan, dll.

Non sampling error ini merupakan kesalahan yang disebabkan oleh manusia, oleh karena itu hampir tidak mungkin untuk memperkecil non sampling error ini, meskipun hal itu bisa dilakukan. Tidak seperti sampling error yang bisa diperkecil dengan menambah sample, non sampling error tidak bisa diperkecil dengan hal seperti itu, bahkan dengan sample yang besar malah akan memperbesar faktor non sampling error. Untuk memperkecilnya adalah dengan meningkatkan kualitas manusia yang berkecimpung dalam penelitian ini, seperti dengan pelatihan-pelatihan, standardiasai kualitas bagi interviewer. pembuatan frame work entry data dengan hati-hati, perencanaan kerja yang baik, insentif yang layak, dan lain-lain.

Pengujian Hipotesis

Hipotesis nol merupakan hipotesis pegangan sementara, sehingga memungkinkan kita untuk memutuskn apakah sesuatu yang kita uji masih sebagaimana yang dispesifikasikan oleh H0 atau tidak. Hipotesis alternative merupakan alternative dari H0, yaitu keputusan apa yang harus kita tentukan bila apa yang kita uji tidak sebagaimana yang dispesifikasikan oleh H0.

Informasi sangat diperlukan dalam menentukan hipotesis, terutama untuk menentukan hipotesis awal (H0). Bila kita ingin mengetahui atau menguji apakah produk baru yang merupakan perbaikan dari produk lama lebih baik atau tidak dibandingkan dengan produk lama, maka informasi yang diperlukan adalah tentang kualitas produk lama tersebut.

Bagaimana menentukan H0 dan H1 ?
H0 disusun berdasarkan atas informasi sebelumnya, pada umumnya data sebelumnya telah tersedia. Sedangan H1 disusun berdasarkan keinginan kita dalam penelitian dan cenderung berlawanan atau tandingan dari H0 tersebut.

Pengujian hipotesis ini merupakan bagian dari statistika inferensia, yaitu pengujian terhadap nilai satu atau lebih parameter berdasarkan nilai penduga bagi prameter yang bersangkutan. Hubungannya dengan H0 dan H1 adalah keduanya merupakan landasan kerja, apabila asumsi berdasarkan nilai-nilai pengamatan dapat diterima kebenarannya maka harus menerima H0 karena bukti untuk menolaknya kurang kuat. Namun apabila data yang diperoleh kurang kuat untuk mendukung pendapat ini, maka yang diterima adalah asumsi lain yang merupakan tandingan dari H0, yaitu H1.

Pengujian hipotesis merupakan cara yang digunakan untuk mengambil kesimpulan berdasarkan statistika, maka dari itu dipengaruhi oleh faktor yang tidak pasti. Sehingga pengambilan keputusan itu mengandung resiko kesalahan. Terdapat dua jenis kesalahan yang timbul dalam pengujian secara statistika, salah jenis pertama yaitu kesalahan yang timbul karena H0 yang ditolak sesungguhnya benar dan salah jenis kedua yang terjadi karena kita menerima berlakunya H0 yang sesungguhnya tidak benar. Untuk mengecilkan peluang terjadinya salah satu jenis kesalahan maka harus dilakukan dengan memperbesar peluang timbulnya kesalahan jenis lain. Nilai peluang keda jenis kesalahan tersebut dapat diperkecil secara bersamaan dengan cara memperbesar ukuran contoh.

Peluang terjadinya kesalahan jenis pertama (alpha, yang ditulis dalam huruf Yunani - α) biasanya telah ditentukan, misalnya α =0.05. Besaran ini disebut juga sebagai ukuran wilayah kritis, yaitu luas wilayah penolakan H0. Daerah penerimaan untuk H0 terdiri dari nilai-nilai criteria uji dalam mana H0 tersebut diterima. Daerah penolakan H0 terdiri dari nilai-nilai criteria uji dalam mana H0 tersebut ditolak, sedangkan kriteria uji yang digunakan untuk memutuskan diterima tidaknya H0 disebut nilai-nilai kritis pengujian, dan dipertimbangkan terletak di daerah penolakan. Kesalahan jenis I diperbuat jika hipotesis nol, H0, yang benar (dianggap benar) ditolak. Peluang untuk berbuat salah jenis pertama ini dilambangkan dengan α dan umumnya disebut taraf nyata pengujian. Taraf nyata alpha adalah peluang atau resiko berbuat salah sebesar alpha dalam pengambilan keputusan.

Peluang terjadinya salah jenis kedua (beta, yang ditulis dalam huruf Yunani - β)sulit menentukannya karena penyebaran hipotesisi tandingan (H1) biasanya tidak diketahui. Apabila salah jenis kedua tidak diketahui, maka penerimaan H0 sebagai sesuatu yang dianggap benar akan mengandung kesalahan yang tidak diketahui berapa besar peluangnya. Kesalahan jenis II diperbuat bila hipotesis alternative (H1) yang benar kita tolak. Peluang berbut salah untuk kesalahan kenis II dilambangkan dengan beta.Kekuatan seuatu uji atau disingkat dengan kekuatan uji adalah peluang untuk menolak ho jika H1 benar

Penolakan dan penerimaan H0 menyebabkan dibuatnya dua macam kesalahan tersebut. Peluang membuat salah jenis satu (α) tergantung pada nilai parameter yang dispesifikasikan dalam H0.

Nilai (1- β) disebut sebagai kuasa pengujian, merupakan peluang menerima H1, apabila hipotesis tersebut benar. Antara kebenaran hipotesis dengan kemungkin tindakan yang diambil berdasarkan hasil pengujian, dapat digambarkan sebagai berikut:



Kriteria (tolok ukur) uji atau statistic uji adalah sebuah peubah acak yang digunakan dalam menentukan apakah hipotesis nol atau hipotesis alternative yang diterima dalam pengujian hipotesis.

Hipotesis

Banyak sekali pengertian hipotesis yang beredar saat ini, menurut Cooper dan Emory, 1996, hipotesis merupakan proposisi yang dirumuskan untuk diuji secara empiris, bersifat sementara atau dugaan. Sedangkan proposisi merupakan suatu pernyataan mengenai konsep –konsep yang dapat dinilai benar atau salah jika merujuk pada fenomena yang dapat diamati. Hipotesis dapat diturunkan dari teori yang berkaitan dengan masalah yang akan diteliti. Jika hipotesis sudah diuji dan dibuktikan kebenarannya maka hipotesisi tersebut dapat menjdi teori.

Hipotesis merupakan jawaban atau kesimpulan sementara terhadap rumusan masalah penelitian, dikatakan sementara karena jawaban yang diberikan baru didasarkan pada teori yang relevan, belum didasarkan pada fakta-fakta empiris yang diperoleh melalui pengumpulan data. Jadi hipotesis dapat dinyatakan sebagai jawaban teoretis terhadap rumusan masalah penelitian, namun belum jawaban yang empiric. Hipotesis digunakan untuk penelitian kuantitatif, sedangkan pada penelitian kualitatif, tidak merumuskan hipotesis, tetapi justru menemukan hipotesis.

Dalam buku Metode Penelitian Bisnis, Sugiyono membagi hipotesis menjadi dua, yaitu hipotesis penelitian dan hipotesis statistic. Dalam hipotesis penelitian tidak menggunakan sampel tapi menggunakan populasi, sehingga tidak ada confidence interval dalam penelitian ini. Sedangkan pada hipotesis statistic menggunakan sampel sebagai data untuk pengambilan kesimpulan, untuk itu dalam penelitian ini menggunakan confidence interval, significancy level, confidence level, margin error dan lain-lain. Hal ini karena keputusan untuk populasi diperoleh dari data sampel, yang merupakan pendugaan terhadap populasi dan bukan hasil yang menggambarkan kondisi sesungguhnya dari populasi. Significancy artinya hipotesis penelitian terbukti pada sampel yang dapat diberlakukan ke populasi

Bentuk-bentuk hipotesis:
1. Hipotesis deskriptif, merupakan jawaban sementara terhadap rumusan masalah deskriptif
2. Hipotesis komparatif, merupakan jawaban sementara terhadap masalah komparatif
3. Hipotesis asosiatif, merupakan jawaban sementara terhadap masalah asosiatif/hubungan

Ciri hipotesis yang baik, antara lain:
1. Merupakan pernyataan yang jelas sehingga tidak menimbulkan penafsiran
2. Merupakan sesuatu yang dapat diuji dengan data yang dikumpulkan dengan metode-metode ilmiah
3. Merupakan dugaan terhadap suatu masalah

Hipotesis berfungsi sebagai pedoman untuk mengarahkan penelitian. Keuntungan dari hipotesis adalah hipotesis member batasan kepada apa yang akan diteliti dan apa yang tidak diteliti. Hipotesis mengarahkan bentuk desain penelitian yang paling sesuai. Selain itu hipotesis memberikan kerangka untuk menyusun kesimpulan yang akan dihasilkan. Hipotesis selain berfungsi untuk menguji kebenaran suatu teori, hipotesis juga dapat digunakan untuk memberikan gagasan baru dalam mengembangkan suatu teori dan memperluas pengetahuan peneliti mengenai suatu gejala yang sedang dipelajari.

Dalam statistika dikenal 2 macam hipotesis, yaitu hipotesis nol (H0) dan hipotesis aternatif (H1). H0 merupakan hipotesis sementara, sehingga memungkinkan untuk memutuskan apakah sesuatu yang diuji masih sebagaimana dispesifisikan oleh H0 atau tidak. H1 merupakan alternative dari H0, yaitu keputusan apa yang harus ditentukan jika yang diuji tidak sebagaimana yang dispesifikasikan oleh H0. H0 disusun berdasarkan informasi yang telah diperoleh sebelumnya, sedangkan H1 disusun berdasarkan alternative jawaban dari H0.

H0 diajukan bila H0 menspesifikasikan sebuah parameter dari suatu model sedemekian rupa sehingga peluang untuk masing-masing dan setiap titik contoh dapat dihitung. H1 adalah suatu alternative apabila kenyataan yang ditunjukan contoh tidak mendukung H0.

Penentuan hipotesis dilandasi pada hasil penelitian sebelumnya atau teori (referensi) dengan tujuan mendukung hasil sebelumnya, membantah atau menyajikan temuan baru.