Sample technique or sampling method

 

Sample technique or sampling method

In Statistics, the sampling method or sampling technique is the process of studying the population by gathering information and analyzing those data. It is the basis of the data where the  sample space is enormous. The statistical research is of two forms:

• In the first form, each domain is studied, and the result can be obtained by computing the sum of all units.
• In the second form, only a unit in the field of the survey is taken. It represents the domain. The result of these samples extends to the domain. This type of study is known as the sample survey.

In this article, let us discuss the different sampling methods in research such as probability sampling and non-probability sampling methods and various methods involved in those two approaches in detail.

What are the sampling methods?

There are several different sampling techniques available, and they can be subdivided into two groups. All these methods of sampling may involve specifically targeting hard or approach to reach groups.

Types of Sampling Method

In Statistics, there are different sampling techniques available to get relevant results from the population. The two different types of sampling methods are::

• Probability Sampling
• Non-probability Sampling

What is Probability Sampling?

The probability sampling method utilizes some form of random selection. In this method, all the eligible individuals have a chance of selecting the sample from the whole sample space. This method is more time consuming and expensive than the non-probability sampling method. The benefit of using probability sampling is that it guarantees the sample that should be the representative of the population.

Probability Sampling Types

Probability Sampling methods are further classified into different types, such as simple random sampling, systematic sampling, stratified sampling, and clustered sampling. Let us discuss the different types of probability sampling methods along with illustrative examples here in detail.

Simple Random Sampling

In simple random sampling technique, every item in the population has an equal and likely chance of being selected in the sample. Since the item selection entirely depends on the chance, this method is known as “Method of chance Selection”. As the sample size is large, and the item is chosen randomly, it is known as “Representative Sampling”.

Example:

Suppose we want to select a simple random sample of 200 students from a school. Here, we can assign a number to every student in the school database from 1 to 500 and use a random number generator to select a sample of 200 numbers.

Systematic Sampling

In the systematic sampling method, the items are selected from the target population by selecting the random selecting point and selecting the other methods after a fixed sample interval. It is calculated by dividing the total population size by the desired population size.

Example:

Suppose the names of 300 students of a school are sorted in the reverse alphabetical order. To select a sample in a systematic sampling method, we have to choose some 15 students by randomly selecting a starting number, say 5.  From number 5 onwards, will select every 15th person from the sorted list. Finally, we can end up with a sample of some students.

Stratified Sampling

In a stratified sampling method, the total population is divided into smaller groups to complete the sampling process. The small group is formed based on a few characteristics in the population. After separating the population into a smaller group, the statisticians randomly select the sample.

For example,  there are three bags (A, B and C), each with different balls. Bag A has 50 balls, bag B has 100 balls, and bag C has 200 balls. We have to choose a sample of balls from each bag proportionally. Suppose 5 balls from bag A, 10 balls from bag B and 20 balls from bag C.

Clustered Sampling

In the clustered sampling method, the cluster or group of people are formed from the population set. The group has similar significatory characteristics. Also, they have an equal chance of being a part of the sample. This method uses simple random sampling for the cluster of population.

Example:

An educational institution has ten branches across the country with almost the number of students. If we want to collect some data regarding facilities and other things, we can’t travel to every unit to collect the required data. Hence, we can use random sampling to select three or four branches as clusters.

All these four methods can be understood in a better manner with the help of the figure given below. The figure contains various examples of how samples will be taken from the population using different techniques.

What is Non-Probability Sampling?

The non-probability sampling method is a technique in which the researcher selects the sample based on subjective judgment rather than the random selection. In this method, not all the members of the population have a chance to participate in the study.

Non-Probability Sampling Types

Non-probability Sampling methods are further classified into different types, such as convenience sampling, consecutive sampling, quota sampling, judgemental sampling, snowball sampling. Here, let us discuss all these types of non-probability sampling in detail.

Convenience Sampling

In a convenience sampling method, the samples are selected from the population directly because they are conveniently available for the researcher. The samples are easy to select, and the researcher did not choose the sample that outlines the entire population.

Example:

In researching customer support services in a particular region, we ask your few customers to complete a survey on the products after the purchase. This is a convenient way to collect data. Still, as we only surveyed customers taking the same product. At the same time, the sample is not representative of all the customers in that area.

Consecutive Sampling

Consecutive sampling is similar to convenience sampling with a slight variation. The researcher picks a single person or a group of people for sampling. Then the researcher researches for a period of time to analyze the result and move to another group if needed.

Quota Sampling

In the quota sampling method, the researcher forms a sample that involves the individuals to represent the population that is based on specific traits or qualities. The researcher chooses the sample subsets that bring the useful collection of data that generalizes the entire people.

Purposive or Judgmental Sampling

In purposive sampling, the samples are selected only based on the researcher’s knowledge. As their knowledge is instrumental in creating the samples, there are the chances of obtaining highly accurate answers with a minimum marginal error. It is also known as judgmental sampling or authoritative sampling.

Snowball Sampling

The snowball sampling is also known as chain-referral sampling technique. In this method, the samples have traits that are difficult to find. So, each identified member of a population is asked to find the other sampling units. Those sampling units also belong to the same targeted population.

 

Probability sampling and Types of Sampling

 

Probability sampling and Types of Sampling 

Probability sampling: It is a sampling technique, in which the subjects of the population get an equal opportunity to be selected as a representative sample. Probability sampling: It is a sampling technique where a researcher sets a selection of a few criteria and chooses members of a population randomly.

 We may remember Probability Sampling like S³C

Ø Simple random sampling: Each individual has the same probability of being chosen to be a part of a sample. It is a reliable method of obtaining information where every single member of a population is chosen randomly, merely by chance. It is one of the best probability sampling techniques for example, in an organization of 200 employees, if the sports team decides on conducting team building activities, it is highly likely that they would prefer picking chits out of a bowl. In this case, each of the 200 employees has an equal opportunity of being selected.

Ø  Systematic sampling: Researchers use this sampling to choose the sample members of a population at regular intervals. This type of sampling method has a predefined range, and hence this sampling technique is the least time-consuming.
For example, a researcher intends to collect a systematic sample of 200 people in a population of 2000. He/she numbers each element of the population from 1-2000 and will choose every 10th individual to be a part of the sample (Total population/ Sample Size = 2000/200 = 10).

Ø Stratified random sampling: It  is a method in which the researcher divides the population into smaller groups that don’t overlap but represent the entire population. While sampling, these groups can be organized and then draw a sample from each group separately. For example, a researcher looking to analyze the characteristics of people belonging to different annual income divisions will create strata (groups) according to the annual family income. For example  less than ₹10,000,  ₹10,000 – ₹20,000; ₹20,000 - ₹30,000; ₹30,000 -₹40,000, etc. By doing this, the researcher concludes the characteristics of people belonging to different income groups. Marketers can analyze which income groups to target and which ones to eliminate to create a roadmap that would bear fruitful results.

Ø Cluster sampling: It is a method where the researchers divide the entire population into sections or clusters that represent a population. Clusters are identified and included in a sample based on demographic parameters like age, sex, location, etc. For example, if the Indian government wishes to evaluate the number of minorities living in the North east, they can divide it into clusters based on states. This way of conducting a survey will be more effective as the results will be organized into states and provide insightful minorities data.

 

Nonprobability sampling: It is a method of sampling wherein; it is not known that which individual from the population will be selected as a sample.   In this sampling, the researcher chooses members for research at random. This sampling method is not a fixed or predefined selection process. This makes it difficult for all elements of a population to have equal opportunities to be included in a sample.

 

                  We may remember Non- Probability Sampling like PIQS

Ø Purposive/ Judgmental sampling:   It is formed by the discretion of the researcher. Researchers purely consider the purpose of the study, along with the understanding of the target audience. For instance, when researchers want to understand the thought process of people interested in studying for their B.Ed. degree. The selection criteria will be: “Are we interested in doing our B.Ed. degree?” and those who respond with a “No” are excluded from the sample.

Ø  Incidental/ Convenience sampling: This method is dependent on the ease of access to subjects such as surveying customers at a mall or passers-by on a busy street. It is usually termed as Convenience sampling because of the researcher’s ease of carrying it out and getting in touch with the subjects. Researchers have nearly no authority to select the sample elements, and it’s purely done based on proximity and not representativeness. For example, start-ups and NGOs usually conduct convenience sampling at a mall to distribute leaflets of upcoming events or promotion of a cause – they do that by standing at the mall entrance and giving out pamphlets randomly.

Ø Quota sampling: In this sampling technique happens based on a pre-set standard. In this case, as a sample is formed based on specific attributes, the created sample will have the same qualities found in the total population. It is a rapid method of collecting samples.

Ø Snowball sampling: It is a sampling method that researchers apply when the subjects are difficult to trace. For example, it will be extremely challenging to survey shelter less people or illegal immigrants. In such cases, using the snowball theory, researchers can track a few categories to interview and derive results. Researchers also implement this sampling method in situations where the topic is highly sensitive and not openly discussed—for example, surveys to gather information about Covid-19. Not many victims will readily respond to the questions. Still, researchers can contact people they might know or volunteers associated with the cause to get in touch with the victims and collect information.

Important questions

1.    Approaches to sampling commonly used in qualitative research design are given in Set - I and their characteristics in Set - II. Match Set - I and Set - II and select appropriate code.

 

 Set - I                                               Set – II

 (Approaches to sampling            (Characteristics in qualitative research)

 (a) Extreme case sampling          (i) Seeks cases that are typical

 (b) Purposive sampling                 (ii) Seeks cases that are highly similar to  

                                                           each other

(c) Snowball sampling                    (iii) Seeks cases that are unusual

                                                            (iv) Seeks help from participants to

                                                                   identify additional participants

                                                            (v) Seeks cases according to his/her

                                                             judgement about the appropriateness

 Code : (a) (b) (c)

    (1) (i) (iv) (iii)

    (2) (ii) (iv) (i)

   (3) (iii) (v) (iv)

   (4) (iv) (ii) (iii)

2.    When the population is heterogeneous which of the following methods will be efficient for a choice of sampling procedure? (1) Random sampling (2) Systematic sampling (3) Stratified sampling (4) Convenience sampling 

Hypothesis

 

Hypothesis

A hypothesis can be defined as a tentative explanation of the research problem, a possible outcome of the research, or an educated guess about the research outcome. Its testing is a form of inferential statistics that allows us to draw conclusions about an entire population based on a representative sample.

A research hypothesis: It can be defined as a clear, specific and predictive statement that states the possible outcome of a scientific study. The result of the research study is based on previous research studies and can be tested by scientific research. It could be understood in terms of Simple Research hypothesis and Complex Research Hypothesis. A simple research hypothesis predicts the relationship between a single independent variable and a single dependent variable. A Complex hypothesis predicts the relationship between two or more independent variables and two or more dependent variables.

Alternative hypothesis: It is usually the one which one wishes to prove. The alternative hypothesis is the other theory about the properties of the population in hypothesis testing. Typically, the alternative hypothesis states that a population parameter does not equal the null hypothesis value. In other words, there is a non-zero effect. If your sample contains sufficient evidence, we can reject the null and favor the alternative hypothesis. The alternative is often identified with H₁

 Null hypothesis: It  is the one which one wishes to disapprove. The null hypothesis is one of two mutually exclusive theories about the properties of the population in hypothesis testing. Typically, the null hypothesis states that there is no effect (i.e., the effect size equals zero). The null is often signified by H₀.

Directional hypothesis: It measures the direction of variation of two variables. This effect of one variable on the other variable can be in positive direction or in negative direction.

 Non-directional hypothesis: It  does not indicate the kind of effects but only shows the relation between two variables.

Characteristics of a Good Hypothesis:

Good hypothesis must be based on a good research question. It should be simple, specific and stated in advance.

  i) Hypothesis should be simple so that it is easily understood by everyone.

 ii) Hypothesis should be clear, specific and precise.

iii) Hypothesis should be capable of being tested.

 iv) Hypothesis should state relationship between variables. 

Some important questions

1.    Using equivalent samples, a researcher obtained a significant correlation 95 times out of 100 trials. He/ She decided to reject the null hypothesis. The alpha level would be : (1) .01 (2) .02 (3) .05 (4) .001

2.    Further, supposing the researcher computes a value of ‘t’ for testing the significance of the difference between mean achievement of the two groups and finds that it is statistically significant. What decision would be warranted on the basis of this evidence? (1) The researcher retains The Null hypothesis and the research hypothesis as well (2) The researcher rejects The Null hypothesis and retains the research hypothesis (3) The researcher rejects both the research hypothesis as well as The Null hypothesis (4) The researcher accepts The Null hypothesis with no decision on the research hypothesis

 

3.    The following example is of a hypothesis in a study undertaken at school level “School children from rural background are prone to less stress as compared to their counterpart in the urban areas”. This statement may be considered as an instance of which type of hypothesis? (1) Principal research hypothesis (2) Action research hypothesis (3) Null hypothesis (4) Directional hypothesis

 

 

 

 

Parametric Test

 

Parametric Test

Descriptive statistics

Descriptive statistics is one of the two main branches of statistics.

Descriptive statistics provide a concise summary of data. We can summarize data numerically or graphically. For example, the manager of a fast food restaurant tracks the wait times for customers during the lunch hour for a week. Then, the manager summarizes the data.

Numeric descriptive statistics

The Researcher calculates the   numeric descriptive statistics:

Graphical descriptive statistics

The Researcher examines the graphs to visualize the wait times.

Inferential statistics 

Inferential statistics is one of the two main branches of statistics. It uses a random sample of data taken from a population to describe and make inferences about the population. Inferential statistics are valuable when examination of each member of an entire population is not convenient or possible. For example, to measure the diameter of each nail that is manufactured in a mill is impractical. We can measure the diameters of a representative random sample of nails. We can use the information from the sample to make generalizations about the diameters of all of the nails.

 

Difference between descriptive and inferential statistics:

1.    Descriptive statistics uses the data to provide descriptions of the population, either through numerical calculations or graphs or tables. Inferential statistics makes inferences and predictions about a population based on a sample of data taken from the population in question.

2.    Descriptive statistics consists of the collection, organization, summarization, and presentation of data. Inferential statistics consists of generalizing from samples to populations, performing estimations and hypothesis tests, determining relationships among variables, and making predictions.

Parametric Tests: Population values are normally distributed.

Reasons to Use Parametric Tests

Reason 1: Parametric tests can perform well with skewed and nonnormal distributions

This may be a surprise but parametric tests can perform well with continuous data that are non-normal if you satisfy the sample size guidelines in the table below.

etric analyses	Sample size guidelines for non-normal data
1-sample t test	Greater than 20
2-sample t test	Each group should be greater than 15
One-Way ANOVA	If you have 2-9 groups, each group should be greater than 15. If you have 10-12 groups, each group should be greater than 20.

Reason 2: Parametric tests can perform well when the spread of each group is different

While nonparametric tests don’t assume that our data follow a normal distribution, they do have other assumptions that can be hard to meet. For nonparametric tests that compare groups, a common assumption is that the data for all groups must have the same spread (dispersion). If our groups have a different spread, the nonparametric tests might not provide valid results.

On the other hand, if we use the 2-sample t test or One-Way ANOVA, we can simply go to the Options sub dialog and uncheck Assume equal variances.

Reason 3: Statistical power

Parametric tests usually have more statistical power than nonparametric tests. Thus, we are more likely to detect a significant effect when one truly exists.

Normal Probability Curve

Normal: It means Average

Probability: It is nothing but a chance of appearing

Curve: A line or outline which gradually deviates from being straight for some or all of its length.

Normal Probability curve is drawn to show the equal distribution of scores in the either side of the mean with a perfect bell-shaped curve without touching the base line.so the right side of the center is a mirror image of the left side.  That is called symmetric. The area under the normal distribution curve represents probability and the total area under the curve sums to one. It is also known as called Gaussian distribution, after the German mathematician Carl Gauss who first described it.

In a normal classroom, we always observe that, most of the students get average marks, very few get excellent marks and very few get poor marks. So if we draw graph or curve of such data we get Normal Probability Curve.

Example: -Many human characteristics like height, weight, strength, learning ability, cooperativeness, social dominance etc.

Application:

1.    To Evaluate student’s performance from their score

2.    To compare two or more distribution terms in of overlapping

3.    To calculate the percentile rank scores in a normal probability distribution.

4.     To normalize a frequency distribution, an important process in standardizing a psychological test or inventory.

5.    To test the significance of observed measures. To find out sampling errors.

6.    To determine the percentage of cases within the given limits or scores.

7.    To know how many students fall below and above the average performance.

8.    It gives the limits of the scores.

9.    To find out the relative difficulty of test items.

10. To find out the number of cases between mean and one standard deviation.

11. To divide a group according to same ability and assigning same grade like A- VERY GOOD B- GOOD C-AVERAGE D-POOR E- VERY POOR

12. To find out the percentage rank of a student from the scores and score from the percentile rank

Non-Parametric Test

                                                                      Non-Parametric Test

Non parametric do not assume that the data is normally distributed. The only non-parametric test you are likely to come across in elementary statistics is the chi-square test. However, there are several others. For example: the Kruskal Willis test is the non-parametric alternative to the One way ANOVA and the Mann Whitney is the non-parametric alternative to the two sample t test.

The main nonparametric tests are:

Ø Sign test : Use this test to estimate the median of a population and compare it to a reference value or target value.

Ø Wilcoxon signed rank test:  With this test, you also estimate the population median and compare it to a reference/target value. However, the test assumes our data comes from a symmetric distribution.  

Ø Friedman test. This test is used to test for differences between groups with ordinal dependent variables. It can also be used for continuous data if the one-way ANOVA with repeated measures is inappropriate.

Ø Kruskal-Wallis test. Use this test instead of a one-way ANOVA to find out if two or more medians are different. Ranks of the data points are used for the calculations, rather than the data points themselves.

Ø Mann-Whitney test. Use this test to compare differences between two independent groups when dependent variables are either ordinal or continuous.

Ø Mood’s Median test. Use this test instead of the sign test when you have two independent samples.

Ø Spearman Rank Correlation  :Use when you want to find a correlation between two sets of data.