Inferential Statistics
- Inferential Statistics – Definition, Types, Examples, Formulas
- Observational Studies and Experiments
- Sample and Population
- Sampling Bias
- Sampling Methods
- Research Study Design
- Population Distribution, Sample Distribution and Sampling Distribution
- Central Limit Theorem
- Point Estimates
- Confidence Intervals
- Introduction to Bootstrapping
- Bootstrap Confidence Interval
- Paired Samples
- Impact of Sample Size on Confidence Intervals
- Introduction to Hypothesis Testing
- Writing Hypotheses
- Hypotheses Test Examples
- Randomization Procedures
- p-values
- Type I and Type II Errors
- P-value Significance Level
- Issues with Multiple Testing
- Confidence Intervals and Hypothesis Testing
- Inference for One Sample
- Inference for Two Samples
- One-Way ANOVA
- Two-Way ANOVA
- Chi-Square Tests
Sampling Methods
Sampling Methods | Types, Techniques & Examples
When conducting research, researchers rarely collect data from every person in a group; instead, they select a sample. To draw valid conclusions from research results, one must carefully choose a sampling method to select a sample that is representative of the group as a whole. There are two primary types of sampling methods in research:
- probability sampling
- non-probability sampling.
Probability sampling involves random selection, allowing researchers to make strong statistical inferences about the whole group.
Non-probability sampling involves non-random selection based on convenience or other criteria, allowing researchers to easily collect data.
Probability sampling methods
Probability sampling is a method of selecting a sample from a population where each individual in the population has an equal chance of being selected. There are several probability sampling methods:
1. Simple random sampling
Each member of the population has an equal chance of being selected. This is typically done by assigning a number to each member of the population and then using a random number generator to select the sample.
Simple random sampling method is a procedure for selecting sample elements from a population. Simple random sampling refers to a sampling method that has the following properties.
- The population consists of N objects.
- The sample consists of n objects.
- All possible samples of n objects are equally likely to occur.
Here we randomly select cases from the population such that each case is equally likely to be selected.
2. Systematic sampling
Systematic sampling method involves selecting every nth member of the population after randomly selecting a starting point.
3. Stratified sampling
In Stratified sampling, population is divided into strata (subgroups) based on specific characteristics, and a random sample is taken from each stratum. This method ensures that each stratum is represented in the sample.
So, in stratified sampling, we divide the population into homogenous group called strata, then randomly sample from within each stratum. If you want to conduct a survey and first you divide the population as male and female them collect randomly 100 female and 100 male then it is called Stratified Sampling.
4. Cluster sampling
In Cluster sampling, population is divided into clusters based on geographic or other characteristics, and a random sample of clusters is selected. Then, all individuals in the selected clusters are included in the sample.
So, in cluster sample, we divide the population in clusters or groups. Then randomly sample a few clusters then randomly sample from within these clusters. Here Sampling error is greater than with random sampling. The main difference between Stratified sampling and cluster sampling is clusters may not be homogeneous.
5. Multi-stage sampling
This method involves using a combination of sampling methods to select the sample. For example, stratified sampling may be used to select clusters, and then simple random sampling may be used to select individuals within those clusters.
Below are the four main types of probability sample.
Non-probability sampling methods
Non-probability sampling methods are a type of sampling method where individuals in the population do not have an equal chance of being selected for the sample. Non-probability sampling methods are typically used when probability sampling methods are not feasible or practical.
Here are some common non-probability sampling methods:
1. Convenience sampling
This method involves selecting individuals who are readily available or easy to access. Convenience sampling is often used in studies where time and resources are limited. Convenience sampling is a non-probability sampling method where participants are selected based on their ease of access or availability.
For example, a researcher may choose to survey people in a shopping mall, university campus, or a specific location where participants can be easily approached. However, convenience sampling can lead to biased results because the sample may not be representative of the entire population.
Suppose you are conducting a survey on job employment of woman and man. Now neighbors of yours are very easily accessible to you and they are more likely to be include in your sample. If you do that then your inference will suffer from convenience sampling bias.
“Statistical inference with convenience samples is a risky business.”- David A. Freedman, Statistical Models and Causal Inference, p. 23
If a convenience sample is used, inferences are not as trustworthy as if a random sample is used.
2. Snowball sampling
This method involves selecting individuals who can refer other individuals to participate in the study. This method is often used when the population is difficult to access or identify.
3. Quota sampling
This method involves selecting individuals based on predetermined quotas, such as a certain number of males or females, a certain age range, or a certain educational level.
4. Purposive sampling
Purposive sampling is a method involves selecting individuals who meet certain predetermined criteria. This method is often used in qualitative research, where the focus is on selecting individuals who can provide rich and detailed information on a specific topic.
Non-probability sampling methods are generally considered less representative of the population than probability sampling methods, as they do not ensure that every member of the population has an equal chance of being selected for the sample. However, non-probability sampling methods can be useful in certain research contexts, such as exploratory studies or when the population is difficult to access.
Other Sources of Bias
Previously, you learned about sampling bias and how simple random sampling methods can be used to avoid sampling bias.
Here, we will discuss three other sources of bias: non-response bias, voluntary response bias, and response bias. These are both problems that should be prevented in the design of a research study.
Non-Response Bias
Systematic favoring of certain outcomes that occurs when the individuals who choose participate in a study differ from the individuals who choose to not participate.
If only a fraction of the randomly sampled people respond to your survey such that the sample is no longer repetitive of the population then it suffers from non-response bias.
Suppose you are conducting a survey on drug intake rate used by young students. In this case, some students might not reveal the information for personal reason. This is called non-response sample bias.
Voluntary Response Bias
Voluntary response, refers to a sampling bias that occurs when participants self-select into a study. This can happen when participants are invited to participate in a study, but are not required to do so, and choose whether or not to participate based on their own preferences or motivations. Participants who are more interested in the topic being studied or who have strong opinions about the topic may be more likely to volunteer to participate, which can bias the results of the study.
So, voluntary response occurs when sample consist of people who volunteer to respond because they have strong opinion on the issue. Often, voluntary response samples oversample people who have strong opinions and undersample people who don’t care much about the topic of the survey. Thus inferences from a voluntary response sample are not as trustworthy as conclusions based on a random sample of the entire population under consideration. Note that in voluntary response there is no initial random sample.
Response Bias
Response bias refers to a systematic tendency for participants in a study to respond in a certain way, based on factors unrelated to the research question or the true underlying phenomenon being studied. Response bias can be caused by factors such as social desirability, demand characteristics, or acquiescence bias. For example, if a participant in a study feels pressure to give an answer that they think will be viewed favorably by the researcher, rather than providing their true beliefs or experiences, this would be an example of response bias.
So , it is systematic favoring of certain outcomes that occurs when participants do not respond truthfully; they may do so to align with social norms or to appease the researcher.
What is simple Random Sampling and Random Assignment?
Simple Random Sampling and Random Assignment are two statistical techniques used in research and experimental design.
Simple Random Sampling is a technique used to select a random sample from a population, in which each member of the population has an equal chance of being selected. This is typically done by assigning a number to each member of the population and then using a random number generator to select the sample. This technique is useful in minimizing bias in the sample and increasing the generalizability of the results to the entire population.
Random Assignment, on the other hand, is a technique used in experimental design to assign participants to different treatment groups randomly. This ensures that any differences between the groups are due to the treatment they receive and not due to pre-existing differences between the participants. Random Assignment is crucial in reducing bias in the experiment and increasing the validity of the results.
Random sampling and random assignment are commonly confused or used interchangeably, though the terms refer to entirely different processes.
If subjects are selected from the population randomly and each members of population has equal chance to get selected and the sample is the representative of the entire population then it is called random sampling. Therefore the studies result are generalizable for population at large. Random assignment is an aspect of experimental design in which study participants are assigned to the treatment or control group using a random procedure.
What is Sampling with Replacement and Without Replacement?
Sampling with replacement and without replacement are two techniques used in statistics for selecting samples from a population.
Sampling with replacement refers to a technique where a unit in a sample is selected from a population, and after it is selected, it is replaced back into the population. This means that the unit may be selected more than once, and it has the same chance of being selected each time.
For example, if you have a bag of ten marbles, and you select one at random with replacement, you could select the same marble multiple times, and each time, you would have a 1 in 10 chance of selecting it.
Sampling without replacement, on the other hand, is a technique where a unit is selected from a population and not replaced back into the population. This means that once a unit has been selected, it cannot be selected again.
For example, if you have a bag of ten marbles, and you select one at random without replacement, you cannot select the same marble again, and the probability of selecting each remaining marble will change after each selection.
Suppose you pick a card from the deck, you can put the card aside or you can put it back into the deck. If you put the card back into the deck, it may be selected more than once; if we put it aside, it can be selected only one time.
When a population element can be selected more than one time, we are sampling with replacement. When a population element can be selected only one time, we are sampling without replacement.