INFERENTIAL STATISTICS
What is the INFERENTIAL STATISTICS?
Inferential statistics is one of the two main branches of statistics. Inferential statistics use 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.
What is SAMPLING?
Sampling is a method of studying from a few selected items,instead of the entire big number of units. The small selection is called sample. The large number of items of units of particular characteristic is called population. Example: We check a sample of rice to see whether the rice well boiled or not. We check a small sample of solution to decide how much a given solution is concentrated
What is the condition or the thing that is necessary for the Sampling to be representative?
In sampling, we assume that samples are drawn from the population and sample means and population means are equal. A population can be defined as a whole that includes all items and characteristics of the research taken into study. However, gathering all this information is time consuming and costly. We therefore make inferences about the population with the help of samples.
What is SAMPLING ERROR?
In statistics, sampling error is the error caused by observing a sample instead of the whole population. The sampling error is the difference between a sample statistic used to estimate a population parameter and the actual but unknown value of the parameter.
What is INFERENCE error?
Inference error versus number of observations. The proportional error (i.e., inference error) denotes the minimal cross-validation error divided by the minimal least-squares error of the linear regression without any regularization terms and averaged over five random networks. The proportional errors
What is POPULATION?
In stats, a sample is a part of a population. A population is a whole, it's every member of a group. A population is the opposite to a sample, which is a fraction or percentage of a group. Sometimes it's possible to survey every member of a group. A classic example is the U.S. Census, where it's the law that you have to respond. Note: if you do manage to survey everyone, it actually is called a census: The U.S. Census is just one example of a census. In most cases, it's impractical to survey everyone. Imagine how long it would take you to call every dog owner in the U.S. to find out what their preferred brand of dog food was. In addition, sometimes people either don't want to respond or forget to respond, leading to incomplete censuses. Incomplete censuses become samples by definition.
What is SAMPLE? In statistics, you'll be working with samples. A sample is just a part of a population. For example, if you want to find out how much the average American earns, you aren't going to want to survey everyone in the population (over 300 million people), so you would choose a small number of people in the population. For example, you might select 10,000 people.
There are two types of SAMPLINGS: Probability and Nonprobability. Please describe each one.
In sampling, we assume that samples are drawn from the population and sample means and population means are equal. A population can be defined as a whole that includes all items and characteristics of the research taken into study. However, gathering all this information is time consuming and costly. We therefore make inferences about the population with the help of samples.
Probability sampling is the sampling technique in which every individual unit of the population has greater than zero probability of getting selected into a sample.
Non-probability sampling is the sampling technique in which some elements of the population have no probability of getting selected into a sample.
Which are the types of NONPROBABILITY SAMPLING?
Convenience Sampling
Convenience sampling is probably the most common of all sampling techniques. With convenience sampling, the samples are selected because they are accessible to the researcher. Subjects are chosen simply because they are easy to recruit. This technique is considered easiest, cheapest and least time consuming.
Quota Sampling
Quota sampling is a non-probability sampling technique wherein the researcher ensures equal or proportionate representation of subjects depending on which trait is considered as basis of the quota.
Snowball Sampling
Snowball sampling is usually done when there is a very small population size. In this type of sampling, the researcher asks the initial subject to identify another potential subject who also meets the criteria of the research. The downside of using a snowball sample is that it is hardly representative of the population.
Judgmental Sampling
Judgmental sampling is more commonly known as purposive sampling. In this type of sampling, subjects are chosen to be part of the sample with a specific purpose in mind. With judgmental sampling, the researcher believes that some subjects are more fit for the research compared to other individuals. This is the reason why they are purposively chosen as subjects.
Consecutive Sampling
Consecutive sampling is very similar to convenience sampling except that it seeks to include ALL accessible subjects as part of the sample. This non-probability sampling technique can be considered as the best of all non-probability samples because it includes all subjects that are available that makes the sample a better representation of the entire population.
What is the SAMPLE size?
The number (n) of observations taken from a population through which statistical inferences for the whole population are made.
The concept of sampling from a larger population to determine how that population behaves, or is likely to behave, is one of the basic premises behind the science of applied statistics.
Which are the types of PROBABILITY SAMPLING?
Simple random sampling: By using the random number generator technique, the researcher draws a sample from the population called simple random sampling. Simple random samplings are of two types. One is when samples are drawn with replacements, and the second is when samples are drawn without replacements.
Equal probability systematic sampling: In this type of sampling method, a researcher starts from a random point and selects every nth subject in the sampling frame. In this method, there is a danger of order bias.
Stratified simple random sampling: In stratified simple random sampling, a proportion from strata of the population is selected using simple random sampling. For example, a fixed proportion is taken from every class from a school.
Multistage stratified random sampling: In multistage stratified random sampling, a proportion of strata is selected from a homogeneous group using simple random sampling. For example, from the nth class and nth stream, a sample is drawn called the multistage stratified random sampling.
Expert sampling: This method is also known as judgment sampling. In this method, a researcher collects the samples by taking interviews from a panel of individuals known to be experts in a field.
Analyzing non-response samples: The following methods are used to handle the non-response sample
Dealing with missing data: In statistics analysis, non-response data is called missing data. During the analysis, we have to delete the missing data, or we have to replace the missing data with other values. In SPSS, missing value analysis is used to handle the non-response data.
Weighting: Weighting is a statistical technique that is used to handle the non-response data. Weighting can be used as a proxy for data. In SPSS commands, "weight by" is used to assign weight. In SAS, the "weight" parameter is used to assign the weight.
Cluster sampling: Cluster sampling occurs when a random sample is drawn from certain aggregational geographical groups.
Multistage cluster sampling: Multistage cluster sampling occurs when a researcher draws a random sample from the smaller unit of an aggregational group.
Types of non-random sampling: Non-random sampling is widely used in qualitative research. Random sampling is too costly in qualitative research. The following are non-random sampling methods:
Quota sampling: This method is similar to the availability sampling method, but with the constraint that the sample is drawn proportionally by strata.
Availability sampling: Availability sampling occurs when the researcher selects the sample based on the availability of a sample. This method is also called haphazard sampling. E-mail surveys are an example of availability sampling.