SEQUENTIAL SAMPLING

Author : Jayashree Jadhav S (2048125)

Sequential sampling is a non-probability sampling technique wherein the researcher picks a single or a group of subjects in a given time interval, conducts his study, analyses the results then picks another group of subjects if needed and so on.

This sampling technique gives the researcher limitless chances of fine tuning his research methods and gaining a vital insight into the study that he is currently pursuing

In sequential sampling, a sequence of one or more samples is taken from a group. Once the group has been sampled, a hypothesis test is performed to see if you can reach a conclusion. If you can’t, the whole procedure is repeated. A characteristic feature of sequential sampling is that the sample size is not set in advance, because you don’t know at the outset how many times you’ll be repeating the process.



Difference of Sequential Sampling from All Other Sampling Techniques

If we are to consider all the other sampling techniques in research, we will all come to a conclusion that the experiment and the data analysis will either boil down to accepting the null hypothesis or disproving the null hypothesis while accepting the alternative hypothesis.

 

 In sequential sampling technique, there exists another step, a third option. The researcher can accept the null hypothesis, accept his alternative hypothesis, or select another pool of subjects and conduct the experiment once again. This entails that the researcher can obtain limitless number of subjects before finally making a decision whether to accept his null or alternative hypothesis.

This method is designed for two clear choices. For example:

·         Is the heat in a system above or below a critical level? Heat is measured in one part of the system to see if it has reached the critical level. If the heat is close to the critical level, but not over it, resample and repeat the calculations.

·         Should I spray pesticide or not? Pests could be counted on a plant. If there are a large number of pests, spray pesticide. If there are a small number of pests, do not spray pesticide. If there are a middling number of pests, sample another plant.

Sequential samples can either be:

·         Item-by-item: one sample at a time.

·         Group: sample sizes of two or more.

 

In order to use this method, you must be able to sample serially. If you have to choose all of your sample items at the same time, you should choose another sampling method (like simple random sampling or a non-probability sampling method).

Three Outcomes

With traditional sampling methods, a hypothesis test has one of two possible results: you either reject the null hypothesis, or you do not. With sequential sampling, you have three possibilities:

1.       Reject the null hypothesis (end the experiment),

2.       Do not reject the null hypothesis (end the experiment),

3.       Fail to draw any conclusion (draw another sample and repeat the test).

Time-Sequential Sampling

In this variant, sometimes called time-sequential classification, you use time as your sampling frame instead of a physical population to sample from. For example, you might choose a sample member at 24-hour intervals.

Advantages of Sequential Sampling

1.     Although it sounds like the process could go on and on forever, sequential sampling usually ends up with smaller samples than traditional (set size) sampling.

The researcher has a limitless option when it comes to sample size and sampling schedule. The sample size can be relatively small of excessively large depending on the decision making of the researcher. Sampling schedule is also completely dependent to the researcher since a second group of samples can only be obtained after conducting the experiment to the initial group of samples.

As mentioned above, this sampling technique enables the researcher to fine-tune his research methods and results analysis. Due to the repetitive nature of this sampling method, minor changes and adjustments can be done during the initial parts of the study to correct and hone the research method.


There is very little effort in the part of the researcher when performing this sampling technique. It is not expensive, not time consuming and not workforce extensive.

Disadvantages of Sequential Sampling

1.     However, the mathematics needed to analyse data for sequential sampling is much more complex and the procedure is generally more time consuming (and can be more expensive) than fixed-size sampling.

2.      This sampling method is hardly representative of the entire population. Its only hope of approaching representativeness is when the researcher chose to use a very large sample size significant enough to represent a big fraction of the entire population.

3.      The sampling technique is also hardly randomized. This contributes to the very little degree representativeness of the sampling technique.


Due to the above mentioned disadvantages, results from this sampling technique cannot be used to create conclusions and interpretations pertaining to the entire population.

Sequential Analysis with R Programming 

The package Sequential is designed for continuous and group sequential analysis, where statistical hypothesis testing is conducted repeatedly on accumulating data that gradually increases the sample size. This is different from standard statistical analysis, where a single analysis is performed using a fixed sample size. It is possible to analyze either Poisson type data or binomial 0/1 type data. For binomial data, it is possible to incorporate an off-set term to account for variable matching ratios. For Poisson data, the critical value is based on a Wald-type upper boundary, which is flat on the scale of the log-likelihood ratio, and on a predetermined maximum sample size. Alternatively, it is also possible to apply a user defined alpha spending function in order to specify non-flat signaling thresholds. For group sequential analyses, there are functions for pre-specified group sizes and for the situation when the group sizes are not known a priori. It is also possible to perform mixed continuous/group sequential analysis, where, for example, there is at first a big batch of data that arrives in one group, followed by continuous sequential analysis. All results are exact, based on iterative numerical calculations, rather than asymptotic theory or computer simulations. In the Sequential package, there are functions to calculate critical values, statistical power, expected time to signal, and expected sample size at the end of the sequential analyses whether the null hypothesis was rejected or not. For example, for any desired power, relative risk and alpha level, the package can calculate the required upper limit on the sample size (maximum length of surveillance), the critical value needed, and the corresponding expected time to signal when the null hypothesis is rejected.









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