The problem with unadjusted multiple and sequential statistical testing by Statswork

- Large number of statistical tests are performed, then there will be a chance of increased false

Bonferroni correction

positive rates or there will be the problem of multiple testing for the sample considered. - Bonferroni correction will be carried out to deal with the multiple testing problems without making any adjustments. - This Bonferroni correction have serious drawback.

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DRAWBACKS OF BONFERRONI CORRECTION

• We perform multiple independent tests, then the probability or chance of getting atleast one false positive is calculated as 1-(1-0.05)^n. • Suppose if n=10, then the probability will be 40.14 %, which is very high. • In such situations, the use of Bonferroni correction is not appropriate.

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Sequential testing

• Sequential testing problem is an alternative to cope up with the multiple testing problems. • Sequential testing means the researchers collect the data until we reach the fixed threshold. • It takes more effort, time and it's expensive in practice. • One can check the decreasing p-value when the samples are tested sequentially.

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Uncorrected Multiple Testing Procedure This procedure seems comfortable, it will have an impact on the estimated values.

When we do sampling sequentially, researchers often face an effect of over estimates.

Uncorrected multiple testing procedure, one would impose the stopping rule, say, stop the process once the false positive rate reaches 25%.

In the same way, sequential testing problem have a serious drawback.

04 05

Effect size is also result in bias nature.

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If, we impose any stopping rule also it will exceed the limit and gives a false discovery rate.

This kind of testing affects the estimated values apart from the probability values.

Sequential sampling, distance between both group means will increase or decrease and if one wish to continue the process of sampling till both groups yields significant results.

Hence, the sequential testing is biased in significance and also in effect size.

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Problem of Sequential and Multiple Testing

Sample size significance for the simulated 10000 sequential strategies.

From the graph, it is noted that the sequential testing (blue curve) is less severe than the uncorrelated multiple testing (red curve).

Problem of Unadjusted Sequential Testing

Concept of sequential testing is actually a great idea only if we make necessary corrections to make the sample to be larger in size.

If we sample the data sequentially in smaller bits and achieve the fixed limit means we actually increasing the sample size to attain our goal.

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• Group sequential analysis or interim analysis the researcher have to make an priori specifications about the data. • For instance, one should make the prior decision that the samples should be taken as 50 samples in first level, 100 in second level, etc., and stops when the desired result is obtained. • Main advantage of this technique is that one can stop the data collection when the desired level is obtained.

Group Sequentia l Analysis

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• Full sequential technique, there is no prior

FULL SEQUENTIAL TECHNIQUE

arrangements is needed. • In early 1940s, Walds used this technique in computing the cumulative log-likelihood ratio for each observation collected and stops the process when a pre-defined threshold is achieved. • This is something like the case in interim analysis. • However, the full sequential technique is not practical. • Suppose if a researcher wants to analyse the sample of 20 group therapy participants, then this may not be appropriate but the group sequential analysis will serves a purpose.

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CONCLUSION S.No

Method Non-sequential analysis

Group sequential analysis

Full sequential analysis

Description

Sample size needed

It collects a single sample and perform the analysis in later stage. It's an straight forward method but has an disadvantage is that one might collect more data than necessary. It is also called an interim analysis which make use of a priori decisions for the analysis and stops when significance is reached. Unlike the above case, it does not requires a prior specifications. It computes a statistical analysis based on the sample once the observation is recorded and stops data collection when it lies outside the specified limit.

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Large

Moderate

Low

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