What are 2 factors influence sampling procedure?

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Factors that Affect the Power of a Statistical Procedure

As discussed on the page Power of a Statistical Procedure, the power of a statistical procedure depends on the specific alternative chosen (for a hypothesis test) or a similar specification, such as width of confidence interval (for a confidence interval).

The following factors also influence power:1. Sample SizePower depends on sample size. Other things being equal, larger sample size yields higher power. Example and more details.

2. VariancePower also depends on variance: smaller variance yields higher power. Example: The pictures below each show the sampling distribution for the mean under the null hypothesis µ = 0 (blue -- on the left in each picture) together with the sampling distribution under the alternate hypothesis µ = 1 (green -- on the right in each picture), both with sample size 25, but for different standard deviations of the underlying distributions. (Different standard deviations might arise from using two different measuring instruments, or from considering two different populations.)

• In the first picture, the standard deviation is 10; in the second picture, it is 5. 
• Note that both graphs are in the same scale. In both pictures, the blue curve is centered at 0 (corresponding to the the null hypothesis) and the green curve is centered at 1 (corresponding to the alternate hypothesis).
• In each picture, the red line is the cut-off for rejection with alpha = 0.05 (for a one-tailed test) -- that is, in each picture, the area under the blue curve to the right of the red line is 0.05. 
• In each picture, the area under the green curve to the right of the red line is the power of the test against the alternate depicted. Note that this area is larger in the second picture (the one with smaller standard deviation) than in the first picture. 

   

The Claremont University's Wise Project's Statistical Power Applet and the Rice Virtual Lab in Statistics' Robustness Simulation can be used to illustrate this dependence in an interactive manner.

Variance can sometimes be reduced by using a better measuring instrument, restricting to a subpopulation, or by choosing a better experimental design (see below).

3. Experimental DesignPower can sometimes be increased by adopting a different experimental design that has lower error variance. For example, stratified sampling or blocking can often reduce error variance and hence increase power. However,

• The power calculation will depend on the experimental design. 
• The statistical analysis will depend on the experimental design. (See
  Using an inappropriate model or research design.)

For more on designs that may increase power, see:

• Lipsey, MW (1990). Design sensitivity: Statistical power for experimental research. Newbury Park, CA: Sage.
• McClelland, Gary H. (2000) Increasing statistical power without increasing sample size, American Psychologist 55(8), 963 - 964

Last updated June 2012

The sample size is the number of participants or specimen required in a study and its estimation is important for both in vivo and in vitro studies. The sample size establishes the power and the impact of the study. The determined size should be optimum and has to be obtained by the scientific method. The arbitrary calculation with less or more can affect the study design and its significance. The larger size can lead to ethical concerns, time consumption, and financial wastage, and smaller sample size affects the effectiveness of the study.[1]

The sample size evaluation primarily depends on the study design and the outcome which is estimated prior to the start of the study. The determination varies with the statistical inference of the study which is done by either confidence interval technique (estimation) or test of significance procedure (hypothesis testing).

The factors affecting sample sizes are study design, method of sampling, and outcome measures – effect size, standard deviation, study power, and significance level.[2,3] The differences exist between the different types of study design alike description and analytical study. In general, the descriptive studies such as questionnaire and surveys require large sample size than analytical studies. All observational studies require more samples than the experimental studies. The estimation varies with the grouping, control, and population size in randomized clinical trials, observational and epidemiological studies. The studies of nonrandomized clinical study, multiple grouping, require more samples. The qualitative data outcome measures require more samples than the quantitative data.

The sample size for a study can be calculated from the standard deviation, significance, power, and effect size.[4,5] The standard deviation and effect size can be either determined from previous studies from literature or from pilot studies. The investigator's consideration on the effect of study plays a critical role in sample size estimation. If the investigator prefers to detect small effect size, it shall be better appreciated with an increased sample size.[6]

The significance level (type 1 error) and the power of the study are fixed before the study. The significance level is normally set at 0.05 or 0.01. For more accuracy, the significance level should be set at lower levels which increase the sample sizes. Anything more than these two levels can affect the study impact and should be done with caution unless it is essential for the study design. For appreciable inference, the power is normally set at 20% chance of missing difference or 80% chance of detecting a difference as statistically significant. This shall provide appreciable study impact.

Numerous methods are listed in literature to estimate the sample size. The researcher should adapt an effective, simple, and consistent system. Negligible errors in formula, grouping, statistical baseline values, study design, and the outcome measures can lead to faulty estimation with major impact on the external validity of the study. It is essential to consider all vital issues, more importantly the loss during follow-up. Nearly 10% of additional samples should be considered to the computed sample size for the follow-up loss.

The sample sizes are determined by nomograms, formulas, tables, and software.[7,8] There are published statistical tables, which provide the sample size for various situations. The statistical tables determine the sample sizes based on efficacy, confidence levels, and variability. It is an easier method comparatively but has assumptions and variability. Similar to the statistical tables, the nomograms determine the sample size with the effect size, standard difference, and confidence interval.

The formula for sample size estimation varies with the type of study designs. It is the more effective way in determining the sample size. It is cumbersome and difficult to the beginners and hence it is wise to take the help of a statistician before the start of the study. The easiest way to determine sample size is with the software. The sample size is determined by software using a target variance, power of statistical test, and confidence interval. G*Power, PS, Russ Lenths power, Minitab, Stata, R package, PASS, and SampSize app are some of the software available to determine the sample size. Unlike using the complicated formulae, these software programs have made the calculation easier and simpler. A caution has to be ascertained during the use of these tools. Understanding of the research design and knowledge on common errors is mandatory. It is essential that these errors are controlled.

The studies in prosthodontics require more effective sample size estimations. It is necessary that all manuscripts either in vivo or in vitro have the sample size estimation. Many of the in vitro studies do not have effective determination and not stated clearly in the manuscript. If the earlier literature was used to determine, then it should effectively match in terms of materials, design, and standardization used in the study and it must be cited in the manuscript. A change of materials cannot be considered for sample size estimation. If no ideal study exist, it is always mandatory that a pilot study should be done to determine the effective sample size. Many studies lack clinical relevance due to inadequate sample size. This shall provide better impact, appreciation, and acceptance from the journals.

REFERENCES

1. Noordzij M, Dekker FW, Zoccali C, Jager KJ. Sample size calculations. Nephron Clin Pract. 2011;118:c319–23. [PubMed] [Google Scholar]

3. Fritz CO, Morris PE, Richler JJ. Effect size estimates: Current use, calculations, and interpretation. J Exp Psychol Gen. 2012;141:2–18. [PubMed] [Google Scholar]

4. Indrayan A, Gupta P. Sampling techniques, confidence intervals, and sample size. Natl Med J India. 2000;13:29–36. [PubMed] [Google Scholar]

5. Lenth RV. Some practical guidelines for effective sample size determination. [Last accessed on 2017 Jul 10];Am Stat. 2001 55:187–93. Available from: http://www.jstor.org/stable/2685797 . [Google Scholar]

6. Lieber RL. Statistical significance and statistical power in hypothesis testing. J Orthop Res. 1990;8:304–9. [PubMed] [Google Scholar]

7. Charan J, Biswas T. How to calculate sample size for different study designs in medical research? Indian J Psychol Med. 2013;35:121–6. [PMC free article] [PubMed] [Google Scholar]

8. Lakshminarayan N. Know your data before you undertake research. J Indian Prosthodont Soc. 2013;13:384–6. [Google Scholar]

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