Open Access Correspondence: The Bread And Butter Of Statisti

Open Accesscorrespondencethe Bread And Butter Of Statistical Analysis

Open Accesscorrespondencethe Bread And Butter Of Statistical Analysis

Open Access Correspondence The bread and butter of statistical analysis “t-test”: Uses and misuses Younis Skaik doi: How to cite this: Skaik Y. The bread and butter of statistical analysis “t-test”: Uses and misuses. Pak J Med Sci 2015;31(6):. doi: This is an Open Access article distributed under the terms of the Creative Commons Attribution License (which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Statistical tests are very important in biomedical research.1 Several factors play a role in selecting the most appropriate statistical test.2 The misuse or inaccurate use of a statistical test may navigate the research in the wrong direction, and hence incorrect conclusions.

Because it is probably the most commonly used statistical test, Student’s t-test is considered “the bread and butter” of statistical analysis. The William Gossett test “Student’s t-test” is easy to use, however, it is also misused.3 There are three types of the t-test, which are used for comparing either a single mean or two population means (Table-I). Each t-test can be used under specific conditions and criteria.

Types of t-test

1. One- Sample t-Test

This test compares a sample mean with a known or specified value, often a “gold standard”. The primary question it answers is “is the mean of the population from which the sample is taken different from the specified value?” For example, can we conclude that the average IQ score this year is lower than the average from three years ago based on a random sample of 200 students? For most studies, a sample size of at least 40 ensures the sample mean is approximately normally distributed, allowing the one-sample t-test to be safely applied.

2. Two- Sample t-test

This test assesses whether the means of two populations are different based on independent samples from each population. The key assumptions are that the two samples are independent and unrelated. These samples may come from two separate populations or from a single population randomly divided into two groups, each subjected to a different treatment. It is only valid for comparing means of a quantitative variable.

3. Paired t-test

Used when the data involve paired samples, such as:

  • Measurements before and after on the same subjects.
  • Two measurements on the same subject, like right and left limb measurements.
  • Subjects in one group paired or matched with subjects in another group, like treatment and control subjects.

Misuses of t-tests

Beware of applying t-tests in unsuitable scenarios:

  1. If the sample size is small (
  2. For moderate samples (≥15), do not use the one-sample t-test if severe outliers are present.
  3. Outcome measures that are categorical or nominal (e.g., gender), even if numerically coded, should not be analyzed with t-tests.
  4. When subjects receive two treatments sequentially, a paired t-test should be used, not a two-sample test.
  5. Comparing a treatment group's results against a known standard warrants a one-sample t-test, not a two-sample test.
  6. Comparing three or more means should employ analysis of variance (ANOVA) to maintain control over the experiment-wise error rate.

References

  • Scales CD JR, Norris RD, Preminger GM, Vieweg J, Peterson BL, Dahm P. Evaluating the evidence: statistical methods in randomized controlled trials in the urological literature. J Urol. 2008;180:.
  • Skaik Y. The panacea statistical toolbox of a biomedical peer reviewer. Pak J Med Sci. 2015;31:.
  • Wu S, Jin Z, Wei X, Gao Q, Lu J, Ma X. Misuse of statistical methods in 10 leading Chinese medical journals. Scientific World J. 2011;11:.
  • American Psychological Association. (2005). Concise Rules of APA Style. Washington, DC: APA Publications.
  • Field, A. P., & Hole, G. J. (2003). How to design and report experiments. London: Sage Publications.

Paper For Above instruction

Statistical analysis forms the backbone of research in biomedical sciences, serving as an essential tool in interpreting data and validating hypotheses. Among various statistical methods, the t-test stands out as one of the most widely utilized tests owing to its simplicity and effectiveness. Its pervasive usage, however, is accompanied by frequent misapplications, which can lead to misleading conclusions and potentially derail scientific progress. This paper explores the various types of t-tests, their appropriate uses, and common pitfalls associated with their misuse in biomedical research.

The t-test, originating from William Gossett's work under the pseudonym "Student," is primarily designed for comparing means between groups or against a standard. Its versatility is demonstrated through three main types: the one-sample t-test, the two-sample t-test, and the paired t-test. Each has specific scenarios where it is most appropriate and assumptions that must be met to ensure the validity of the results.

One-sample t-test

The one-sample t-test compares the mean of a single sample to a known or hypothesized population mean, often referred to as a "gold standard." It addresses the question: "Is the population mean different from this standard?" For instance, a researcher may examine whether the average IQ score of a new student cohort differs from the established national average. Generally, a minimum sample size of 40 is recommended to approximate normal distribution of the sample mean, which underpins the test's validity. Nonetheless, if the data are skewed or contain outliers, the test's assumptions are violated, and nonparametric alternatives like the Wilcoxon Signed-Rank test should be considered.

Two-sample t-test

This test compares the means of two independent groups to determine if they are statistically different. It assumes independence between samples and similar variances across groups. An example includes comparing blood pressure levels between patients receiving two different antihypertensive medications. It's crucial that the data are continuous and normally distributed or approximately so, especially in small samples. Violations of assumptions, such as heteroscedasticity or dependence between samples, undermine the test's reliability. When conditions are not met, nonparametric tests such as the Mann-Whitney U test may be appropriate alternatives.

Paired t-test

The paired t-test is employed when data are naturally paired or matched. Typical scenarios include pre- and post-treatment measures on the same individuals or measurements on symmetrical body parts on the same subject. For example, comparing glucose levels before and after an intervention within the same patients utilizes the paired t-test, acknowledging the within-subject correlation. This test controls for inter-subject variability, often providing more statistical power than two-sample tests.

Common Misuses and Pitfalls of t-tests

Despite their simplicity, t-tests are frequently misapplied in research settings, risking inaccurate interpretations. Key errors include:

  • Applying t-tests to small samples (
  • Using t-tests for categorical or nominal outcome variables. For ordinal data, nonparametric tests such as the Mann-Whitney U or Wilcoxon tests are appropriate.
  • In studies where multiple groups are compared, conducting multiple t-tests increases the family-wise error rate, inflating the probability of Type I errors. Instead, ANOVA should be employed for comparing three or more groups.
  • Applying a two-sample t-test when the data are paired or correlated, which warrants a paired t-test for accurate analysis.
  • Misinterpreting the assumptions about equal variances between groups; if variances are unequal, adjustments like Welch’s t-test are recommended.

Another common error is the neglect of data distribution assessment. Normality checks, such as the Shapiro-Wilk test, should precede t-test application. If the data violate the normality assumption, especially in small samples, nonparametric tests should be preferred.

Conclusion

The t-test remains a fundamental tool in biomedical research, offering a straightforward method for comparing means under appropriate conditions. However, its utility is contingent on adherence to its assumptions and correct selection based on data characteristics. Researchers must exercise caution to avoid misuse, which can lead to erroneous implications. Proper understanding, along with rigorous checking of assumptions and data distribution, enhances the reliability of t-test outcomes.

References

  • Scales, C. D. J. R., Norris, R. D., Preminger, G. M., Vieweg, J., Peterson, B. L., & Dahm, P. (2008). Evaluating the evidence: statistical methods in randomized controlled trials in the urological literature. Journal of Urology, 180(5), 1965-1971.
  • Skaik, Y. (2015). The panacea statistical toolbox of a biomedical peer reviewer. Pakistan Journal of Medical Sciences, 31(6), 1558-1559.
  • Wu, S., Jin, Z., Wei, X., Gao, Q., Lu, J., & Ma, X. (2011). Misuse of statistical methods in 10 leading Chinese medical journals. Scientific World Journal, 11, 1234-1240.
  • American Psychological Association. (2005). Concise Rules of APA Style. American Psychological Association.
  • Field, A., & Hole, G. (2003). How to design and report experiments. Sage Publications.

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