how to find p value from confidence interval

Dtsch Arztebl Int. 2009 May; 106(19): 335–339.

Review Article

Confidence Interval or P-Value?

Part 4 of a Series on Evaluation of Scientific Publications

Jean-Baptist du Prel

^oneJohannes Gutenberg-Universität Mainz: Zentrum für Kinder- und Jugendmedizin, Zentrum Präventive Pädiatrie

Gerhard Hommel

²Johannes Gutenberg-Universität Mainz: Institut für Medizinische Biometrie, Epidemiologie und Informatik

Bernd Röhrig

^twoJohannes Gutenberg-Universität Mainz: Institut für Medizinische Biometrie, Epidemiologie und Informatik

Maria Blettner

²Johannes Gutenberg-Universität Mainz: Institut für Medizinische Biometrie, Epidemiologie und Informatik

Received 2008 Jul 23; Accepted 2008 Aug 21.

Abstract

Groundwork

An understanding of p-values and confidence intervals is necessary for the evaluation of scientific articles. This commodity will inform the reader of the significant and interpretation of these two statistical concepts.

Methods

The uses of these 2 statistical concepts and the differences between them are discussed on the basis of a selective literature search concerning the methods employed in scientific articles.

Results/Conclusions

P-values in scientific studies are used to determine whether a zip hypothesis formulated before the operation of the study is to be accepted or rejected. In exploratory studies, p-values enable the recognition of any statistically noteworthy findings. Confidence intervals provide information about a range in which the true value lies with a certain degree of probability, likewise as about the management and forcefulness of the demonstrated outcome. This enables conclusions to be drawn well-nigh the statistical plausibility and clinical relevance of the written report findings. Information technology is often useful for both statistical measures to exist reported in scientific articles, considering they provide complementary types of information.

Keywords: publications, clinical enquiry, p-value, statistics, conviction interval

People who read scientific articles must be familiar with the estimation of p-values and confidence intervals when assessing the statistical findings. Some volition have asked themselves why a p-value is given as a measure of statistical probability in sure studies, while other studies give a conviction interval and still others give both. The authors explain the two parameters on the footing of a selective literature search and depict when p-values or confidence intervals should exist given. The two statistical concepts will and then be compared and evaluated.

What is a p-value?

In confirmatory (evidential) studies, null hypotheses are formulated, which are then rejected or retained with the help of statistical tests. The p-value is a probability, which is the result of such a statistical examination. This probability reflects the measure of evidence against the null hypothesis. Small-scale p-values correspond to strong testify. If the p-value is beneath a predefined limit, the results are designated as "statistically meaning" (ane). The phrase "statistically striking results" is also used in exploratory studies.

If it is to be shown that a new drug is better than an former one, the first step is to show that the two drugs are not equivalent. Thus, the hypothesis of equality is to be rejected. The cypher hypothesis (H₀) to be rejected is then formulated in this example as follows: "In that location is no difference between the ii treatments with respect to their result." For example, there might exist no difference between two antihypertensives with respect to their power to reduce blood pressure level. The culling hypothesis (H_ane) so states that at that place is a difference between the two treatments. This can either exist formulated as a two-tailed hypothesis (whatever difference) or as a one-tailed hypothesis (positive or negative effect). In this case, the expression "one-tailed" means that the direction of the expected effect is laid down when the alternative hypothesis is formulated. For example, if at that place is clear preliminary prove that an antihypertensive has on average a stronger hypertensive upshot than the comparator drug, the alternative hypothesis tin can be formulated as follows: "The difference between the mean hypotensive activity of antihypertensive 1 and the hateful hypotensive action of antihypertensive 2 is positive." Nevertheless, as this requires plausible assumptions almost the direction of the effect, the two-tailed hypothesis is often formulated.

For case, the data from a randomized clinical study are to be used to estimate the effect force relevant to the question to be answered. This could, for example, exist the difference betwixt the mean subtract in blood pressure level with a new and with an old antihypertensive. On this basis, the nothing hypothesis formulated in accelerate is tested with the help of a significance exam. The p-value gives the probability of obtaining the present test upshot—or an even more than farthermost one—if the nada hypothesis is correct. A small-scale p-value signifies that the probability is small-scale that the difference can purely exist assigned to chance. In our instance, the observed difference in mean systolic pressure level might not be due to a existent difference in the hypotensive activity of the two antihypertensives, but might exist due to chance. Nevertheless, if the p-value is < 0.05, the chance that this is the case is under 5%. To permit a decision betwixt the zippo hypothesis and the culling hypothesis, significance limits are oft specified in advance, at a level of significance α. The level of significance of 0.05 (or five%) is often called. If the p-value is less than this limit, the event is significant and it is agreed that the cypher hypothesis should be rejected and the alternative hypothesis—that in that location is a difference—is accepted. The specification of the level of significance also fixes the probability that the null hypothesis is wrongly rejected.

P-values alone exercise not allow whatsoever direct statement almost the direction or size of a divergence or of a relative risk between dissimilar groups (1). Even so, this would exist particularly useful when the results are not significant (2). For this purpose, confidence limits contain more information. Aside from p-values, at to the lowest degree a measure of the effect strength must be reported—for example, the difference between the mean decreases in blood pressure in the two treatment groups (3). In the final assay, the definition of a significance limit is capricious and p-values can be given even without a significance limit being selected. The smaller the p-value, the less plausible is the null hypothesis that in that location is no divergence between the treatment groups.

Confidence limits—from the dichotomous test conclusion to the outcome range estimate

The confidence interval is a range of values calculated by statistical methods which includes the desired truthful parameter (for case, the arithmetic mean, the difference between 2 means, the odds ratio etc.) with a probability defined in accelerate (coverage probability, confidence probability, or confidence level). The conviction level of 95% is commonly selected. This means that the confidence interval covers the true value in 95 of 100 studies performed (four, v). The advantage of conviction limits in comparison with p-values is that they reflect the results at the level of data measurement (half dozen). For case, the lower and upper limits of the hateful systolic blood pressure level difference between the two handling groups are given in mm Hg in our instance.

The size of the confidence interval depends on the sample size and the standard divergence of the report groups (5). If the sample size is large, this leads to "more conviction" and a narrower confidence interval. If the confidence interval is wide, this may mean that the sample is minor. If the dispersion is high, the conclusion is less sure and the confidence interval becomes wider. Finally, the size of the confidence interval is influenced past the selected level of conviction. A 99% confidence interval is wider than a 95% confidence interval. In general, with a college probability to cover the truthful value the confidence interval becomes wider.

In contrast to p-values, conviction intervals point the management of the effect studied. Conclusions nigh statistical significance are possible with the aid of the confidence interval. If the confidence interval does not include the value of nada consequence, information technology can be assumed that there is a statistically significant result. In the example of the difference of the mean systolic claret force per unit area between the two handling groups, the question is whether the value 0 mm Hg is within the 95% confidence interval (= non significant) or outside it (= significant). The situation is equivalent with the relative risk; if the confidence interval contains the relative risk of 1.00, the result is not significant. It would so have to exist examined whether the confidence interval for the relative run a risk is completely nether 1.00 (= protective effect) or completely in a higher place it (= increment in risk).

Effigy 1 shows the difference for the example of the mean systolic claret pressure departure between 2 groups. The confidence interval for the mean blood pressure level difference is narrow with pocket-size variation inside the sample (= low dispersion) (figure 1b), low confidence level (figure 1d) and large sample size (effigy 1f). In this instance, there is no significant divergence between the mean systolic blood pressures in the groups if the dispersion is high (figure 1c), the confidence level is high (figure 1e) or the sample size is minor (figure 1g), as the value zippo is and then contained in the confidence interval.

An external file that holds a picture, illustration, etc. Object name is Dtsch_Arztebl_Int-106-0335_001.jpg

Using the example of the difference in the mean systolic blood pressure betwixt 2 groups, it is examined how the size of the confidence interval (a) can be modified by changes in dispersion (b, c), confidence interval (d, e), and sample size (f, chiliad). The departure betwixt the mean systolic claret pressure in group ane (150 mm Hg) and in group 2 (145 mm Hg) was five mmHg. Case modified from (6)

Although signal estimates, such equally the arithmetics mean, the difference between 2 means or the odds ratio, provide the best approximation to the truthful value, they do not provide whatever information well-nigh how exact they are. This is achieved by confidence intervals. Information technology is of class impossible to make whatever precise statement virtually the size of the difference betwixt the estimated parameters for the sample and the truthful value for the population, every bit the truthful value is unknown. However, one would like to take some confidence that the point judge is in the vicinity of the true value (vii). Confidence intervals can be used to describe the probability that the true value is within a given range.

If a confidence interval is given, several conclusions tin can be made. Firstly, values below the lower limit or in a higher place the upper limit are not excluded, but are improbable. With the confidence limit of 95%, each of these probabilities is only 2.5%. Values within the confidence limits, just most to the limits, are mostly less likely than values most the betoken estimate, which in our case with the two antihypertensives is the departure in the hateful values of the reduction in blood pressure in the two treatment groups in mm Hg. Whatever the size of the conviction interval, the betoken gauge based on the sample is the best approximation to the true value for the population. Values in the vicinity of the point gauge are mostly plausible values. This is peculiarly the instance if it can be causeless that the values are normally distributed.

A frequent procedure is to cheque whether confidence intervals include a certain limit or non and, if they practice not, to regard the findings every bit being significant. Information technology is notwithstanding a better approach to exploit the additional data in conviction intervals. Particularly with so-called shut results, the possibility should exist considered that the result might have been significant with a larger sample.

Of import international journals of medical science, such as the Lancet and the British Medical Journal, besides every bit the International Committee of Medical Journal Editors (ICMJE), recommend the use of conviction intervals (6). In particular, confidence intervals are of great help in interpreting the results of randomized clinical studies and meta-analyses. Thus the apply of confidence intervals is expressly demanded in international agreements and in the CONSORT statement (8) for reporting randomized clinical studies and in the QUORUM statement (9) for reporting systematic reviews.

Statistical significance versus clinical relevance

A clear distinction must exist fabricated betwixt statistical significance and clinical relevance (or clinical significance). Aside from the effect forcefulness, p-values incorporate the case numbers and the variability of the sample data. Even if the limit for statistical significance is laid down in advance, the reader must still judge the clinical relevance of statistically pregnant differences for himself. The same numerical value for the difference may be "statistically significant" if a large sample is taken and "non significant" if the sample is smaller. On the other hand, results of high clinical relevance are not automatically unimportant if there is no statistical significance. The crusade may be that the sample is too small or that the dispersion in the samples is likewise great—for example, if the patient grouping is highly heterogenous. For this reason, a decision for significance or lack of significance on the ground of the p-value alone may be simplistic.

This can exist illustrated using the example of systolic claret pressure level. Figure 2 specifies a relevance limit r. A systolic claret pressure difference of at least 4 mm Hg betwixt the two groups is then defined as clinically relevant. If the blood pressure level divergence is neither statistically significant nor clinically relevant (figure 2a) or statistically meaning and clinically relevant (figure 2b), interpretation is easy. All the same, statistically significant differences in blood pressure level may lie under the limit for clinical relevance and are and then of no clinical importance (figure 2c). On the other hand, there may exist real and clinically of import differences in systolic blood pressure between the handling groups, fifty-fifty though statistical significance has not been accomplished (figure 2d).

An external file that holds a picture, illustration, etc. Object name is Dtsch_Arztebl_Int-106-0335_002.jpg

Statistical significance and clinical relevance

Unfortunately, statistical significance is often thought to be equivalent to clinical relevance. Many enquiry workers, readers, and journals ignore findings which are potentially clinically useful only considering they are not statistically significant (4). At this point, we can criticize the do of some scientific journals of preferably publishing pregnant results. A written report has shown that this is mainly the example in high–bear upon factor journals (10). This tin can misconstrue the facts ("publication bias"). Moreover, it can oft be seen that a non-significant difference is interpreted as meaning that there is no difference (for case, betwixt two treatment groups). A p-value of >0.05 only signifies that the evidence is not acceptable to reject the null hypothesis—for example, that at that place is no difference between 2 culling treatments. This does non imply that the two treatments are equivalent. The quantitative compilation of comparable studies in the form of systematic reviews or meta-analyses tin then assist to identify differences which had not been recognized considering the number of cases in individual studies had been besides depression. A special article in this series is devoted to this subject.

P-values versus conviction intervals—What are the differences?

The essential differences between p-values and confidence intervals are equally follows:

The advantage of confidence intervals in comparing to giving p-values after hypothesis testing is that the result is given directly at the level of data measurement. Confidence intervals provide data about statistical significance, as well every bit the direction and forcefulness of the outcome (eleven). This also allows a decision about the clinical relevance of the results. If the error probability is given in advance, the size of the confidence interval depends on the data variability and the instance number in the sample examined (12).
P-values are clearer than confidence intervals. It can exist judged whether a value is greater or less than a previously specified limit. This allows a rapid conclusion equally to whether a value is statistically meaning or not. All the same, this type of "diagnosis on sight" can exist misleading, as it can lead to clinical decisions solely based on statistics.
Hypothesis testing using a p-value is a binary (yes-or-no) decision. The reduction of statistical inference (anterior inference from a single sample to the total population) to this level may be simplistic. The simple stardom between "pregnant" and "non-significant" in isolation is non very reliable. For instance, there is niggling departure between the show for p-values of 0.04 and of 0.06. Nevertheless, binary decisions based on these minor differences lead to antipodal decisions (1, 13). For this reason, p-values must always be given completely (suggestion: always to iii decimal places) (14).
When a indicate estimate is used (for case, deviation in means, relative chance), an endeavour is made to draw conclusions almost the state of affairs in the target population on the basis of just a single value for the sample. Even though this figure is the best possible approximation to the true value, it is not very probable that the values are exactly the same. In dissimilarity, confidence intervals provide a range of possible plausible values for the target population, as well as the probability with which this range covers the real value.
In contrast to confidence intervals, p-values requite the difference from a previously specified statistical level α (15). This facilitates the evaluation of a "shut" issue.
Statistical significance must exist distinguished from medical relevance or biological importance. If the sample size is large enough, even very small differences may be statistically meaning (16, 17). On the other hand, even big differences may lead to not-significant results if the sample is as well small (12). Even so, the investigator should be more interested in the size of the deviation in therapeutic effect between two treatment groups in clinical studies, equally this is what is important for successful handling, rather than whether the upshot is statistically significant or not (eighteen).

Conclusion

Taken in isolation, p-values provide a measure out of the statistical plausibility of a result. With a defined level of significance, p-values allow a decision near the rejection or maintenance of a previously formulated null hypothesis in confirmatory studies. Only very restricted statements about issue strength are possible on the footing of p-values. Confidence intervals provide an adequately plausible range for the true value related to the measurement of the point estimate. Statements are possible on the management of the furnishings, too as its strength and the presence of a statistically significant issue. In decision, it should be clearly stated that p-values and conviction intervals are not contradictory statistical concepts. If the size of the sample and the dispersion or a point judge are known, conviction intervals tin can be calculated from p-values, and conversely. The two statistical concepts are complementary.

Acknowledgments

Translated from the original German by Rodney A. Yeates, M.A., Ph.D.

Footnotes

Disharmonize of interest statement

The authors declare that there is no disharmonize of interest as divers past the guidelines of the International Committee of Medical Journal Editors.

References

1. Bland M, Peacock J. Interpreting statistics with confidence. The Obstetrician and Gynaecologist. 2002;iv:176–180. [Google Scholar]

2. Houle TT. Importance of outcome sizes for the accumulation of knowledge. Anesthesiology. 2007;106:415–417. [PubMed] [Google Scholar]

3. Faller H. Signifikanz, Effektstärke und Konfidenzintervall. Rehabilitation. 2004;43:174–178. [PubMed] [Google Scholar]

4. Greenfield ML, Kuhn JE, Wojtys EM. A statistics primer. Confidence intervals. AmJ Sports Med. 1998;26:145–149. No abstruse bachelor. Erratum in: Am J Sports Med 1999; 27: 544. [PubMed] [Google Scholar]

5. Bender R, Lange St. Was ist ein Konfidenzintervall? Dtsch Med Wschr. 2001;126 [PubMed] [Google Scholar]

six. Altman DG. Altman DG, Machin D, Bryant TN, Gardner MJ, editors. Confidence intervals in practice. BMJ Books. 2002:half-dozen–nine. [Google Scholar]

7. Weiss C, Weiß C. Basiswissen Medizinische Statistik. Springer Verlag; 1999. Intervallschätzungen. Die Bedeutung eines Konfidenzintervalls; pp. 191–192. [Google Scholar]

8. Moher D, Schulz KF Altman DG für die CONSORT Gruppe. Das COSORT Statement: Überarbeitete Empfehlungen zur Qualitätsverbesserung von Reports randomisierter Studien im Parallel-Pattern. Dtsch Med Wschr. 2004;129:xvi–twenty. [PubMed] [Google Scholar]

ix. Moher D, Cook DJ, Eastwood South, Olkin I, Rennie D, Stroup DF. Improving the quality of reports of meta-analyses of randomized controlled trials: the QUOROM statement. Quality of Reporting of Meta-analyses. Lancet. 1999;354:1896–1900. [PubMed] [Google Scholar]

ten. Easterbrook PJ, Berlin JA, Gopalan R, Matthews DR. Publication bias in clinical research. Lancet. 1991;337:867–872. [PubMed] [Google Scholar]

11. Shakespeare TP, Gebski VJ, Veness MJ, Simes J. Improving interpretation of clinical studies by utilize of confidence levels, clinical significance curves, and riskbenefit contours. Lancet. 2001;357:1349–1353. Review. [PubMed] [Google Scholar]

12. Gardner MJ, Altman DG. Confidence intervals rather than P-values: estimation rather than hypothesis testing. Br Med J. 1986;292:746–750. [PMC gratis article] [PubMed] [Google Scholar]

thirteen. Guyatt Thou, Jaeschke R, Heddle N, Cook D, Shannon H, Walter S. Basic statistics for clinicians: ane. hypothesis testing. CMAJ. 1995;152:27–32. Review. [PMC complimentary commodity] [PubMed] [Google Scholar]

14. ICH ix: Statisticlal Principles for Clinical Trials. International Conference on Harmonization; London UK. 1998. Adopted by CPMP July 1998 (CPMP/ICH/363/96) [Google Scholar]

xv. Feinstein AR. P-values and confidence intervals: two sides of the same unsatisfactory coin. J Clin Epidemiol. 1998;51:355–360. [PubMed] [Google Scholar]

16. Guyatt M, Jaeschke R, Heddle N, Melt D, Shannon H, Walter S. Basic statistics for clinicians: 2. interpreting study results: confidence intervals. CMAJ. 1995;152:169–173. [PMC complimentary article] [PubMed] [Google Scholar]

17. Sim J, Reid N. Statistical inference past confidence intervals: issues of interpretation and utilization. Phys Ther. 1999;79:186–195. [PubMed] [Google Scholar]

xviii. Gardner MJ, Altman DG. Altman DG, Machin D, Bryant TN, Gardner MJ, editors. Confidence intervals rather than P values Statistics with confidence. Confidence intervals and statistical guidelines. BMJ Books. (2d Edition) 2002:15–27. [Google Scholar]

Articles from Deutsches Ärzteblatt International are provided here courtesy of Deutscher Arzte-Verlag GmbH

Source: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2689604/

Posted by: cobbposis1961.blogspot.com