Overlapping Confidence Intervals For Standard Error Intervals
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On Judging The Significance Of Differences By Examining The Overlap Between Confidence Intervals
Insect Sciv.3; 2003PMC524673 J Insect Sci. 2003; 3: 34. Published online 2003 Oct overlapping confidence intervals and p-values 30. PMCID: PMC524673Overlapping confidence intervals or standard error intervals: What do they mean in terms of statistical significance?Mark E. Payton,1 Matthew H. comparing confidence intervals for significance Greenstone,2 and Nathaniel Schenker31Department of Statistics, 301 MSCS Building, Oklahoma State University, Stillwater, OK 74078-10562U.S. Department of Agriculture, Agricultural Research Service, Insect Biocontrol Lab, Bldg. 011A, Rm. 214, BARC-West, 10300, Baltimore Avenue, Beltsville, MD 207053Office of Research and Methodology, National Center for Health Statistics, 3311
Comparing Two 95 Confidence Intervals
Toledo Road, Room 3209, Hyattsville, MD 20782, Email: ude.etatsko@notyapmAuthor information ► Article notes ► Copyright and License information ►Received 2003 Jun 20; Accepted 2003 Oct 2.Copyright © 2003. Open access; copyright is maintained by the authors.This article has been cited by other articles in PMC.AbstractWe investigate the procedure of checking for overlap between confidence intervals or standard error intervals to draw conclusions regarding hypotheses about differences between population parameters. Mathematical expressions and algebraic manipulations are given, and computer simulations are performed to assess the usefulness of confidence and standard error intervals in this manner. We make recommendations for their use in situations in which standard tests of hypotheses do not exist. An example is given that tests this methodology for comparing effective dose levels in independent probit regressions, an application that is also
a sample survey produces a proportion or a mean as a response, we can use the methods in section 10.2 and confidence interval contains 0 10.3 to find a confidence interval for the true population values. standard error bars In this section we discuss confidence intervals for comparative studies. How do we assess the difference
Interpreting Confidence Intervals
between two proportions or means when they come from a comparative observational study or experiment? To address this question, we first need a new rule. Standard https://www.ncbi.nlm.nih.gov/pmc/articles/PMC524673/ Error of a DifferenceWhen two samples are independent of each other,Standard Error for a Difference between two sample summaries =\[\sqrt{(\text{standard error in first sample})^{2} + (\text{standard error in second sample})^{2}}\] Example 10.6.A medical researcher conjectures that smoking can result in wrinkled skin around the eyes. The researcher recruited150 smokersand250 nonsmokersto take part in https://onlinecourses.science.psu.edu/stat100/node/57 an observational study and found that 95of thesmokersand105of thenonsmokerswere seen to have prominent wrinkles around the eyes (based on a standardized wrinkle score administered by a person who did not know if the subject smoked or not). Some results from the study are found inTable 10.2. Table 10.2. Results of the Smoking and wrinkles study (example 10.6) SmokersNonsmokersSample Size150250Sample Proportion with Prominent Wrinkles95/150 = 0.63105/250 = 0.42Standard Error for Proportion\(\sqrt{\frac{0.63(0.37)}{150}} = 0.0394\)\(\sqrt{\frac{0.42(0.58)}{250}} = 0.0312\)How do the smokers compare to the non-smokers? The difference between the two sample proportions is 0.63 - 0.42 = 0.21. We would like to make a CI for the true difference that would exist between these two groups in the population. So we compute\[\text{Standard Error for Difference} = \sqrt{0.0394^{2}+0.0312^{2}} ≈ 0.05\]If we think about all possible ways to draw a sample of 150 smokers and 250 non-smokers then the differences we'd see between sample proportions would approximately follow the normal curve. Thus, a 95% C
in a publication or presentation, you may be tempted to draw conclusions about the statistical significance of differences between group means by looking at whether the error bars overlap. Let's https://egret.psychol.cam.ac.uk/statistics/local_copies_of_sources_Cardinal_and_Aitken_ANOVA/errorbars.htm look at two contrasting examples. What can you conclude when standard error bars http://scienceblogs.com/cognitivedaily/2008/07/31/most-researchers-dont-understa-1/ do not overlap? When standard error (SE) bars do not overlap, you cannot be sure that the difference between two means is statistically significant. Even though the error bars do not overlap in experiment 1, the difference is not statistically significant (P=0.09 by unpaired t test). This is also true confidence interval when you compare proportions with a chi-square test. What can you conclude when standard error bars do overlap? No surprises here. When SE bars overlap, (as in experiment 2) you can be sure the difference between the two means is not statistically significant (P>0.05). What if you are comparing more than two groups? Post tests following one-way ANOVA account for multiple comparisons, overlapping confidence intervals so they yield higher P values than t tests comparing just two groups. So the same rules apply. If two SE error bars overlap, you can be sure that a post test comparing those two groups will find no statistical significance. However if two SE error bars do not overlap, you can't tell whether a post test will, or will not, find a statistically significant difference. What if the error bars do not represent the SEM? Error bars that represent the 95% confidence interval (CI) of a mean are wider than SE error bars -- about twice as wide with large sample sizes and even wider with small sample sizes. If 95% CI error bars do not overlap, you can be sure the difference is statistically significant (P < 0.05). However, the converse is not true--you may or may not have statistical significance when the 95% confidence intervals overlap. Some graphs and tables show the mean with the standard deviation (SD) rather than the SEM. The SD quantifies variability, but does not account for sample size. To assess statistical significance, you must take into account
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