Hello Markos, from my experiences, Frank is correct. Several issues I think are important and I offer some input as I too learn from this e-mail thread...

generally, if errors bars overlap, then there is no difference...if they do not overlap, you still cannot be sure that the difference is statistically significant. For example, for instances of independent means, the error bars representing 95% confidence intervals can overlap (intuitively you will conclude no difference) yet still can turn out to be statistically significant at the 5% level.

This confuses the reader often and I struggle with it often...we often do not know why and under what conditions do we use error bars in the data....So you cannot conclude there is a difference even if there is no overlap.. Also, the literature strongly advises that it is best to use inferential error bars such as SE (standard error) and CI (confidence interval) and not Standard Deviation (SD) which as Frank explained yields the variance/variability in the sample data. Moreover, when n is small, the purist might argue it is best to simply plot the data for visual inspections. I have learnt that an important aspect in assessing your results and making a reasonable interpretation is whether the experiment and results are from independent experiments or replicates. n is also important. Is the data independent (between subjects variability) or paired (within subjects variability, repeated measures)?

I include 2 good readings to share as they have been informative to me....one is a very good paper in pdf format by Cumming and Finch 'Inference by Eye'....

Confidence Intervals and How to Read Pictures of Data http://homepage.psy.utexas.edu/homepage/class/Psy391P/CI's%20by%20Eye.2005.pdf

it includes an important rules of thumb or rules of eye:

Abbreviated Statements of Rules of Eye for Simple Figures Showing Means With Error Bars

You should:

1. Identify what the means and error bars represent.

Do bars show confidence intervals (CIs) or standard errors

(SEs)? What is the experimental design?

2. Make a substantive interpretation of the means.

3. Make a substantive interpretation of the CIs or other

error bars.

4. For a comparison of two independent means, p

.05 when proportion overlap of the 95% CIs is about .50 or

less. (Proportion overlap is expressed as a proportion of the

average margin of error for the two groups.) In addition,

p .01 when the proportion overlap is about 0 or there is

a positive gap (see Figure 5). (Rule 4 applies when both

sample sizes are at least 10 and the two margins of error do

not differ by more than a factor of 2.)

5. For paired data, interpret the mean of the differences

and error bars for this mean. In general, beware

of bars on separate means for a repeated-measure independent

variable: They are irrelevant for inferences about

differences.

6. SE bars are about half the size of 95% CI bars and

give approximately a 68% CI, when n is at least 10.

7. For a comparison of two independent means, p

.05 when the proportion gap between SE bars is at least

about 1. (Proportion gap is expressed as a proportion of the

average SE for the two groups.) In addition, p .01 when

the proportion gap is at least about 2 (see Figure 6). (Rule

7 applies when both sample sizes are at least 10 and the two

SEs do not differ by more than a factor of 2

and....

http://blogs.sas.com/jmp/index.php?/archives/127-What-Good-Are-Error-Bars.html

Hope these help...

Best,

Paul

--- On Tue, 3/31/09, Underwood, Frank <fu2@EVANSVILLE..EDU> wrote:

From: Underwood, Frank <[log in to unmask]>
Subject: Re: Question
To: [log in to unmask]
Received: Tuesday, March 31, 2009, 5:29 PM

Assessing the mean and a measure of error using a plot is a good initial look at the data, but is not sufficient to determine whether the difference is statistically significant. The choice of the error bar is important in this visual estimation, and the appropriate error term to plot is the standard error of the mean, not the standard deviation. The SD provides the variance in the sample, whereas the standard error of the mean provides an estimate of the true mean of the population from which the sample was taken. The statistical analysis makes an inference about the population based on the data from the sample; therefore, population estimates are the better method to assess differences.

Frank Underwood

From: Evidence based health (EBH) [mailto:[log in to unmask]] On Behalf Of Markos Kashiouris
Sent: Tuesday, March 31, 2009 10:31 AM
To: [log in to unmask]
Subject: Question

Frequently in basic research papers, data are graphically presented in a bar-format with one standard-deviation up and down represents the error bar. I have been working in a lab in the past. The data were presented in such way that if the SD error bars didn't overlap in the comparison groups eg cell counting etc the researchers presented their data as significant.

These basic-science research papers are the basis of the pyramid which leads to animal studies and higher phase trials including human research. I was wandering if this reporting method is statistically justified and if not what the error bars shall include

: 2 standard deviations each side (up or down from the bar), one SD each side of the bar or using the Standard Error?

Thank you.

Markos Kashiouris, MD

PGY2 Resident in Internal Medicine